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5.01:_The_Nature_of_Energy
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<div class="box-objectives"> <span id="Learning_Objectives"></span><span id="Learning_Objectives"></span><h5 class="box-legend"><span class="lt-icon-default"><span style="display:none;"> </span>Learning Objectives</span></h5> <ul> <li class="lt-chem-21720" style="background-color: unset;">To understand the concept of energy and its various forms.</li> <li class="lt-chem-21720" style="background-color: unset;">To know the relationship between energy, work, and heat.</li> </ul> </div> <p class="lt-chem-21720" style="background-color: unset;">Because energy takes many forms, only some of which can be seen or felt, it is defined by its effect on matter. For example, microwave ovens produce energy to cook food, but we cannot see that energy. In contrast, we can see the energy produced by a light bulb when we switch on a lamp. In this section, we describe the forms of energy and discuss the relationship between energy, heat, and work.</p> <span id="Forms_of_Energy"></span><span id="Forms_of_Energy"></span><h2 style="background-color: unset;" class="lt-chem-21720">Forms of Energy</h2> <p class="lt-chem-21720" style="background-color: unset;">The forms of energy include thermal energy, radiant energy, electrical energy, nuclear energy, and chemical energy (Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="98" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-99-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 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Thermal energy results from atomic and molecular motion; the faster the motion, the greater the thermal energy. The temperature of an object is a measure of its thermal energy content. Radiant energy is the energy carried by light, microwaves, and radio waves. Objects left in bright sunshine or exposed to microwaves become warm because much of the radiant energy they absorb is converted to thermal energy. Electrical energy results from the flow of electrically charged particles. When the ground and a cloud develop a separation of charge, for example, the resulting flow of electrons from one to the other produces lightning, a natural form of electrical energy. Nuclear energy is stored in the nucleus of an atom, and chemical energy is stored within a chemical compound because of a particular arrangement of atoms.</p> <figure><img alt="Images representing different forms of energy: thermal, electrical, nuclear, and chemical, with associated visuals for each type." style="width: 615px; height: 528px;" class="internal" loading="lazy" width="720" height="619" src="https://chem.libretexts.org/@api/deki/files/58262/04b4f98587e12228da011e206633a6b5.jpg?revision=1&size=bestfit&width=615&height=528" /> <figcaption><span class="title-prefix">Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="99" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-100-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-100-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-100-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use data-c="35" href="#MJX-100-NCM-N-35"></use></g><g data-mml-node="TeXAtom" 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data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>:</span> Forms of Energy. (a) <em>Thermal energy</em> results from atomic and molecular motion; molten steel at 2000°C has a very high thermal energy content. (b) <em>Radiant energy</em> (e.g., from the sun) is the energy in light, microwaves, and radio waves. (c) Lightning is an example of <em>electrical energy</em>, which is due to the flow of electrically charged particles. (d) <em>Nuclear energy</em> is released when particles in the nucleus of the atom are rearranged. (e) <em>Chemical energy</em> results from the particular arrangement of atoms in a chemical compound; the heat and light produced in this reaction are due to energy released during the breaking and reforming of chemical bonds.</figcaption> </figure> <p class="lt-chem-21720" style="background-color: unset;">Electrical energy, nuclear energy, and chemical energy are different forms of potential energy (PE), which is energy stored in an object because of the relative positions or orientations of its components. A brick lying on the windowsill of a 10th-floor office has a great deal of potential energy, but until its position changes by falling, the energy is contained. In contrast, kinetic energy (KE) is energy due to the motion of an object. When the brick falls, its potential energy is transformed to kinetic energy, which is then transferred to the object on the ground that it strikes. The electrostatic attraction between oppositely charged particles is a form of potential energy, which is converted to kinetic energy when the charged particles move toward each other.</p> <p class="verill_1.0-ch05_s01_s01_p03" lt-chem-21720" style="background-color: unset;">Energy can be converted from one form to another (Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="100" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-101-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 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href="#MJX-101-NCM-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container>) or, as we saw with the brick, transferred from one object to another. For example, when you climb a ladder to a high diving board, your body uses chemical energy produced by the combustion of organic molecules. As you climb, the chemical energy is converted to <em>mechanical work</em> to overcome the force of gravity. When you stand on the end of the diving board, your potential energy is greater than it was before you climbed the ladder: the greater the distance from the water, the greater the potential energy. When you then dive into the water, your potential energy is converted to kinetic energy as you fall, and when you hit the surface, some of that energy is transferred to the water, causing it to splash into the air. Chemical energy can also be converted to radiant energy; one common example is the light emitted by fireflies, which is produced from a chemical reaction.</p> <figure><img alt="Silhouette of people jumping off a pier into water, with arrows illustrating the concepts of potential and kinetic energy." style="width: 373px; height: 303px;" class="internal" loading="lazy" width="373px" height="303px" src="https://chem.libretexts.org/@api/deki/files/58263/a0d22f5e75d45b6d3a8e174c7fd1078b.jpg?revision=1&size=bestfit&width=373&height=303" /> <figcaption><span class="title-prefix">Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="101" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-102-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 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666Z"></path><path id="MJX-102-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use data-c="35" href="#MJX-102-NCM-N-35"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(500,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-102-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="31" href="#MJX-102-NCM-N-31"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-102-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="32" href="#MJX-102-NCM-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container>:</span> Interconversion of Forms of Energy. When a swimmer steps off the platform to dive into the water, potential energy is converted to kinetic energy. As the swimmer climbs back up to the top of the diving platform, chemical energy is converted to mechanical work.</figcaption> </figure> <p class="verill_1.0-ch05_s01_s01_p04" lt-chem-21720" style="background-color: unset;">Although energy can be converted from one form to another, <em>the total amount of energy in the universe remains constant</em>. This is known as the <strong>law of conservation of energy</strong>: <em>Energy cannot be created or destroyed.</em></p> <span id="Energy.2C_Heat.2C_and_Work"></span><span id="Energy.2C_Heat.2C_and_Work"></span><h2 style="background-color: unset;" class="lt-chem-21720">Energy, Heat, and Work</h2> <p class="lt-chem-21720" style="background-color: unset;">One definition of energy is the capacity to do work. The easiest form of work to visualize is mechanical work (Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="102" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-103-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 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data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-103-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:3" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="33" href="#MJX-103-NCM-N-33"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{3}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="3}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{3};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:3" data-semantic-level-number="1" data-speech-node="true">3</mn></mrow></math></mjx-assistive-mml></mjx-container>), which is the energy required to move an object a distance d when opposed by a force F, such as gravity:</p> <p class="title editabe= lt-chem-21720" style="background-color: unset;"><span class="MathJax"><span class="math" style="width:11.516em;display:inline-block;">work = force x distance</span></span></p> <p class="mt-align-center lt-chem-21720" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="103" style="font-size: 85%; min-width: 24.334ex; position: relative;"><svg width="100%" height="2.262ex" role="img" focusable="false" data-mjx-viewbox="0 -750 10755.6 1000" aria-hidden="true" style="vertical-align: -0.566ex; min-width: 24.334ex;"><defs><path id="MJX-104-NCM-I-1D464" d="M590 391C590 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data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.1.1}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.1.1}" data-semantic-level-number="4" data-speech-node="true">5.1.1</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" 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data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-children="7,9" data-semantic-content="10,7" data-semantic-parent="12" data-semantic-owns="7 10 9" data-semantic-level-number="3" data-speech-node="true"><mi data-latex="F" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="11" data-semantic-attributes="latex:F" data-semantic-operator="appl" data-semantic-level-number="4" data-speech-node="true">F</mi><mspace width="0.167em" data-latex="\,"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="11" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="4" data-speech-node="true">⁡</mo><mi data-latex="\label{5.1.1}" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="11" data-semantic-attributes="latex:\label{5.1.1}" data-semantic-level-number="4" data-speech-node="true">d</mi></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21720" style="background-color: unset;">Because the force (F) that opposes the action is equal to the mass (m) of the object times its acceleration (a), we can also write Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="104" 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192 53Z"></path><path id="MJX-105-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.1.1}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.01:_The_Nature_of_Energy#mjx-eqn:5.1.1"><g data-mml-node="mrow" data-latex="\ref{5.1.1}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" 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data-semantic-level-number="0" data-speech-node="true">5.1.1</mtext></mrow></math></mjx-assistive-mml></mjx-container> as follows:</p> <p class="title editabe= lt-chem-21720" style="background-color: unset;"><span class="title-prefix">work= mass x acceleration x distance</span></p> <p class="mt-align-center lt-chem-21720" style="background-color: unset;"><span class="title-prefix"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="105" style="font-size: 85%; min-width: 26.196ex; position: relative;"><svg width="100%" height="2.262ex" role="img" focusable="false" data-mjx-viewbox="0 -750 11578.6 1000" aria-hidden="true" style="vertical-align: -0.566ex; min-width: 26.196ex;"><defs><path id="MJX-106-NCM-I-1D464" d="M590 391C590 382 595 372 606 362C629 340 641 313 641 281C641 264 635 237 623 198C586 78 539 18 482 18C435 18 412 45 412 100C412 119 416 142 423 171C441 243 460 314 477 387C479 394 480 398 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data-semantic-attributes="latex:a" data-semantic-level-number="4" data-speech-node="true">a</mi><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="14" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true"></mspace><mi data-latex="\label{5.1.2}" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="14" data-semantic-attributes="latex:\label{5.1.2}" data-semantic-level-number="4" data-speech-node="true">d</mi></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></span></p> <p class="lt-chem-21720" style="background-color: unset;">Recall from that weight is a force caused by the gravitational attraction between two masses, such as you and Earth.</p> <p class="lt-chem-21720" style="background-color: unset;">Consider the mechanical work required for you to travel from the first floor of a building to the second. Whether you take an elevator or an escalator, trudge upstairs, or leap up the stairs two at a time, energy is expended to overcome the force of gravity. The amount of work done (<em>w</em>) and thus the energy required depends on three things:</p> <ol> <li class="lt-chem-21720" style="background-color: unset;">the height of the second floor (the distance <em>d</em>);</li> <li class="lt-chem-21720" style="background-color: unset;">your mass, which must be raised that distance against the downward acceleration due to gravity; and</li> <li class="lt-chem-21720" style="background-color: unset;">your path.</li> </ol> <figure><img style="width: 444px; height: 359px;" class="internal" alt="A muscular weightlifter performs a clean lift with a heavy barbell. 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display="inline"><math data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container>:</span> An Example of Mechanical Work. One form of energy is mechanical work, the energy required to move an object of mass <em>m</em> a distance <em>d</em> when opposed by a force <em>F</em>, such as gravity.</figcaption> </figure> <p class="lt-chem-21720" style="background-color: unset;">In contrast, heat (<em>q</em>) is thermal energy that can be transferred from an object at one temperature to an object at another temperature. The net transfer of thermal energy stops when the two objects reach the same temperature.</p> <p class="lt-chem-21720" style="background-color: unset;">Energy is an <em>extensive </em>property of matter—for example, the amount of <strong class="emphasis bold">thermal energy</strong> in an object is proportional to both its mass and its temperature. A water heater that holds 150 L of water at 50°C contains much more thermal energy than does a 1 L pan of water at 50°C. Similarly, a bomb contains much more chemical energy than does a firecracker. We now present a more detailed description of kinetic and potential energy.</p> <span id="Kinetic_and_Potential_Energy"></span><span id="Kinetic_and_Potential_Energy"></span><h2 style="background-color: unset;" class="lt-chem-21720">Kinetic and Potential Energy</h2> <p class="lt-chem-21720" style="background-color: unset;">The kinetic energy of an object is related to its mass <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="107" style="font-size: 85%; position: relative;"><svg width="1.986ex" height="1.025ex" role="img" focusable="false" viewbox="0 -442 878 453" aria-hidden="true" style="vertical-align: -0.025ex;"><defs><path id="MJX-108-NCM-I-1D45A" d="M657 442C596 442 543 412 498 353C489 412 451 442 383 442C324 442 273 416 231 363C223 407 188 442 137 442C96 442 66 409 45 344C34 312 29 293 29 287C29 278 34 273 45 273C50 273 53 274 56 276C61 285 64 292 66 299C84 375 107 413 134 413C152 413 161 399 161 371C161 358 156 331 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data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:m" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D45A" href="#MJX-108-NCM-I-1D45A"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="m" data-semantic-structure="0"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:m" data-semantic-level-number="0" data-speech-node="true">m</mi></math></mjx-assistive-mml></mjx-container> and velocity <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="108" style="font-size: 85%; position: relative;"><svg width="1.097ex" height="1.025ex" role="img" focusable="false" viewbox="0 -442 485 453" aria-hidden="true" style="vertical-align: 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data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="17" data-semantic-parent="19" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true" transform="translate(940,0)"><use data-c="2062" href="#MJX-110-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-id="11" data-semantic-parent="19" data-semantic-attributes="latex:m" data-semantic-level-number="4" data-speech-node="true" transform="translate(940,0)"><use data-c="1D45A" href="#MJX-110-NCM-I-1D45A"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="18" data-semantic-parent="19" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true" transform="translate(1818,0)"><use data-c="2062" href="#MJX-110-NCM-N-2062"></use></g><g data-mml-node="msup" data-latex="v^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:5" data-semantic-id="14" data-semantic-children="12,13" data-semantic-parent="19" data-semantic-attributes="latex:v^2" data-semantic-owns="12 13" data-semantic-level-number="4" data-speech-node="true" transform="translate(1818,0)"><g data-mml-node="mi" data-latex="v" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-id="12" data-semantic-parent="14" data-semantic-attributes="latex:v" data-semantic-level-number="5" data-speech-node="true"><use data-c="1D463" href="#MJX-110-NCM-I-1D463"></use></g><g data-mml-node="mn" transform="translate(518,413) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-id="13" data-semantic-parent="14" data-semantic-attributes="latex:2" data-semantic-level-number="5" data-speech-node="true"><use data-c="32" href="#MJX-110-NCM-N-32"></use></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="2834 -1264 1 2028"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:5.1.4" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="22" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true" transform="translate(0,670)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-id="3" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mtext" data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true"><use data-c="28" href="#MJX-110-NCM-N-28"></use></g><g data-mml-node="mtext" data-latex="\text{5.1.3}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.1.3}" data-semantic-level-number="4" data-speech-node="true" transform="translate(389,0)"><use data-c="35" href="#MJX-110-NCM-N-35"></use><use data-c="2E" href="#MJX-110-NCM-N-2E" transform="translate(500,0)"></use><use data-c="31" href="#MJX-110-NCM-N-31" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-110-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="33" href="#MJX-110-NCM-N-33" transform="translate(1556,0)"></use></g><g data-mml-node="mtext" data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" transform="translate(2445,0)"><use data-c="29" href="#MJX-110-NCM-N-29"></use></g></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="KE=\dfrac{1}{2}mv^2 \label{5.1.4} " display="block" data-semantic-structure="(23 (22 (20 (16 5 15 6) 7 (19 (10 8 9) 17 11 18 (14 12 13))) (4 (3 0 1 2))))"><mtable displaystyle="true" data-latex="KE=\dfrac{1}{2}mv^2 \label{5.1.4}" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="22" data-semantic-attributes="latex:KE=\dfrac{1}{2}mv^2 \label{5.1.4} " data-semantic-owns="22" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="20" data-semantic-content="4" data-semantic-parent="23" data-semantic-owns="20 4" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="22" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.1.3}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.1.3}" data-semantic-level-number="4" data-speech-node="true">5.1.3</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="16,19" data-semantic-content="7" data-semantic-parent="22" data-semantic-owns="16 7 19" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="5,6" data-semantic-content="15" data-semantic-parent="20" data-semantic-owns="5 15 6" data-semantic-level-number="3" data-speech-node="true"><mi data-latex="K" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="16" data-semantic-attributes="latex:K" data-semantic-level-number="4" data-speech-node="true">K</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="16" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="E" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="16" data-semantic-attributes="latex:E" data-semantic-level-number="4" data-speech-node="true">E</mi></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="10,11,14" data-semantic-content="17,18" data-semantic-parent="20" data-semantic-owns="10 17 11 18 14" data-semantic-level-number="3" data-speech-node="true"><mfrac data-latex="\dfrac{1}{2}" data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-children="8,9" data-semantic-parent="19" data-semantic-attributes="latex:\dfrac{1}{2}" data-semantic-owns="8 9" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:1" data-semantic-level-number="5" data-speech-node="true">1</mn><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:2" data-semantic-level-number="5" data-speech-node="true">2</mn></mfrac><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:m" data-semantic-level-number="4" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><msup data-latex="v^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="12,13" data-semantic-parent="19" data-semantic-attributes="latex:v^2" data-semantic-owns="12 13" data-semantic-level-number="4" data-speech-node="true"><mi data-latex="v" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="14" data-semantic-attributes="latex:v" data-semantic-level-number="5" data-speech-node="true">v</mi><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="14" data-semantic-attributes="latex:2" data-semantic-level-number="5" data-speech-node="true">2</mn></msup></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21720" style="background-color: unset;">For example, the kinetic energy of a 1360 kg (approximately 3000 lb) automobile traveling at a velocity of 26.8 m/s (approximately 60 mi/h) is</p> <p class="mt-align-center lt-chem-21720" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="110" style="font-size: 85%; min-width: 62.436ex; position: relative;"><svg width="100%" height="4.588ex" role="img" focusable="false" data-mjx-viewbox="0 -1264 27596.7 2028" 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href="#MJX-111-NCM-N-35"></use><use data-c="2E" href="#MJX-111-NCM-N-2E" transform="translate(500,0)"></use><use data-c="31" href="#MJX-111-NCM-N-31" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-111-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="34" href="#MJX-111-NCM-N-34" transform="translate(1556,0)"></use></g><g data-mml-node="mtext" data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" transform="translate(2445,0)"><use data-c="29" href="#MJX-111-NCM-N-29"></use></g></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="KE=\dfrac{1}{2}(1360 kg)(26.8 ms)^2= 4.88 \times 10^5 g \cdot m^2 \label{5.1.5} " display="block" data-semantic-structure="(54 (53 (51 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data-speech-node="true">⁢</mo><msup data-latex=")^2" data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-annotation="depth:5" data-semantic-fencepointer="20" data-semantic-="" data-semantic-children="41,21" data-semantic-parent="46" data-semantic-attributes="latex:)^2" data-semantic-owns="41 21" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="40" data-semantic-content="16,20" data-semantic-parent="22" data-semantic-owns="16 40 20" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="41" data-semantic-attributes="latex:(" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="17,18,19" data-semantic-content="38,39" data-semantic-parent="41" data-semantic-owns="17 38 18 39 19" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="26.8" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:26.8" data-semantic-level-number="7" data-speech-node="true">26.8</mn><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:m" data-semantic-level-number="7" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:s" data-semantic-level-number="7" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="41" data-semantic-attributes="latex:)" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="22" data-semantic-attributes="latex:2" data-semantic-level-number="5" data-speech-node="true">2</mn></msup></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="51" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="24,50" data-semantic-content="25" data-semantic-parent="51" data-semantic-owns="24 25 50" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="4.88" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:4.88" data-semantic-level-number="4" data-speech-node="true">4.88</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="4" data-speech-node="true">×</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="48,33" data-semantic-content="30" data-semantic-parent="49" data-semantic-owns="48 30 33" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="28,29" data-semantic-content="47" data-semantic-parent="50" data-semantic-owns="28 47 29" data-semantic-level-number="5" data-speech-node="true"><msup data-latex="10^5" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="26,27" data-semantic-parent="48" data-semantic-attributes="latex:10^5" data-semantic-owns="26 27" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:10" data-semantic-level-number="7" data-speech-node="true">10</mn><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:5" data-semantic-level-number="7" data-speech-node="true">5</mn></msup><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="48" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:g" data-semantic-level-number="6" data-speech-node="true">g</mi></mrow><mo data-latex="\cdot" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:\cdot" data-semantic-operator="infixop,⋅" data-semantic-level-number="5" data-speech-node="true">⋅</mo><msup data-latex="m^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="31,32" data-semantic-parent="50" data-semantic-attributes="latex:m^2" data-semantic-owns="31 32" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="33" data-semantic-attributes="latex:m" data-semantic-level-number="6" data-speech-node="true">m</mi><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="33" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true">2</mn></msup></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21720" style="background-color: unset;">Because all forms of energy can be interconverted, energy in any form can be expressed using the same units as kinetic energy. The SI unit of energy, the joule (J),<span class="footnote"> is named after the British physicist James Joule (1818–1889), an early worker in the field of energy.</span> is defined as 1 kilogram·meter<sup>2</sup>/second<sup>2</sup> (kg·m<sup>2</sup>/s<sup>2</sup>). Because a joule is such a small quantity of energy, chemists usually express energy in kilojoules (1 kJ = 10<sup>3</sup> J). For example, the kinetic energy of the 1360 kg car traveling at 26.8 m/s is 4.88 × 10<sup>5</sup> J or 4.88 × 10<sup>2</sup> kJ. It is important to remember that <em>the units of energy are the same regardless of the form of energy</em>, whether thermal, radiant, chemical, or any other form. Because heat and work result in changes in energy, their units must also be the same.</p> <p class="mt-align-center lt-chem-21720" style="background-color: unset;"><img alt="A red convertible car is shown moving horizontally at 60 mph, with potential energy calculation labeled above." style="width: 469px; height: 194px;" class="internal" loading="lazy" width="469px" height="194px" src="https://chem.libretexts.org/@api/deki/files/58266/14465abccda34c597d6106b06e6d87b7.jpg?revision=1&size=bestfit&width=469&height=194" /></p> <p class="lt-chem-21720" style="background-color: unset;">To demonstrate, let’s calculate the potential energy of the same 1360 kg automobile if it were parked on the top level of a parking garage 36.6 m (120 ft) high. Its potential energy is equivalent to the amount of work required to raise the vehicle from street level to the top level of the parking garage, which is <em>w</em> = <em>Fd</em>. According to Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="111" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-112-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-112-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-112-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path><path id="MJX-112-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.1.2}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.01:_The_Nature_of_Energy#mjx-eqn:5.1.2"><g data-mml-node="mrow" data-latex="\ref{5.1.2}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.1.2};href:#mjx-eqn%3A5.1.2" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-112-NCM-N-35"></use><use data-c="2E" href="#MJX-112-NCM-N-2E" transform="translate(500,0)"></use><use data-c="31" href="#MJX-112-NCM-N-31" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-112-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="32" href="#MJX-112-NCM-N-32" transform="translate(1556,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.1.2}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.1.2" data-latex="\ref{5.1.2}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.1.2};href:#mjx-eqn%3A5.1.2" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.1.2</mtext></mrow></math></mjx-assistive-mml></mjx-container>, the force (<em>F</em>) exerted by gravity on any object is equal to its mass (<em>m</em>, in this case, 1360 kg) times the acceleration (<em>a</em>) due to gravity (<em>g</em>, 9.81 m/s<sup>2</sup> at Earth’s surface). The distance (<em>d</em>) is the height (<em>h</em>) above street level (in this case, 36.6 m). 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m}{s^2}\right)(36.6\;m) = 4.88 \times 10^5\; \frac{Kg \cdot m}{s^2} \label{5.1.6b} " data-semantic-structure="(67 (66 (64 (57 5 56 6) 7 (60 (52 8 (51 9 10 (50 11 49 12)) 13) 58 (25 14 (23 (19 15 18 17) (22 20 21)) 24) 59 (55 26 (54 27 53 29) 30)) 31 (63 32 33 (62 (36 34 35) 61 (48 (44 (43 38 42 39) 40 41) (47 45 46))))) (4 (3 0 1 2))))"><g data-mml-node="mtable" data-latex="PE=(1360, Kg)\left(\dfrac{9.81\, m}{s^2}\right)(36.6\;m) = 4.88 \times 10^5 \; \frac{Kg \cdot m}{s^2} \label{5.1.6b}" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-id="67" data-semantic-children="66" data-semantic-attributes="latex:PE=(1360, Kg)\left(\dfrac{9.81\, m}{s^2}\right)(36.6\\0003Bm) = 4.88 \times 10^5\\0003B \frac{Kg \cdot m}{s^2} \label{5.1.6b} " data-semantic-owns="66" data-semantic-level-number="0" data-speech-node="true" transform="translate(3634,0) translate(-3634,0)"><g transform="translate(0 1328) matrix(1 0 0 -1 0 0) scale(46.04)"><svg 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data-semantic-id="57" data-semantic-children="5,6" data-semantic-content="56" data-semantic-parent="64" data-semantic-owns="5 56 6" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mi" data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-id="5" data-semantic-parent="57" data-semantic-attributes="latex:P" data-semantic-level-number="4" data-speech-node="true"><use data-c="1D443" href="#MJX-114-NCM-I-1D443"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="56" data-semantic-parent="57" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true" transform="translate(754,0)"><use data-c="2062" href="#MJX-114-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="E" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-id="6" data-semantic-parent="57" data-semantic-attributes="latex:E" data-semantic-level-number="4" data-speech-node="true" transform="translate(754,0)"><use data-c="1D438" href="#MJX-114-NCM-I-1D438"></use></g></g><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-id="7" data-semantic-parent="64" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true" transform="translate(1797.8,0)"><use data-c="3D" href="#MJX-114-NCM-N-3D"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-id="60" data-semantic-children="52,25,55" data-semantic-content="58,59" data-semantic-parent="64" data-semantic-owns="52 58 25 59 55" data-semantic-level-number="3" data-speech-node="true" transform="translate(2853.6,0)"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-id="52" data-semantic-children="51" data-semantic-content="8,13" data-semantic-parent="60" data-semantic-owns="8 51 13" data-semantic-level-number="4" data-speech-node="true"><g data-mml-node="mo" data-latex="(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-id="8" data-semantic-parent="52" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true"><use data-c="28" href="#MJX-114-NCM-N-28"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:6" data-semantic-id="51" data-semantic-children="9,10,50" data-semantic-content="10" data-semantic-parent="52" data-semantic-owns="9 10 50" data-semantic-level-number="5" data-speech-node="true" transform="translate(389,0)"><g data-mml-node="mn" data-latex="1360" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="9" data-semantic-parent="51" data-semantic-attributes="latex:1360" data-semantic-level-number="6" data-speech-node="true"><use data-c="31" href="#MJX-114-NCM-N-31"></use><use data-c="33" href="#MJX-114-NCM-N-33" transform="translate(500,0)"></use><use data-c="36" href="#MJX-114-NCM-N-36" transform="translate(1000,0)"></use><use data-c="30" href="#MJX-114-NCM-N-30" transform="translate(1500,0)"></use></g><g data-mml-node="mo" data-latex="," data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-annotation="depth:7" data-semantic-id="10" data-semantic-parent="51" data-semantic-attributes="latex:," data-semantic-operator="punctuated" data-semantic-level-number="6" data-speech-node="true" transform="translate(2000,0)"><use data-c="2C" href="#MJX-114-NCM-N-2C"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-id="50" data-semantic-children="11,12" data-semantic-content="49" data-semantic-parent="51" data-semantic-owns="11 49 12" data-semantic-level-number="6" data-speech-node="true" transform="translate(2444.7,0)"><g data-mml-node="mi" data-latex="K" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="11" data-semantic-parent="50" data-semantic-attributes="latex:K" data-semantic-level-number="7" data-speech-node="true"><use data-c="1D43E" href="#MJX-114-NCM-I-1D43E"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-id="49" data-semantic-parent="50" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true" transform="translate(889,0)"><use data-c="2062" href="#MJX-114-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="12" data-semantic-parent="50" data-semantic-attributes="latex:g" data-semantic-level-number="7" data-speech-node="true" transform="translate(889,0)"><use data-c="1D454" href="#MJX-114-NCM-I-1D454"></use></g></g></g><g data-mml-node="mo" data-latex=")" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-id="13" data-semantic-parent="52" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true" transform="translate(4199.7,0)"><use data-c="29" href="#MJX-114-NCM-N-29"></use></g></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="58" data-semantic-parent="60" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true" transform="translate(4588.7,0)"><use data-c="2062" href="#MJX-114-NCM-N-2062"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="INNER" data-latex="\left(\dfrac{9.81\, m}{s^2}\right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-id="25" data-semantic-children="23" data-semantic-content="14,24" data-semantic-parent="60" data-semantic-attributes="latex:\left(\dfrac{9.81\, m}{s^2}\right);texclass:INNER" data-semantic-owns="14 23 24" data-semantic-level-number="4" data-speech-node="true" transform="translate(4755.3,0)"><g data-mml-node="mo" data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-id="14" data-semantic-parent="25" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true"><use data-c="28" href="#MJX-114-NCM-S5-28"></use></g><g data-mml-node="mfrac" data-latex="\dfrac{9.81\, m}{s^2}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-id="23" data-semantic-children="19,22" data-semantic-parent="25" data-semantic-attributes="latex:\dfrac{9.81\, m}{s^2}" data-semantic-owns="19 22" data-semantic-level-number="5" data-speech-node="true" transform="translate(663,0)"><g data-mml-node="mrow" data-latex="9.81\, m" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-id="19" data-semantic-children="15,17" data-semantic-content="18" data-semantic-parent="23" data-semantic-attributes="latex:9.81\, m" data-semantic-owns="15 18 17" data-semantic-level-number="6" data-speech-node="true" transform="translate(220,676)"><g data-mml-node="mn" data-latex="9.81" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="15" data-semantic-parent="19" data-semantic-attributes="latex:9.81" data-semantic-level-number="7" data-speech-node="true"><use data-c="39" href="#MJX-114-NCM-N-39"></use><use data-c="2E" href="#MJX-114-NCM-N-2E" transform="translate(500,0)"></use><use data-c="38" href="#MJX-114-NCM-N-38" transform="translate(778,0)"></use><use data-c="31" href="#MJX-114-NCM-N-31" transform="translate(1278,0)"></use></g><g data-mml-node="mspace" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-id="18" data-semantic-parent="19" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true" transform="translate(1778,0)"></g><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="17" data-semantic-parent="19" data-semantic-attributes="latex:m" data-semantic-level-number="7" data-speech-node="true" transform="translate(1945,0)"><use data-c="1D45A" href="#MJX-114-NCM-I-1D45A"></use></g></g><g data-mml-node="msup" data-latex="s^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:7" data-semantic-id="22" data-semantic-children="20,21" data-semantic-parent="23" data-semantic-attributes="latex:s^2" data-semantic-owns="20 21" data-semantic-level-number="6" data-speech-node="true" transform="translate(1178.7,-719.9)"><g data-mml-node="mi" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="20" data-semantic-parent="22" data-semantic-attributes="latex:s" data-semantic-level-number="7" data-speech-node="true"><use data-c="1D460" href="#MJX-114-NCM-I-1D460"></use></g><g data-mml-node="mn" transform="translate(502,289) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="21" data-semantic-parent="22" data-semantic-attributes="latex:2" data-semantic-level-number="7" data-speech-node="true"><use data-c="32" href="#MJX-114-NCM-N-32"></use></g></g><rect width="3023" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-id="24" data-semantic-parent="25" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true" transform="translate(3926,0)"><use data-c="29" href="#MJX-114-NCM-S5-29"></use></g></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="59" data-semantic-parent="60" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true" transform="translate(9344.3,0)"><use data-c="2062" href="#MJX-114-NCM-N-2062"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-id="55" data-semantic-children="54" data-semantic-content="26,30" data-semantic-parent="60" data-semantic-owns="26 54 30" data-semantic-level-number="4" data-speech-node="true" transform="translate(9511,0)"><g data-mml-node="mo" data-latex="(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-id="26" data-semantic-parent="55" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true"><use data-c="28" href="#MJX-114-NCM-N-28"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:6" data-semantic-id="54" data-semantic-children="27,29" data-semantic-content="53" data-semantic-parent="55" data-semantic-owns="27 53 29" data-semantic-level-number="5" data-speech-node="true" transform="translate(389,0)"><g data-mml-node="mn" data-latex="36.6" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="27" data-semantic-parent="54" data-semantic-attributes="latex:36.6" data-semantic-level-number="6" data-speech-node="true"><use data-c="33" href="#MJX-114-NCM-N-33"></use><use data-c="36" href="#MJX-114-NCM-N-36" transform="translate(500,0)"></use><use data-c="2E" href="#MJX-114-NCM-N-2E" transform="translate(1000,0)"></use><use data-c="36" href="#MJX-114-NCM-N-36" transform="translate(1278,0)"></use></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-id="53" data-semantic-parent="54" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true" transform="translate(1778,0)"></g><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="29" data-semantic-parent="54" data-semantic-attributes="latex:m" data-semantic-level-number="6" data-speech-node="true" transform="translate(2056,0)"><use data-c="1D45A" href="#MJX-114-NCM-I-1D45A"></use></g></g><g data-mml-node="mo" data-latex=")" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-id="30" data-semantic-parent="55" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true" transform="translate(3323,0)"><use data-c="29" href="#MJX-114-NCM-N-29"></use></g></g></g><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-id="31" data-semantic-parent="64" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true" transform="translate(16354.3,0)"><use data-c="3D" href="#MJX-114-NCM-N-3D"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="63" data-semantic-children="32,62" data-semantic-content="33" data-semantic-parent="64" data-semantic-owns="32 33 62" data-semantic-level-number="3" data-speech-node="true" transform="translate(17410.1,0)"><g data-mml-node="mn" data-latex="4.88" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-id="32" data-semantic-parent="63" data-semantic-attributes="latex:4.88" data-semantic-level-number="4" data-speech-node="true"><use data-c="34" href="#MJX-114-NCM-N-34"></use><use data-c="2E" href="#MJX-114-NCM-N-2E" transform="translate(500,0)"></use><use data-c="38" href="#MJX-114-NCM-N-38" transform="translate(778,0)"></use><use data-c="38" href="#MJX-114-NCM-N-38" transform="translate(1278,0)"></use></g><g data-mml-node="mo" data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="33" data-semantic-parent="63" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="4" data-speech-node="true" transform="translate(2000.2,0)"><use data-c="D7" href="#MJX-114-NCM-N-D7"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="62" data-semantic-children="36,48" data-semantic-content="61" data-semantic-parent="63" data-semantic-owns="36 61 48" data-semantic-level-number="4" data-speech-node="true" transform="translate(3000.4,0)"><g data-mml-node="msup" data-latex="10^5" data-semantic-type="superscript" data-semantic-role="integer" 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data-semantic-level-number="6" data-speech-node="true"><use data-c="35" href="#MJX-114-NCM-N-35"></use></g></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:6" data-semantic-id="61" data-semantic-parent="62" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true" transform="translate(1436.6,0)"></g><g data-mml-node="mfrac" data-latex="\label{5.1.6b}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-id="48" data-semantic-children="44,47" data-semantic-parent="62" data-semantic-attributes="latex:\label{5.1.6b}" data-semantic-owns="44 47" data-semantic-level-number="5" data-speech-node="true" transform="translate(1714.6,0)"><g data-mml-node="mrow" data-latex="Kg \cdot m" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-id="44" 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2156"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:5.1.6b" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="66" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true" transform="translate(0,716)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-id="3" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mtext" data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true"><use data-c="28" href="#MJX-114-NCM-N-28"></use></g><g data-mml-node="mtext" data-latex="\text{5.1.6}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.1.6}" data-semantic-level-number="4" data-speech-node="true" transform="translate(389,0)"><use data-c="35" href="#MJX-114-NCM-N-35"></use><use data-c="2E" href="#MJX-114-NCM-N-2E" transform="translate(500,0)"></use><use data-c="31" href="#MJX-114-NCM-N-31" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-114-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="36" href="#MJX-114-NCM-N-36" transform="translate(1556,0)"></use></g><g data-mml-node="mtext" data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" transform="translate(2445,0)"><use data-c="29" href="#MJX-114-NCM-N-29"></use></g></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="PE=(1360, Kg)\left(\dfrac{9.81\, m}{s^2}\right)(36.6\;m) = 4.88 \times 10^5\; \frac{Kg \cdot m}{s^2} \label{5.1.6b} " display="block" data-semantic-structure="(67 (66 (64 (57 5 56 6) 7 (60 (52 8 (51 9 10 (50 11 49 12)) 13) 58 (25 14 (23 (19 15 18 17) (22 20 21)) 24) 59 (55 26 (54 27 53 29) 30)) 31 (63 32 33 (62 (36 34 35) 61 (48 (44 (43 38 42 39) 40 41) (47 45 46))))) (4 (3 0 1 2))))"><mtable displaystyle="true" data-latex="PE=(1360, Kg)\left(\dfrac{9.81\, m}{s^2}\right)(36.6\;m) = 4.88 \times 10^5 \; \frac{Kg \cdot m}{s^2} \label{5.1.6b}" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="66" data-semantic-attributes="latex:PE=(1360, Kg)\left(\dfrac{9.81\, m}{s^2}\right)(36.6\\0003Bm) = 4.88 \times 10^5\\0003B \frac{Kg \cdot m}{s^2} \label{5.1.6b} " data-semantic-owns="66" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="64" data-semantic-content="4" data-semantic-parent="67" data-semantic-owns="64 4" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="66" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.1.6}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.1.6}" data-semantic-level-number="4" data-speech-node="true">5.1.6</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="57,60,63" data-semantic-content="7,31" data-semantic-parent="66" data-semantic-owns="57 7 60 31 63" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="5,6" data-semantic-content="56" data-semantic-parent="64" data-semantic-owns="5 56 6" data-semantic-level-number="3" data-speech-node="true"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="57" data-semantic-attributes="latex:P" data-semantic-level-number="4" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="57" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="E" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="57" data-semantic-attributes="latex:E" data-semantic-level-number="4" data-speech-node="true">E</mi></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="64" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="52,25,55" data-semantic-content="58,59" data-semantic-parent="64" data-semantic-owns="52 58 25 59 55" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="51" data-semantic-content="8,13" data-semantic-parent="60" data-semantic-owns="8 51 13" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="52" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="9,10,50" data-semantic-content="10" data-semantic-parent="52" data-semantic-owns="9 10 50" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="1360" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="51" data-semantic-attributes="latex:1360" data-semantic-level-number="6" data-speech-node="true">1360</mn><mo data-latex="," data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="51" data-semantic-attributes="latex:," data-semantic-operator="punctuated" data-semantic-level-number="6" data-speech-node="true">,</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="11,12" data-semantic-content="49" data-semantic-parent="51" data-semantic-owns="11 49 12" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="K" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:K" data-semantic-level-number="7" data-speech-node="true">K</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="50" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:g" data-semantic-level-number="7" data-speech-node="true">g</mi></mrow></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="52" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="60" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{9.81\, m}{s^2}\right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="23" data-semantic-content="14,24" data-semantic-parent="60" data-semantic-attributes="latex:\left(\dfrac{9.81\, m}{s^2}\right);texclass:INNER" data-semantic-owns="14 23 24" data-semantic-level-number="4" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{9.81\, m}{s^2}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="19,22" data-semantic-parent="25" data-semantic-attributes="latex:\dfrac{9.81\, m}{s^2}" data-semantic-owns="19 22" data-semantic-level-number="5" data-speech-node="true"><mrow data-latex="9.81\, m" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="15,17" data-semantic-content="18" data-semantic-parent="23" data-semantic-attributes="latex:9.81\, m" data-semantic-owns="15 18 17" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="9.81" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:9.81" data-semantic-level-number="7" data-speech-node="true">9.81</mn><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="19" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:m" data-semantic-level-number="7" data-speech-node="true">m</mi></mrow><msup data-latex="s^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="20,21" data-semantic-parent="23" data-semantic-attributes="latex:s^2" data-semantic-owns="20 21" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="22" data-semantic-attributes="latex:s" data-semantic-level-number="7" data-speech-node="true">s</mi><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" 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data-semantic-="" data-semantic-children="54" data-semantic-content="26,30" data-semantic-parent="60" data-semantic-owns="26 54 30" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="55" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="27,29" data-semantic-content="53" data-semantic-parent="55" data-semantic-owns="27 53 29" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="36.6" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" 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data-semantic-children="44,47" data-semantic-parent="62" data-semantic-attributes="latex:\label{5.1.6b}" data-semantic-owns="44 47" data-semantic-level-number="5" data-speech-node="true"><mrow data-latex="Kg \cdot m" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="43,41" data-semantic-content="40" data-semantic-parent="48" data-semantic-attributes="latex:Kg \cdot m" data-semantic-owns="43 40 41" data-semantic-level-number="6" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="38,39" data-semantic-content="42" data-semantic-parent="44" data-semantic-owns="38 42 39" data-semantic-level-number="7" data-speech-node="true"><mi data-latex="K" data-semantic-type="identifier" data-semantic-role="latinletter" 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data-semantic-attributes="latex:\cdot" data-semantic-operator="infixop,⋅" data-semantic-level-number="7" data-speech-node="true">⋅</mo><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:m" data-semantic-level-number="7" data-speech-node="true">m</mi></mrow><msup data-latex="s^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="45,46" data-semantic-parent="48" data-semantic-attributes="latex:s^2" data-semantic-owns="45 46" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="47" 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data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-id="3" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mtext" data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true"><use data-c="28" href="#MJX-115-NCM-N-28"></use></g><g data-mml-node="mtext" data-latex="\text{5.1.7}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.1.7}" data-semantic-level-number="4" data-speech-node="true" transform="translate(389,0)"><use data-c="35" href="#MJX-115-NCM-N-35"></use><use data-c="2E" href="#MJX-115-NCM-N-2E" transform="translate(500,0)"></use><use data-c="31" href="#MJX-115-NCM-N-31" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-115-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="37" href="#MJX-115-NCM-N-37" transform="translate(1556,0)"></use></g><g data-mml-node="mtext" data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" transform="translate(2445,0)"><use data-c="29" href="#MJX-115-NCM-N-29"></use></g></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="=4.88 \times 10^5 J = 488\; kJ \label{5.1.6c} " display="block" data-semantic-structure="(27 (26 (24 17 5 (20 6 7 (19 (10 8 9) 18 11)) 12 (23 13 21 15 22 16)) (4 (3 0 1 2))))"><mtable displaystyle="true" data-latex="=4.88 \times 10^5 J = 488\; kJ \label{5.1.6c}" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="26" data-semantic-attributes="latex:=4.88 \times 10^5 J = 488\\0003B kJ \label{5.1.6c} " data-semantic-owns="26" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="24" data-semantic-content="4" data-semantic-parent="27" data-semantic-owns="24 4" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="26" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.1.7}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.1.7}" data-semantic-level-number="4" data-speech-node="true">5.1.7</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="17,20,23" data-semantic-content="5,12" data-semantic-parent="26" data-semantic-owns="17 5 20 12 23" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="24" data-semantic-level-number="3" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="6,19" data-semantic-content="7" data-semantic-parent="24" data-semantic-owns="6 7 19" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="4.88" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:4.88" data-semantic-level-number="4" data-speech-node="true">4.88</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" 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data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:10" data-semantic-level-number="6" data-speech-node="true">10</mn><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:5" data-semantic-level-number="6" data-speech-node="true">5</mn></msup><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="19" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:J" data-semantic-level-number="5" data-speech-node="true">J</mi></mrow></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="13,15,16" data-semantic-content="21,22" data-semantic-parent="24" data-semantic-owns="13 21 15 22 16" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="488" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:488" data-semantic-level-number="4" data-speech-node="true">488</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="23" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:k" data-semantic-level-number="4" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="23" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="\label{5.1.6c}" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:\label{5.1.6c}" data-semantic-level-number="4" data-speech-node="true">J</mi></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21720" style="background-color: unset;">The units of potential energy are the same as the units of kinetic energy. Notice that in this case the potential energy of the stationary automobile at the top of a 36.6 m high parking garage is the same as its kinetic energy at 60 mi/h.</p> <p class="mt-align-center lt-chem-21720" style="background-color: unset;"><img alt="Diagram showing a red car at the top of a vertical path, with a height of 36.6 m and potential energy listed as 4.88 x 10² kJ." style="width: 308px; height: 300px;" class="internal" loading="lazy" width="308px" height="300px" src="https://chem.libretexts.org/@api/deki/files/58267/1da5f0cd7ded86927c7166b30cb758e3.jpg?revision=1&size=bestfit&width=308&height=300" /></p> <p class="lt-chem-21720" style="background-color: unset;">If the vehicle fell from the roof of the parking garage, its potential energy would be converted to kinetic energy, and it is reasonable to infer that the vehicle would be traveling at 60 mi/h just before it hit the ground, neglecting air resistance. After the car hit the ground, its potential and kinetic energy would both be zero.</p> <div class="informalfigure small block">Potential energy is usually defined relative to an arbitrary standard position (in this case, the street was assigned an elevation of zero). As a result, we usually calculate only differences in potential energy: in this case, the difference between the potential energy of the car on the top level of the parking garage and the potential energy of the same car on the street at the base of the garage.</div> <div class="informalfigure small block"> <figure><img alt="Comparison of two diagrams showing measurements of heights and distances, with a figure standing next to a vertical wall." style="width: 655px; height: 269px;" class="internal" loading="lazy" width="655px" height="269px" src="https://chem.libretexts.org/@api/deki/files/58280/Figure_.jpg?revision=1&size=bestfit&width=655&height=269" /> <figcaption>When the car is falling from the top of the parking structure it has a kinetic energy of 488 kilojoules. When the car hits the floor is has a potential and kinetic energy of zero.</figcaption> </figure> </div> <span id="Units_of_Energy"></span><span id="Units_of_Energy"></span><h2 style="background-color: unset;" class="lt-chem-21720">Units of Energy</h2> <p class="lt-chem-21720" style="background-color: unset;">The units of energy are the same for all forms of energy. Energy can also be expressed in the non-SI units of calories (cal), where 1 cal was originally defined as the amount of energy needed to raise the temperature of exactly 1 g of water from 14.5°C to 15.5°C.<span class="footnote">We specify the exact temperatures because the amount of energy needed to raise the temperature of 1 g of water 1°C varies slightly with elevation. To three significant figures, however, this amount is 1.00 cal over the temperature range 0°C–100°C.</span> The name is derived from the Latin <em>calor</em>, meaning “heat.” Although energy may be expressed as either calories or joules, calories were defined in terms of heat, whereas joules were defined in terms of motion. 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href="#MJX-117-NCM-N-31" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-117-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="39" href="#MJX-117-NCM-N-39" transform="translate(1556,0)"></use></g><g data-mml-node="mtext" data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" transform="translate(2445,0)"><use data-c="29" href="#MJX-117-NCM-N-29"></use></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="1 \;J = 0.2390\; cal \label{5.1.7b} " display="block" data-semantic-structure="(23 (22 (20 (15 5 14 7) 8 (19 9 16 11 17 12 18 13)) (4 (3 0 1 2))))"><mtable displaystyle="true" data-latex="1 \;J = 0.2390\; cal \label{5.1.7b}" data-semantic-type="multiline" 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data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.1.9}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.1.9}" data-semantic-level-number="4" data-speech-node="true">5.1.9</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="15,19" data-semantic-content="8" data-semantic-parent="22" data-semantic-owns="15 8 19" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="5,7" data-semantic-content="14" data-semantic-parent="20" data-semantic-owns="5 14 7" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:1" data-semantic-level-number="4" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="15" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true"></mspace><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:J" data-semantic-level-number="4" data-speech-node="true">J</mi></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="9,11,12,13" data-semantic-content="16,17,18" data-semantic-parent="20" data-semantic-owns="9 16 11 17 12 18 13" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="0.2390" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:0.2390" data-semantic-level-number="4" data-speech-node="true">0.2390</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true"></mspace><mi data-latex="c" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:c" data-semantic-level-number="4" data-speech-node="true">c</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:a" data-semantic-level-number="4" data-speech-node="true">a</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="\label{5.1.7b}" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:\label{5.1.7b}" data-semantic-level-number="4" data-speech-node="true">l</mi></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21720" style="background-color: unset;">In this text, we will use the SI units—joules (J) and kilojoules (kJ)—exclusively, except when we deal with nutritional information.</p> <div class="box-example"> <span id="Example_.5C(.5CPageIndex.7B1.7D.5C)"></span><span id="Example_.5C(.5CPageIndex.7B1.7D.5C)"></span><h5 class="box-legend"><span class="lt-icon-default">Example <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="117" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-118-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-118-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-118-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use data-c="35" href="#MJX-118-NCM-N-35"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(500,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-118-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="31" href="#MJX-118-NCM-N-31"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-118-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-118-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container></span></h5> <ol start="1" style="list-style-type: lower-alpha;"> <li class="lt-chem-21720" style="background-color: unset;">If the mass of a baseball is 149 g, what is the kinetic energy of a fastball clocked at 100 mi/h?</li> <li class="lt-chem-21720" style="background-color: unset;">A batter hits a pop fly, and the baseball (with a mass of 149 g) reaches an altitude of 250 ft. If we assume that the ball was 3 ft above home plate when hit by the batter, what is the increase in its potential energy?</li> </ol> <p class="lt-chem-21720" style="background-color: unset;"><strong class="emphasis bold">Given: </strong>mass and velocity or height</p> <p class="lt-chem-21720" style="background-color: unset;"><strong class="emphasis bold">Asked for: </strong>kinetic and potential energy</p> <p class="lt-chem-21720" style="background-color: unset;"><strong class="emphasis bold">Strategy:</strong></p> <p class="lt-chem-21720" style="background-color: unset;">Use Equation 5.1.4 to calculate the kinetic energy and Equation 5.1.6 to calculate the potential energy, as appropriate.</p> <p class="lt-chem-21720" style="background-color: unset;"><strong class="emphasis bold">Solution:</strong></p> <ol start="1" style="list-style-type: lower-alpha;"> <li class="lt-chem-21720" style="background-color: unset;">The kinetic energy of an object is given by <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="118" style="font-size: 85%; position: relative;"><svg width="5.867ex" height="2.737ex" role="img" focusable="false" viewbox="0 -864.9 2593.1 1209.9" aria-hidden="true" style="vertical-align: -0.781ex;"><defs><path id="MJX-119-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path><path id="MJX-119-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"></path><path id="MJX-119-NCM-N-2062" d=""></path><path id="MJX-119-NCM-I-1D45A" d="M657 442C596 442 543 412 498 353C489 412 451 442 383 442C324 442 273 416 231 363C223 407 188 442 137 442C96 442 66 409 45 344C34 312 29 293 29 287C29 278 34 273 45 273C50 273 53 274 56 276C61 285 64 292 66 299C84 375 107 413 134 413C152 413 161 399 161 371C161 358 156 331 145 290L88 63C84 51 79 25 79 19C79-1 90-11 111-11C131-11 145-1 152 19C153 24 160 49 171 92L192 181L222 295C233 318 250 341 272 365C301 397 337 413 380 413C413 413 429 391 429 348C429 335 424 308 414 267L387 153C380 124 364 64 356 32C355 25 354 21 354 19C354-1 365-11 387-11C398-11 406-8 413-1C428 14 429 21 435 48L494 285C497 298 511 321 535 353C565 393 605 413 654 413C687 413 703 391 703 348C703 309 683 236 642 129C633 106 629 87 629 74C629 25 666-11 714-11C759-11 793 14 818 64C838 104 848 131 848 144C848 153 843 158 832 158C825 157 818 148 813 137C791 58 759 18 716 18C703 18 696 28 696 47C696 62 702 84 714 115C755 222 775 295 775 333C775 404 728 442 657 442Z"></path><path id="MJX-119-NCM-I-1D463" d="M369 391C369 383 378 370 394 350C410 330 418 307 418 281C418 252 404 203 375 134C354 86 306 18 247 18C201 18 178 45 178 100C178 139 197 208 235 307C243 328 247 345 247 357C247 407 213 442 163 442C119 442 84 417 59 367C39 326 29 300 29 287C29 278 34 273 45 273C58 273 60 279 64 293C87 373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 159 10C186-4 214-11 243-11C332-11 394 85 420 162C452 256 468 325 468 369C468 418 452 442 421 442C396 442 369 416 369 391Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex=" \frac{1}{2} mv^2" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-id="9" data-semantic-children="2,3,6" data-semantic-content="7,8" data-semantic-attributes="latex: \frac{1}{2} mv^2" data-semantic-owns="2 7 3 8 6" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(9 (2 0 1) 7 3 8 (6 4 5))"><g data-mml-node="mfrac" data-latex="\frac{1}{2}" data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="2" data-semantic-children="0,1" data-semantic-parent="9" data-semantic-attributes="latex:\frac{1}{2}" data-semantic-owns="0 1" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mn" transform="translate(220,394) scale(0.707)" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="2" data-semantic-attributes="latex:1" data-semantic-level-number="2" data-speech-node="true"><use data-c="31" href="#MJX-119-NCM-N-31"></use></g><g data-mml-node="mn" transform="translate(220,-345) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="1" data-semantic-parent="2" data-semantic-attributes="latex:2" data-semantic-level-number="2" data-speech-node="true"><use data-c="32" href="#MJX-119-NCM-N-32"></use></g><rect width="553.6" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="7" data-semantic-parent="9" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(793.6,0)"><use data-c="2062" href="#MJX-119-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="3" data-semantic-parent="9" data-semantic-attributes="latex:m" data-semantic-level-number="1" data-speech-node="true" transform="translate(793.6,0)"><use data-c="1D45A" href="#MJX-119-NCM-I-1D45A"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="8" data-semantic-parent="9" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(1671.6,0)"><use data-c="2062" href="#MJX-119-NCM-N-2062"></use></g><g data-mml-node="msup" data-latex="v^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:2" data-semantic-id="6" data-semantic-children="4,5" data-semantic-parent="9" data-semantic-attributes="latex:v^2" data-semantic-owns="4 5" data-semantic-level-number="1" data-speech-node="true" transform="translate(1671.6,0)"><g data-mml-node="mi" data-latex="v" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="4" data-semantic-parent="6" data-semantic-attributes="latex:v" data-semantic-level-number="2" data-speech-node="true"><use data-c="1D463" href="#MJX-119-NCM-I-1D463"></use></g><g data-mml-node="mn" transform="translate(518,363) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="5" data-semantic-parent="6" data-semantic-attributes="latex:2" data-semantic-level-number="2" data-speech-node="true"><use data-c="32" href="#MJX-119-NCM-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex=" \frac{1}{2} mv^2" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="2,3,6" data-semantic-content="7,8" data-semantic-attributes="latex: \frac{1}{2} mv^2" data-semantic-owns="2 7 3 8 6" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(9 (2 0 1) 7 3 8 (6 4 5))"><mfrac data-latex="\frac{1}{2}" data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-children="0,1" data-semantic-parent="9" data-semantic-attributes="latex:\frac{1}{2}" data-semantic-owns="0 1" data-semantic-level-number="1" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:1" data-semantic-level-number="2" data-speech-node="true">1</mn><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:2" data-semantic-level-number="2" data-speech-node="true">2</mn></mfrac><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="9" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="9" data-semantic-attributes="latex:m" data-semantic-level-number="1" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="9" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><msup data-latex="v^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="4,5" data-semantic-parent="9" data-semantic-attributes="latex:v^2" data-semantic-owns="4 5" data-semantic-level-number="1" data-speech-node="true"><mi data-latex="v" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:v" data-semantic-level-number="2" data-speech-node="true">v</mi><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:2" data-semantic-level-number="2" data-speech-node="true">2</mn></msup></math></mjx-assistive-mml></mjx-container> In this case, we know both the mass and the velocity, but we must convert the velocity to SI units: <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="119" style="font-size: 85%; min-width: 85.256ex; position: relative;"><svg width="100%" height="6.765ex" role="img" focusable="false" data-mjx-viewbox="0 -1745 37683.1 2990" aria-hidden="true" style="vertical-align: -2.817ex; min-width: 85.256ex;"><defs><path id="MJX-120-NCM-I-1D463" d="M369 391C369 383 378 370 394 350C410 330 418 307 418 281C418 252 404 203 375 134C354 86 306 18 247 18C201 18 178 45 178 100C178 139 197 208 235 307C243 328 247 345 247 357C247 407 213 442 163 442C119 442 84 417 59 367C39 326 29 300 29 287C29 278 34 273 45 273C58 273 60 279 64 293C87 373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 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\;\cancel{mi}} \right) (\dfrac{1000\; m}{1\; \cancel{km}})= 44.7 \;m/s \nonumber " data-semantic-structure="(128 (127 (125 (112 1 2 (21 3 (19 (12 4 11 (10 (9 6 8 7))) (18 13 17 (16 15))) 20)) 22 (43 23 (41 (29 24 28 (27 26)) (40 30 39 (38 (37 32 35 33 36 34)))) 42) 44 (114 (64 45 (62 (56 46 55 (54 (53 48 51 49 52 50))) (61 57 60 59)) 63) 113 (86 65 (84 (74 66 73 (72 (71 68 70 69))) (83 75 82 (81 (80 77 79 78)))) 85)) 87 (118 (111 88 (103 (93 89 92 91) (102 94 101 (100 (99 96 98 97)))) 104) 105 (117 (116 106 115 108) 109 110))) 0))"><g data-mml-node="mtable" data-latex="v= \left(\dfrac{100\; \cancel{mi}}{1\;\cancel{h}} \right) \left(\dfrac{1 \;\cancel{h}}{60 \;\cancel{min}} \right) \left(\dfrac{1 \; \cancel{min}}{60 \;s} \right)\left(\dfrac{1.61\; \cancel{km}}{1 \;\cancel{mi}} \right) (\dfrac{1000\; m}{1\; \cancel{km}})= 44.7 \;m/s \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-id="128" data-semantic-children="127" data-semantic-attributes="latex: v= \left(\dfrac{100\\0003B \cancel{mi}}{1\\0003B\cancel{h}} \right) \left(\dfrac{1 \\0003B\cancel{h}}{60 \\0003B\cancel{min}} \right) \left(\dfrac{1 \\0003B \cancel{min}}{60 \\0003Bs} \right)\left(\dfrac{1.61\\0003B \cancel{km}}{1 \\0003B\cancel{mi}} \right) (\dfrac{1000\\0003B m}{1\\0003B \cancel{km}})= 44.7 \\0003Bm/s \nonumber " data-semantic-owns="127" data-semantic-level-number="0" data-speech-node="true" transform="translate(800,0) translate(-800,0)"><g transform="translate(0 1745) matrix(1 0 0 -1 0 0) scale(46.04)"><svg data-table="true" preserveaspectratio="xMidYMid" viewbox="18041.6 -1745 1 2990"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-id="127" data-semantic-children="125" data-semantic-content="0" data-semantic-parent="128" data-semantic-owns="125 0" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mtd"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="text" data-semantic-annotation="depth:3" data-semantic-id="125" data-semantic-children="112,22,43,44,114,87,118" data-semantic-parent="127" data-semantic-collapsed="(125 (c 119 120 121 122 123 124) 112 22 43 44 114 87 118)" data-semantic-owns="112 22 43 44 114 87 118" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-id="112" data-semantic-children="1,21" data-semantic-content="2" data-semantic-parent="125" data-semantic-owns="1 2 21" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mi" data-latex="v" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-id="1" data-semantic-parent="112" data-semantic-attributes="latex:v" data-semantic-level-number="4" data-speech-node="true"><use data-c="1D463" href="#MJX-120-NCM-I-1D463"></use></g><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-id="2" data-semantic-parent="112" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true" transform="translate(762.8,0)"><use data-c="3D" href="#MJX-120-NCM-N-3D"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="INNER" data-latex="\left(\dfrac{100\; \cancel{mi}}{1\;\cancel{h}} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-id="21" data-semantic-children="19" data-semantic-content="3,20" data-semantic-parent="112" data-semantic-attributes="latex:\left(\dfrac{100\\0003B \cancel{mi}}{1\\0003B\cancel{h}} \right);texclass:INNER" data-semantic-owns="3 19 20" data-semantic-level-number="4" data-speech-node="true" transform="translate(1818.6,0)"><g data-mml-node="mo" data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-id="3" data-semantic-parent="21" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true"><use data-c="28" href="#MJX-120-NCM-S7-28"></use></g><g data-mml-node="mfrac" data-latex="\dfrac{100\; \cancel{mi}}{1\;\cancel{h}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-id="19" data-semantic-children="12,18" data-semantic-parent="21" data-semantic-attributes="latex:\dfrac{100\\0003B \cancel{mi}}{1\\0003B\cancel{h}}" data-semantic-owns="12 18" data-semantic-level-number="5" data-speech-node="true" transform="translate(875,0)"><g 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data-c="1D460" href="#MJX-120-NCM-I-1D460"></use></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -1745 1 2990"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="127" data-semantic-level-number="2" data-speech-node="true"></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" v= \left(\dfrac{100\; \cancel{mi}}{1\;\cancel{h}} \right) \left(\dfrac{1 \;\cancel{h}}{60 \;\cancel{min}} \right) \left(\dfrac{1 \; \cancel{min}}{60 \;s} \right)\left(\dfrac{1.61\; \cancel{km}}{1 \;\cancel{mi}} \right) (\dfrac{1000\; m}{1\; \cancel{km}})= 44.7 \;m/s \nonumber " display="block" data-semantic-structure="(128 (127 (125 (112 1 2 (21 3 (19 (12 4 11 (10 (9 6 8 7))) (18 13 17 (16 15))) 20)) 22 (43 23 (41 (29 24 28 (27 26)) (40 30 39 (38 (37 32 35 33 36 34)))) 42) 44 (114 (64 45 (62 (56 46 55 (54 (53 48 51 49 52 50))) (61 57 60 59)) 63) 113 (86 65 (84 (74 66 73 (72 (71 68 70 69))) (83 75 82 (81 (80 77 79 78)))) 85)) 87 (118 (111 88 (103 (93 89 92 91) (102 94 101 (100 (99 96 98 97)))) 104) 105 (117 (116 106 115 108) 109 110))) 0))"><mtable displaystyle="true" data-latex="v= \left(\dfrac{100\; \cancel{mi}}{1\;\cancel{h}} \right) \left(\dfrac{1 \;\cancel{h}}{60 \;\cancel{min}} \right) \left(\dfrac{1 \; \cancel{min}}{60 \;s} \right)\left(\dfrac{1.61\; \cancel{km}}{1 \;\cancel{mi}} \right) (\dfrac{1000\; m}{1\; \cancel{km}})= 44.7 \;m/s \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="127" data-semantic-attributes="latex: v= \left(\dfrac{100\\0003B \cancel{mi}}{1\\0003B\cancel{h}} \right) \left(\dfrac{1 \\0003B\cancel{h}}{60 \\0003B\cancel{min}} \right) \left(\dfrac{1 \\0003B \cancel{min}}{60 \\0003Bs} \right)\left(\dfrac{1.61\\0003B \cancel{km}}{1 \\0003B\cancel{mi}} \right) (\dfrac{1000\\0003B m}{1\\0003B \cancel{km}})= 44.7 \\0003Bm/s \nonumber " data-semantic-owns="127" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="125" data-semantic-content="0" data-semantic-parent="128" data-semantic-owns="125 0" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="127" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="text" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="112,22,43,44,114,87,118" data-semantic-parent="127" data-semantic-collapsed="(125 (c 119 120 121 122 123 124) 112 22 43 44 114 87 118)" data-semantic-owns="112 22 43 44 114 87 118" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="1,21" data-semantic-content="2" data-semantic-parent="125" data-semantic-owns="1 2 21" data-semantic-level-number="3" data-speech-node="true"><mi data-latex="v" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="112" data-semantic-attributes="latex:v" data-semantic-level-number="4" data-speech-node="true">v</mi><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="112" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{100\; \cancel{mi}}{1\;\cancel{h}} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="19" data-semantic-content="3,20" data-semantic-parent="112" data-semantic-attributes="latex:\left(\dfrac{100\\0003B \cancel{mi}}{1\\0003B\cancel{h}} \right);texclass:INNER" data-semantic-owns="3 19 20" data-semantic-level-number="4" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{100\; \cancel{mi}}{1\;\cancel{h}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="12,18" data-semantic-parent="21" data-semantic-attributes="latex:\dfrac{100\\0003B \cancel{mi}}{1\\0003B\cancel{h}}" data-semantic-owns="12 18" data-semantic-level-number="5" data-speech-node="true"><mrow data-latex="100\; \cancel{mi}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="4,10" data-semantic-content="11" data-semantic-parent="19" data-semantic-attributes="latex:100\\0003B \cancel{mi}" data-semantic-owns="4 11 10" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="100" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:100" data-semantic-level-number="7" data-speech-node="true">100</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="12" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{mi}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="9" data-semantic-parent="12" data-semantic-attributes="latex:\cancel{mi}" data-semantic-owns="9" data-semantic-level-number="7" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="6,7" data-semantic-content="8" data-semantic-parent="10" data-semantic-owns="6 8 7" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="9" data-semantic-attributes="latex:m" data-semantic-level-number="9" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="9" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="9" data-semantic-attributes="latex:i" data-semantic-level-number="9" data-speech-node="true">i</mi></mrow></menclose></mrow><mrow data-latex="1\;\cancel{h}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="13,16" data-semantic-content="17" data-semantic-parent="19" data-semantic-attributes="latex:1\\0003B\cancel{h}" data-semantic-owns="13 17 16" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="18" data-semantic-attributes="latex:1" data-semantic-level-number="7" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="18" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{h}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="15" data-semantic-parent="18" data-semantic-attributes="latex:\cancel{h}" data-semantic-owns="15" data-semantic-level-number="7" data-speech-node="true"><mi data-latex="h" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="16" data-semantic-attributes="latex:h" data-semantic-level-number="8" data-speech-node="true">h</mi></menclose></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">)</mo></mrow></mrow><mo data-semantic-type="text" data-semantic-role="space" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="125" data-semantic-level-number="3" data-speech-node="true"> </mo><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{1 \;\cancel{h}}{60 \;\cancel{min}} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="41" data-semantic-content="23,42" data-semantic-parent="125" data-semantic-attributes="latex:\left(\dfrac{1 \\0003B\cancel{h}}{60 \\0003B\cancel{min}} \right);texclass:INNER" data-semantic-owns="23 41 42" data-semantic-level-number="3" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="43" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{1 \;\cancel{h}}{60 \;\cancel{min}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="29,40" data-semantic-parent="43" data-semantic-attributes="latex:\dfrac{1 \\0003B\cancel{h}}{60 \\0003B\cancel{min}}" data-semantic-owns="29 40" data-semantic-level-number="4" data-speech-node="true"><mrow data-latex="1 \;\cancel{h}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="24,27" data-semantic-content="28" data-semantic-parent="41" data-semantic-attributes="latex:1 \\0003B\cancel{h}" data-semantic-owns="24 28 27" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="29" data-semantic-attributes="latex:1" data-semantic-level-number="6" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="29" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{h}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="26" data-semantic-parent="29" data-semantic-attributes="latex:\cancel{h}" data-semantic-owns="26" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="h" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="27" data-semantic-attributes="latex:h" data-semantic-level-number="7" data-speech-node="true">h</mi></menclose></mrow><mrow data-latex="60 \;\cancel{min}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="30,38" data-semantic-content="39" data-semantic-parent="41" data-semantic-attributes="latex:60 \\0003B\cancel{min}" data-semantic-owns="30 39 38" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="60" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:60" data-semantic-level-number="6" data-speech-node="true">60</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="40" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{min}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="37" data-semantic-parent="40" data-semantic-attributes="latex:\cancel{min}" data-semantic-owns="37" data-semantic-level-number="6" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="32,33,34" data-semantic-content="35,36" data-semantic-parent="38" data-semantic-owns="32 35 33 36 34" data-semantic-level-number="7" data-speech-node="true"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:m" data-semantic-level-number="8" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="37" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:i" data-semantic-level-number="8" data-speech-node="true">i</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="37" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:n" data-semantic-level-number="8" data-speech-node="true">n</mi></mrow></menclose></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="43" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mo></mrow><mo data-semantic-type="text" data-semantic-role="space" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="125" data-semantic-level-number="3" data-speech-node="true"> </mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="64,86" data-semantic-content="113" data-semantic-parent="125" data-semantic-owns="64 113 86" data-semantic-level-number="3" data-speech-node="true"><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{1 \; \cancel{min}}{60 \;s} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="62" data-semantic-content="45,63" data-semantic-parent="114" data-semantic-attributes="latex:\left(\dfrac{1 \\0003B \cancel{min}}{60 \\0003Bs} \right);texclass:INNER" data-semantic-owns="45 62 63" data-semantic-level-number="4" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="64" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{1 \; \cancel{min}}{60 \;s}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="56,61" data-semantic-parent="64" data-semantic-attributes="latex:\dfrac{1 \\0003B \cancel{min}}{60 \\0003Bs}" data-semantic-owns="56 61" data-semantic-level-number="5" data-speech-node="true"><mrow data-latex="1 \; \cancel{min}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="46,54" data-semantic-content="55" data-semantic-parent="62" data-semantic-attributes="latex:1 \\0003B \cancel{min}" data-semantic-owns="46 55 54" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="56" data-semantic-attributes="latex:1" data-semantic-level-number="7" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="56" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{min}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="53" data-semantic-parent="56" data-semantic-attributes="latex:\cancel{min}" data-semantic-owns="53" data-semantic-level-number="7" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="48,49,50" data-semantic-content="51,52" data-semantic-parent="54" data-semantic-owns="48 51 49 52 50" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="53" data-semantic-attributes="latex:m" data-semantic-level-number="9" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="53" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="53" data-semantic-attributes="latex:i" data-semantic-level-number="9" data-speech-node="true">i</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="53" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="53" data-semantic-attributes="latex:n" data-semantic-level-number="9" data-speech-node="true">n</mi></mrow></menclose></mrow><mrow data-latex="60 \;s" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="57,59" data-semantic-content="60" data-semantic-parent="62" data-semantic-attributes="latex:60 \\0003Bs" data-semantic-owns="57 60 59" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="60" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="61" data-semantic-attributes="latex:60" data-semantic-level-number="7" data-speech-node="true">60</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="61" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="61" data-semantic-attributes="latex:s" data-semantic-level-number="7" data-speech-node="true">s</mi></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="64" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="114" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{1.61\; \cancel{km}}{1 \;\cancel{mi}} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="84" data-semantic-content="65,85" data-semantic-parent="114" data-semantic-attributes="latex:\left(\dfrac{1.61\\0003B \cancel{km}}{1 \\0003B\cancel{mi}} \right);texclass:INNER" data-semantic-owns="65 84 85" data-semantic-level-number="4" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="86" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{1.61\; \cancel{km}}{1 \;\cancel{mi}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="74,83" data-semantic-parent="86" data-semantic-attributes="latex:\dfrac{1.61\\0003B \cancel{km}}{1 \\0003B\cancel{mi}}" data-semantic-owns="74 83" data-semantic-level-number="5" data-speech-node="true"><mrow data-latex="1.61\; \cancel{km}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="66,72" data-semantic-content="73" data-semantic-parent="84" data-semantic-attributes="latex:1.61\\0003B \cancel{km}" data-semantic-owns="66 73 72" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="1.61" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="74" data-semantic-attributes="latex:1.61" data-semantic-level-number="7" data-speech-node="true">1.61</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="74" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{km}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="71" data-semantic-parent="74" data-semantic-attributes="latex:\cancel{km}" data-semantic-owns="71" data-semantic-level-number="7" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="68,69" data-semantic-content="70" data-semantic-parent="72" data-semantic-owns="68 70 69" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="71" data-semantic-attributes="latex:k" data-semantic-level-number="9" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="71" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="71" data-semantic-attributes="latex:m" data-semantic-level-number="9" data-speech-node="true">m</mi></mrow></menclose></mrow><mrow data-latex="1 \;\cancel{mi}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="75,81" data-semantic-content="82" data-semantic-parent="84" data-semantic-attributes="latex:1 \\0003B\cancel{mi}" data-semantic-owns="75 82 81" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="83" data-semantic-attributes="latex:1" data-semantic-level-number="7" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="83" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{mi}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="80" data-semantic-parent="83" data-semantic-attributes="latex:\cancel{mi}" data-semantic-owns="80" data-semantic-level-number="7" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="77,78" data-semantic-content="79" data-semantic-parent="81" data-semantic-owns="77 79 78" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="80" data-semantic-attributes="latex:m" data-semantic-level-number="9" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="80" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="80" data-semantic-attributes="latex:i" data-semantic-level-number="9" data-speech-node="true">i</mi></mrow></menclose></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="86" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">)</mo></mrow></mrow><mo data-semantic-type="text" data-semantic-role="space" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="125" data-semantic-level-number="3" data-speech-node="true"> </mo><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="111,117" data-semantic-content="105" data-semantic-parent="125" data-semantic-owns="111 105 117" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="103" data-semantic-content="88,104" data-semantic-parent="118" data-semantic-owns="88 103 104" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="111" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{1000\; m}{1\; \cancel{km}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="93,102" data-semantic-parent="111" data-semantic-attributes="latex:\dfrac{1000\\0003B m}{1\\0003B \cancel{km}}" data-semantic-owns="93 102" data-semantic-level-number="5" data-speech-node="true"><mrow data-latex="1000\; m" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="89,91" data-semantic-content="92" data-semantic-parent="103" data-semantic-attributes="latex:1000\\0003B m" data-semantic-owns="89 92 91" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="1000" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:1000" data-semantic-level-number="7" data-speech-node="true">1000</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="93" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:m" data-semantic-level-number="7" data-speech-node="true">m</mi></mrow><mrow data-latex="1\; \cancel{km}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="94,100" data-semantic-content="101" data-semantic-parent="103" data-semantic-attributes="latex:1\\0003B \cancel{km}" data-semantic-owns="94 101 100" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="102" data-semantic-attributes="latex:1" data-semantic-level-number="7" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="102" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{km}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="99" data-semantic-parent="102" data-semantic-attributes="latex:\cancel{km}" data-semantic-owns="99" data-semantic-level-number="7" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="96,97" data-semantic-content="98" data-semantic-parent="100" data-semantic-owns="96 98 97" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="99" data-semantic-attributes="latex:k" data-semantic-level-number="9" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="99" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="99" data-semantic-attributes="latex:m" data-semantic-level-number="9" data-speech-node="true">m</mi></mrow></menclose></mrow></mfrac><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="111" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">)</mo></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="118" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="division" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="116,110" data-semantic-content="109" data-semantic-parent="118" data-semantic-owns="116 109 110" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="106,108" data-semantic-content="115" data-semantic-parent="117" data-semantic-owns="106 115 108" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="44.7" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="116" data-semantic-attributes="latex:44.7" data-semantic-level-number="6" data-speech-node="true">44.7</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="116" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="116" data-semantic-attributes="latex:m" data-semantic-level-number="6" data-speech-node="true">m</mi></mrow><mo data-latex="/" data-semantic-type="operator" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="117" data-semantic-attributes="latex:/" data-semantic-operator="infixop,/" data-semantic-level-number="5" data-speech-node="true">/</mo><mi data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="117" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="5" data-speech-node="true">s</mi></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container> <p class="lt-chem-21720" style="background-color: unset;">The kinetic energy of the baseball is therefore <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="120" style="font-size: 85%; min-width: 79.08ex; position: relative;"><svg width="100%" height="6.765ex" role="img" focusable="false" data-mjx-viewbox="0 -1745 34953.5 2990" aria-hidden="true" style="vertical-align: -2.817ex; min-width: 79.08ex;"><defs><path id="MJX-121-NCM-I-1D43E" d="M804 680C783 680 715 683 694 683C679 683 671 675 671 659C671 651 678 646 692 643C706 640 714 635 714 628C714 617 703 602 680 585L302 296L379 602C384 623 393 636 406 641C412 643 429 644 458 644C484 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 684 199 676 199 660C199 649 210 644 232 644C252 644 293 647 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 38 37 38 16C38 5 44 0 57 0L183 3L246 2C257 2 299 0 310 0C326 0 334 8 334 24C334 34 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data-semantic-level-number="8" data-speech-node="true" transform="translate(2000,0)"></g><g data-mml-node="menclose" data-latex="\cancel{g}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:9" data-semantic-id="19" data-semantic-children="18" data-semantic-parent="21" data-semantic-attributes="latex:\cancel{g}" data-semantic-owns="18" data-semantic-level-number="8" data-speech-node="true" transform="translate(2278,0)"><g transform="translate(267, 0)"><g data-mml-node="mi" data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-id="18" data-semantic-parent="19" data-semantic-attributes="latex:g" data-semantic-level-number="9" data-speech-node="true"><use data-c="1D454" href="#MJX-121-NCM-I-1D454"></use></g></g><line x1="33.5" y1="-438.5" x2="977.5" y2="675.5" stroke-width="67"></line></g></g><rect width="3489" 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data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true"><use data-c="28" href="#MJX-121-NCM-S5-28"></use></g><g data-mml-node="mfrac" data-latex="\dfrac{44.7 \;m}{s}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:8" data-semantic-id="32" data-semantic-children="30,31" data-semantic-parent="34" data-semantic-attributes="latex:\dfrac{44.7 \\0003Bm}{s}" data-semantic-owns="30 31" data-semantic-level-number="7" data-speech-node="true" transform="translate(663,0)"><g data-mml-node="mrow" data-latex="44.7 \;m" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:9" data-semantic-id="30" data-semantic-children="26,28" data-semantic-content="29" data-semantic-parent="32" data-semantic-attributes="latex:44.7 \\0003Bm" data-semantic-owns="26 29 28" data-semantic-level-number="8" data-speech-node="true" transform="translate(220,676)"><g data-mml-node="mn" data-latex="44.7" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-id="26" data-semantic-parent="30" data-semantic-attributes="latex:44.7" data-semantic-level-number="9" data-speech-node="true"><use data-c="34" href="#MJX-121-NCM-N-34"></use><use data-c="34" href="#MJX-121-NCM-N-34" transform="translate(500,0)"></use><use data-c="2E" href="#MJX-121-NCM-N-2E" transform="translate(1000,0)"></use><use data-c="37" href="#MJX-121-NCM-N-37" transform="translate(1278,0)"></use></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:10" data-semantic-id="29" data-semantic-parent="30" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true" transform="translate(1778,0)"></g><g data-mml-node="mi" 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data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="40" data-semantic-parent="42" data-semantic-attributes="latex:10" data-semantic-level-number="6" data-speech-node="true"><use data-c="31" href="#MJX-121-NCM-N-31"></use><use data-c="30" href="#MJX-121-NCM-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mn" transform="translate(1033,413) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="41" data-semantic-parent="42" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true"><use data-c="32" href="#MJX-121-NCM-N-32"></use></g></g></g></g><g data-mml-node="mo" data-semantic-type="text" data-semantic-role="space" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-id="43" data-semantic-parent="79" data-semantic-level-number="3" data-speech-node="true" transform="translate(22997,0)"><use data-c="2009" href="#MJX-121-NCM-N-2009"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-id="76" data-semantic-children="56,75" data-semantic-content="57" data-semantic-parent="79" data-semantic-owns="56 57 75" data-semantic-level-number="3" data-speech-node="true" transform="translate(23197,0)"><g data-mml-node="mfrac" data-latex="\dfrac{kg⋅m^2}{s^2}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:5" data-semantic-id="56" data-semantic-children="52,55" data-semantic-parent="76" data-semantic-attributes="latex:\dfrac{kg⋅m^2}{s^2}" data-semantic-owns="52 55" data-semantic-level-number="4" data-speech-node="true"><g data-mml-node="mrow" data-latex="kg⋅m^2" data-semantic-type="infixop" data-semantic-role="multiplication" 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data-speech-node="true"><use data-c="1D458" href="#MJX-121-NCM-I-1D458"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-id="50" data-semantic-parent="51" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true" transform="translate(521,0)"><use data-c="2062" href="#MJX-121-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="45" data-semantic-parent="51" data-semantic-attributes="latex:g" data-semantic-level-number="7" data-speech-node="true" transform="translate(521,0)"><use data-c="1D454" href="#MJX-121-NCM-I-1D454"></use></g></g><g data-mml-node="mo" data-latex="⋅" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-id="46" data-semantic-parent="52" data-semantic-attributes="latex:⋅" data-semantic-operator="infixop,⋅" data-semantic-level-number="6" data-speech-node="true" transform="translate(1220.2,0)"><use data-c="22C5" href="#MJX-121-NCM-N-22C5"></use></g><g data-mml-node="msup" data-latex="m^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:7" data-semantic-id="49" data-semantic-children="47,48" data-semantic-parent="52" data-semantic-attributes="latex:m^2" data-semantic-owns="47 48" data-semantic-level-number="6" data-speech-node="true" transform="translate(1720.4,0)"><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="47" data-semantic-parent="49" data-semantic-attributes="latex:m" data-semantic-level-number="7" data-speech-node="true"><use 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data-semantic-level-number="4" data-speech-node="true" transform="translate(3752.8,0)"><use data-c="3D" href="#MJX-121-NCM-N-3D"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="75" data-semantic-children="58,74" data-semantic-content="59" data-semantic-parent="76" data-semantic-owns="58 59 74" data-semantic-level-number="4" data-speech-node="true" transform="translate(4808.6,0)"><g data-mml-node="mn" data-latex="1.49" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-id="58" data-semantic-parent="75" data-semantic-attributes="latex:1.49" data-semantic-level-number="5" data-speech-node="true"><use data-c="31" href="#MJX-121-NCM-N-31"></use><use data-c="2E" href="#MJX-121-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-121-NCM-N-34" transform="translate(778,0)"></use><use data-c="39" href="#MJX-121-NCM-N-39" transform="translate(1278,0)"></use></g><g data-mml-node="mo" data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-id="59" data-semantic-parent="75" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="5" data-speech-node="true" transform="translate(2000.2,0)"><use data-c="D7" href="#MJX-121-NCM-N-D7"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-id="74" data-semantic-children="62,64" data-semantic-content="73" data-semantic-parent="75" data-semantic-owns="62 73 64" data-semantic-level-number="5" data-speech-node="true" transform="translate(3000.4,0)"><g data-mml-node="msup" data-latex="10^2" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:7" data-semantic-id="62" data-semantic-children="60,61" data-semantic-parent="74" data-semantic-attributes="latex:10^2" data-semantic-owns="60 61" data-semantic-level-number="6" data-speech-node="true"><g data-mml-node="mn" data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="60" data-semantic-parent="62" data-semantic-attributes="latex:10" data-semantic-level-number="7" data-speech-node="true"><use data-c="31" href="#MJX-121-NCM-N-31"></use><use data-c="30" href="#MJX-121-NCM-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mn" transform="translate(1033,413) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="61" data-semantic-parent="62" data-semantic-attributes="latex:2" data-semantic-level-number="7" data-speech-node="true"><use data-c="32" href="#MJX-121-NCM-N-32"></use></g></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-id="73" data-semantic-parent="74" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true" transform="translate(1436.6,0)"></g><g data-mml-node="mi" data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="64" data-semantic-parent="74" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true" transform="translate(1714.6,0)"><use data-c="1D43D" href="#MJX-121-NCM-I-1D43D"></use></g></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -1745 1 2990"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="81" data-semantic-level-number="2" data-speech-node="true"></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" KE= 1492 \;\cancel{g} \left(\dfrac{1\; kg}{1000 \;\cancel{g}} \right) \left(\dfrac{44.7 \;m}{s} \right)^2= 1.49 \times 10^2 \dfrac{kg⋅m^2}{s^2}= 1.49 \times10^2\; J \nonumber " display="block" data-semantic-structure="(82 (81 (79 (72 (66 1 65 2) 3 (70 4 67 (7 6) 68 (24 8 (22 (15 9 13 11 14 12) (21 16 20 (19 18))) 23) 69 (36 (34 25 (32 (30 26 29 28) 31) 33) 35)) 37 (71 38 39 (42 40 41))) 43 (76 (56 (52 (51 44 50 45) 46 (49 47 48)) (55 53 54)) 57 (75 58 59 (74 (62 60 61) 73 64)))) 0))"><mtable displaystyle="true" data-latex="KE= 1492 \;\cancel{g} \left(\dfrac{1\; kg}{1000 \;\cancel{g}} \right) \left(\dfrac{44.7 \;m}{s} \right)^2 = 1.49 \times 10^2  \dfrac{kg⋅m^2}{s^2}= 1.49 \times10^2 \; J \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="81" data-semantic-attributes="latex: KE= 1492 \\0003B\cancel{g} \left(\dfrac{1\\0003B kg}{1000 \\0003B\cancel{g}} \right) \left(\dfrac{44.7 \\0003Bm}{s} \right)^2= 1.49 \times 10^2 \dfrac{kg⋅m^2}{s^2}= 1.49 \times10^2\\0003B J \nonumber " data-semantic-owns="81" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="79" data-semantic-content="0" data-semantic-parent="82" data-semantic-owns="79 0" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="81" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="text" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="72,43,76" data-semantic-parent="81" data-semantic-collapsed="(79 (c 77 78) 72 43 76)" data-semantic-owns="72 43 76" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="66,70,71" data-semantic-content="3,37" data-semantic-parent="79" data-semantic-owns="66 3 70 37 71" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="1,2" data-semantic-content="65" data-semantic-parent="72" data-semantic-owns="1 65 2" data-semantic-level-number="4" data-speech-node="true"><mi data-latex="K" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="66" data-semantic-attributes="latex:K" data-semantic-level-number="5" data-speech-node="true">K</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="66" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi data-latex="E" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="66" data-semantic-attributes="latex:E" data-semantic-level-number="5" data-speech-node="true">E</mi></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="72" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="4,7,24,36" data-semantic-content="67,68,69" data-semantic-parent="72" data-semantic-owns="4 67 7 68 24 69 36" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="1492" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="70" data-semantic-attributes="latex:1492" data-semantic-level-number="5" data-speech-node="true">1492</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="70" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{g}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="6" data-semantic-parent="70" data-semantic-attributes="latex:\cancel{g}" data-semantic-owns="6" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:g" data-semantic-level-number="6" data-speech-node="true">g</mi></menclose><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="70" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{1\; kg}{1000 \;\cancel{g}} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="22" data-semantic-content="8,23" data-semantic-parent="70" data-semantic-attributes="latex:\left(\dfrac{1\\0003B kg}{1000 \\0003B\cancel{g}} \right);texclass:INNER" data-semantic-owns="8 22 23" data-semantic-level-number="5" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{1\; kg}{1000 \;\cancel{g}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="15,21" data-semantic-parent="24" data-semantic-attributes="latex:\dfrac{1\\0003B kg}{1000 \\0003B\cancel{g}}" data-semantic-owns="15 21" data-semantic-level-number="6" data-speech-node="true"><mrow data-latex="1\; kg" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="9,11,12" data-semantic-content="13,14" data-semantic-parent="22" data-semantic-attributes="latex:1\\0003B kg" data-semantic-owns="9 13 11 14 12" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:1" data-semantic-level-number="8" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:k" data-semantic-level-number="8" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:g" data-semantic-level-number="8" data-speech-node="true">g</mi></mrow><mrow data-latex="1000 \;\cancel{g}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="16,19" data-semantic-content="20" data-semantic-parent="22" data-semantic-attributes="latex:1000 \\0003B\cancel{g}" data-semantic-owns="16 20 19" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="1000" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:1000" data-semantic-level-number="8" data-speech-node="true">1000</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{g}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-children="18" data-semantic-parent="21" data-semantic-attributes="latex:\cancel{g}" data-semantic-owns="18" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:g" data-semantic-level-number="9" data-speech-node="true">g</mi></menclose></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="70" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><msup data-latex="\left(\dfrac{44.7 \;m}{s} \right)^2" data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="34,35" data-semantic-parent="70" data-semantic-attributes="latex:\left(\dfrac{44.7 \\0003Bm}{s} \right)^2" data-semantic-owns="34 35" data-semantic-level-number="5" data-speech-node="true"><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{44.7 \;m}{s} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:7" data-semantic-="" data-semantic-children="32" data-semantic-content="25,33" data-semantic-parent="36" data-semantic-attributes="latex:\left(\dfrac{44.7 \\0003Bm}{s} \right);texclass:INNER" data-semantic-owns="25 32 33" data-semantic-level-number="6" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="34" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{44.7 \;m}{s}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="30,31" data-semantic-parent="34" data-semantic-attributes="latex:\dfrac{44.7 \\0003Bm}{s}" data-semantic-owns="30 31" data-semantic-level-number="7" data-speech-node="true"><mrow data-latex="44.7 \;m" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="26,28" data-semantic-content="29" data-semantic-parent="32" data-semantic-attributes="latex:44.7 \\0003Bm" data-semantic-owns="26 29 28" data-semantic-level-number="8" data-speech-node="true"><mn data-latex="44.7" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:44.7" data-semantic-level-number="9" data-speech-node="true">44.7</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="30" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:m" data-semantic-level-number="9" data-speech-node="true">m</mi></mrow><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:s" data-semantic-level-number="8" data-speech-node="true">s</mi></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="34" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true">2</mn></msup></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="72" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="38,42" data-semantic-content="39" data-semantic-parent="72" data-semantic-owns="38 39 42" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="1.49" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="71" data-semantic-attributes="latex:1.49" data-semantic-level-number="5" data-speech-node="true">1.49</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="71" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="5" data-speech-node="true">×</mo><msup data-latex="10^2" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="40,41" data-semantic-parent="71" data-semantic-attributes="latex:10^2" data-semantic-owns="40 41" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="42" data-semantic-attributes="latex:10" data-semantic-level-number="6" data-speech-node="true">10</mn><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="42" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true">2</mn></msup></mrow></mrow><mo data-semantic-type="text" data-semantic-role="space" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="79" data-semantic-level-number="3" 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data-semantic-level-number="5" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="44,45" data-semantic-content="50" data-semantic-parent="52" data-semantic-owns="44 50 45" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="51" data-semantic-attributes="latex:k" data-semantic-level-number="7" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="51" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi 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data-semantic-parent="75" data-semantic-owns="62 73 64" data-semantic-level-number="5" data-speech-node="true"><msup data-latex="10^2" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="60,61" data-semantic-parent="74" data-semantic-attributes="latex:10^2" data-semantic-owns="60 61" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="62" data-semantic-attributes="latex:10" data-semantic-level-number="7" data-speech-node="true">10</mn><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="62" data-semantic-attributes="latex:2" data-semantic-level-number="7" data-speech-node="true">2</mn></msup><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true">J</mi></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> </li> <li class="lt-chem-21720" style="background-color: unset;">The increase in potential energy is the same as the amount of work required to raise the ball to its new altitude, which is (250 − 3) = 247 feet above its initial position. 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197 139 197C168 197 192 221 192 250Z"></path><path id="MJX-122-NCM-I-1D43D" d="M633 667C633 678 627 683 615 683C596 683 525 680 506 680L361 683C344 683 336 675 336 659C336 649 349 644 374 644C419 644 446 642 453 637C456 635 457 632 457 627C457 624 456 617 454 607L340 153C324 89 273 8 202 8C157 8 128 25 114 60L120 60C156 60 188 91 188 127C188 158 172 173 141 173C97 173 71 134 71 90C71 20 132-22 205-22C255-22 301-6 344 26C387 58 415 97 427 144L542 606C551 642 555 644 602 644C623 644 633 646 633 667Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.021719,-0.021719) translate(0, -1904)"><g data-mml-node="math" data-latex=" PE= 149\;\cancel{g} \left(\dfrac{1\; kg}{1000\; \cancel{g}} \right)\left(\dfrac{9.81\; m}{s^2} \right) \left(247\; \cancel{ft} \right) \left(\dfrac{0.3048\; m}{1 \;\cancel{ft}} \right)= 1.10 \times 10^2 \dfrac{kg⋅m^2}{s^2}= 1.10 \times 10^2\; J \nonumber " data-semantic-structure="(114 (113 (111 (104 (96 1 95 2) 3 (102 4 97 (7 6) 98 (24 8 (22 (15 9 13 11 14 12) (21 16 20 (19 18))) 23) 99 (36 25 (34 (30 26 29 28) (33 31 32)) 35) 100 (48 37 (47 38 46 (44 (43 40 42 41))) 45) 101 (66 49 (64 (54 50 53 52) (63 55 62 (61 (60 57 59 58)))) 65)) 67 (103 68 69 (72 70 71))) 73 (108 (86 (82 (81 74 80 75) 76 (79 77 78)) (85 83 84)) 87 (107 88 89 (106 (92 90 91) 105 94)))) 0))"><g data-mml-node="mtable" data-latex="PE= 149\;\cancel{g} \left(\dfrac{1\; kg}{1000\; \cancel{g}} \right)\left(\dfrac{9.81\; m}{s^2} \right) \left(247\; \cancel{ft} \right) \left(\dfrac{0.3048\; m}{1 \;\cancel{ft}} \right)= 1.10 \times 10^2  \dfrac{kg⋅m^2}{s^2}= 1.10 \times 10^2 \; J \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-id="114" data-semantic-children="113" data-semantic-attributes="latex: PE= 149\\0003B\cancel{g} \left(\dfrac{1\\0003B kg}{1000\\0003B \cancel{g}} \right)\left(\dfrac{9.81\\0003B m}{s^2} \right) \left(247\\0003B \cancel{ft} \right) 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data-speech-node="true" transform="translate(521,0)"><use data-c="1D454" href="#MJX-122-NCM-I-1D454"></use></g></g><g data-mml-node="mo" data-latex="⋅" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-id="76" data-semantic-parent="82" data-semantic-attributes="latex:⋅" data-semantic-operator="infixop,⋅" data-semantic-level-number="6" data-speech-node="true" transform="translate(1220.2,0)"><use data-c="22C5" href="#MJX-122-NCM-N-22C5"></use></g><g data-mml-node="msup" data-latex="m^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:7" data-semantic-id="79" data-semantic-children="77,78" data-semantic-parent="82" data-semantic-attributes="latex:m^2" data-semantic-owns="77 78" data-semantic-level-number="6" data-speech-node="true" transform="translate(1720.4,0)"><g data-mml-node="mi" data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="77" data-semantic-parent="79" data-semantic-attributes="latex:m" data-semantic-level-number="7" data-speech-node="true"><use data-c="1D45A" href="#MJX-122-NCM-I-1D45A"></use></g><g data-mml-node="mn" transform="translate(911,363) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="78" data-semantic-parent="79" data-semantic-attributes="latex:2" data-semantic-level-number="7" data-speech-node="true"><use data-c="32" href="#MJX-122-NCM-N-32"></use></g></g></g><g data-mml-node="msup" data-latex="s^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:6" data-semantic-id="85" data-semantic-children="83,84" data-semantic-parent="86" data-semantic-attributes="latex:s^2" data-semantic-owns="83 84" data-semantic-level-number="5" data-speech-node="true" transform="translate(1284.7,-719.9)"><g data-mml-node="mi" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="83" data-semantic-parent="85" data-semantic-attributes="latex:s" data-semantic-level-number="6" data-speech-node="true"><use data-c="1D460" href="#MJX-122-NCM-I-1D460"></use></g><g data-mml-node="mn" transform="translate(502,289) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="84" data-semantic-parent="85" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true"><use data-c="32" href="#MJX-122-NCM-N-32"></use></g></g><rect width="3235" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-id="87" data-semantic-parent="108" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true" transform="translate(3752.8,0)"><use data-c="3D" href="#MJX-122-NCM-N-3D"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="107" data-semantic-children="88,106" data-semantic-content="89" data-semantic-parent="108" data-semantic-owns="88 89 106" data-semantic-level-number="4" data-speech-node="true" transform="translate(4808.6,0)"><g data-mml-node="mn" data-latex="1.10" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-id="88" data-semantic-parent="107" data-semantic-attributes="latex:1.10" data-semantic-level-number="5" data-speech-node="true"><use data-c="31" href="#MJX-122-NCM-N-31"></use><use data-c="2E" href="#MJX-122-NCM-N-2E" transform="translate(500,0)"></use><use data-c="31" href="#MJX-122-NCM-N-31" transform="translate(778,0)"></use><use data-c="30" href="#MJX-122-NCM-N-30" transform="translate(1278,0)"></use></g><g data-mml-node="mo" data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-id="89" data-semantic-parent="107" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="5" data-speech-node="true" transform="translate(2000.2,0)"><use data-c="D7" href="#MJX-122-NCM-N-D7"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-id="106" data-semantic-children="92,94" data-semantic-content="105" data-semantic-parent="107" data-semantic-owns="92 105 94" data-semantic-level-number="5" data-speech-node="true" transform="translate(3000.4,0)"><g data-mml-node="msup" data-latex="10^2" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:7" data-semantic-id="92" data-semantic-children="90,91" data-semantic-parent="106" data-semantic-attributes="latex:10^2" data-semantic-owns="90 91" data-semantic-level-number="6" data-speech-node="true"><g data-mml-node="mn" data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="90" data-semantic-parent="92" data-semantic-attributes="latex:10" data-semantic-level-number="7" data-speech-node="true"><use data-c="31" href="#MJX-122-NCM-N-31"></use><use data-c="30" href="#MJX-122-NCM-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mn" transform="translate(1033,413) scale(0.707)" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-id="91" data-semantic-parent="92" data-semantic-attributes="latex:2" data-semantic-level-number="7" data-speech-node="true"><use data-c="32" href="#MJX-122-NCM-N-32"></use></g></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-id="105" data-semantic-parent="106" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true" transform="translate(1436.6,0)"></g><g data-mml-node="mi" data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="94" data-semantic-parent="106" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true" transform="translate(1714.6,0)"><use data-c="1D43D" href="#MJX-122-NCM-I-1D43D"></use></g></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -1904 1 3308"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="113" data-semantic-level-number="2" data-speech-node="true"></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" PE= 149\;\cancel{g} \left(\dfrac{1\; kg}{1000\; \cancel{g}} \right)\left(\dfrac{9.81\; m}{s^2} \right) \left(247\; \cancel{ft} \right) \left(\dfrac{0.3048\; m}{1 \;\cancel{ft}} \right)= 1.10 \times 10^2 \dfrac{kg⋅m^2}{s^2}= 1.10 \times 10^2\; J \nonumber " display="block" data-semantic-structure="(114 (113 (111 (104 (96 1 95 2) 3 (102 4 97 (7 6) 98 (24 8 (22 (15 9 13 11 14 12) (21 16 20 (19 18))) 23) 99 (36 25 (34 (30 26 29 28) (33 31 32)) 35) 100 (48 37 (47 38 46 (44 (43 40 42 41))) 45) 101 (66 49 (64 (54 50 53 52) (63 55 62 (61 (60 57 59 58)))) 65)) 67 (103 68 69 (72 70 71))) 73 (108 (86 (82 (81 74 80 75) 76 (79 77 78)) (85 83 84)) 87 (107 88 89 (106 (92 90 91) 105 94)))) 0))"><mtable displaystyle="true" data-latex="PE= 149\;\cancel{g} \left(\dfrac{1\; kg}{1000\; \cancel{g}} \right)\left(\dfrac{9.81\; m}{s^2} \right) \left(247\; \cancel{ft} \right) \left(\dfrac{0.3048\; m}{1 \;\cancel{ft}} \right)= 1.10 \times 10^2  \dfrac{kg⋅m^2}{s^2}= 1.10 \times 10^2 \; J \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="113" data-semantic-attributes="latex: PE= 149\\0003B\cancel{g} \left(\dfrac{1\\0003B kg}{1000\\0003B \cancel{g}} \right)\left(\dfrac{9.81\\0003B m}{s^2} \right) \left(247\\0003B \cancel{ft} \right) \left(\dfrac{0.3048\\0003B m}{1 \\0003B\cancel{ft}} \right)= 1.10 \times 10^2 \dfrac{kg⋅m^2}{s^2}= 1.10 \times 10^2\\0003B J \nonumber " data-semantic-owns="113" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="111" data-semantic-content="0" data-semantic-parent="114" data-semantic-owns="111 0" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="113" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="text" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="104,73,108" data-semantic-parent="113" data-semantic-collapsed="(111 (c 109 110) 104 73 108)" data-semantic-owns="104 73 108" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="96,102,103" data-semantic-content="3,67" data-semantic-parent="111" data-semantic-owns="96 3 102 67 103" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="1,2" data-semantic-content="95" data-semantic-parent="104" data-semantic-owns="1 95 2" data-semantic-level-number="4" data-speech-node="true"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="96" data-semantic-attributes="latex:P" data-semantic-level-number="5" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="96" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi data-latex="E" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="96" data-semantic-attributes="latex:E" data-semantic-level-number="5" data-speech-node="true">E</mi></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="104" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="4,7,24,36,48,66" data-semantic-content="97,98,99,100,101" data-semantic-parent="104" data-semantic-owns="4 97 7 98 24 99 36 100 48 101 66" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="149" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="102" data-semantic-attributes="latex:149" data-semantic-level-number="5" data-speech-node="true">149</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="102" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{g}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="6" data-semantic-parent="102" data-semantic-attributes="latex:\cancel{g}" data-semantic-owns="6" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:g" data-semantic-level-number="6" data-speech-node="true">g</mi></menclose><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="102" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{1\; kg}{1000\; \cancel{g}} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="22" data-semantic-content="8,23" data-semantic-parent="102" data-semantic-attributes="latex:\left(\dfrac{1\\0003B kg}{1000\\0003B \cancel{g}} \right);texclass:INNER" data-semantic-owns="8 22 23" data-semantic-level-number="5" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{1\; kg}{1000\; \cancel{g}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="15,21" data-semantic-parent="24" data-semantic-attributes="latex:\dfrac{1\\0003B kg}{1000\\0003B \cancel{g}}" data-semantic-owns="15 21" data-semantic-level-number="6" data-speech-node="true"><mrow data-latex="1\; kg" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="9,11,12" data-semantic-content="13,14" data-semantic-parent="22" data-semantic-attributes="latex:1\\0003B kg" data-semantic-owns="9 13 11 14 12" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:1" data-semantic-level-number="8" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:k" data-semantic-level-number="8" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:g" data-semantic-level-number="8" data-speech-node="true">g</mi></mrow><mrow data-latex="1000\; \cancel{g}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="16,19" data-semantic-content="20" data-semantic-parent="22" data-semantic-attributes="latex:1000\\0003B \cancel{g}" data-semantic-owns="16 20 19" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="1000" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:1000" data-semantic-level-number="8" data-speech-node="true">1000</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{g}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-children="18" data-semantic-parent="21" data-semantic-attributes="latex:\cancel{g}" data-semantic-owns="18" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:g" data-semantic-level-number="9" data-speech-node="true">g</mi></menclose></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="102" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{9.81\; m}{s^2} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="34" data-semantic-content="25,35" data-semantic-parent="102" data-semantic-attributes="latex:\left(\dfrac{9.81\\0003B m}{s^2} \right);texclass:INNER" data-semantic-owns="25 34 35" data-semantic-level-number="5" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{9.81\; m}{s^2}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="30,33" data-semantic-parent="36" data-semantic-attributes="latex:\dfrac{9.81\\0003B m}{s^2}" data-semantic-owns="30 33" data-semantic-level-number="6" data-speech-node="true"><mrow data-latex="9.81\; m" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="26,28" data-semantic-content="29" data-semantic-parent="34" data-semantic-attributes="latex:9.81\\0003B m" data-semantic-owns="26 29 28" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="9.81" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:9.81" data-semantic-level-number="8" data-speech-node="true">9.81</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="30" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:m" data-semantic-level-number="8" data-speech-node="true">m</mi></mrow><msup data-latex="s^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="31,32" data-semantic-parent="34" data-semantic-attributes="latex:s^2" data-semantic-owns="31 32" data-semantic-level-number="7" data-speech-node="true"><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="33" data-semantic-attributes="latex:s" data-semantic-level-number="8" data-speech-node="true">s</mi><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="33" data-semantic-attributes="latex:2" data-semantic-level-number="8" data-speech-node="true">2</mn></msup></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="102" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left(247\; \cancel{ft} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="47" data-semantic-content="37,45" data-semantic-parent="102" data-semantic-attributes="latex:\left(247\\0003B \cancel{ft} \right);texclass:INNER" data-semantic-owns="37 47 45" data-semantic-level-number="5" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="38,44" data-semantic-content="46" data-semantic-parent="48" data-semantic-owns="38 46 44" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="247" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:247" data-semantic-level-number="7" data-speech-node="true">247</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="47" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{ft}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="43" data-semantic-parent="47" data-semantic-attributes="latex:\cancel{ft}" data-semantic-owns="43" data-semantic-level-number="7" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-children="40,41" data-semantic-content="42,40" data-semantic-parent="44" data-semantic-owns="40 42 41" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="f" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:10" data-semantic-="" data-semantic-parent="43" data-semantic-attributes="latex:f" data-semantic-operator="appl" data-semantic-level-number="9" data-speech-node="true">f</mi><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:10" data-semantic-="" data-semantic-parent="43" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="9" data-speech-node="true">⁡</mo><mi data-latex="t" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:10" data-semantic-="" data-semantic-parent="43" data-semantic-attributes="latex:t" data-semantic-level-number="9" data-speech-node="true">t</mi></mrow></menclose></mrow><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="102" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left(\dfrac{0.3048\; m}{1 \;\cancel{ft}} \right)" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="64" data-semantic-content="49,65" data-semantic-parent="102" data-semantic-attributes="latex:\left(\dfrac{0.3048\\0003B m}{1 \\0003B\cancel{ft}} \right);texclass:INNER" data-semantic-owns="49 64 65" data-semantic-level-number="5" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="66" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{0.3048\; m}{1 \;\cancel{ft}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="54,63" data-semantic-parent="66" data-semantic-attributes="latex:\dfrac{0.3048\\0003B m}{1 \\0003B\cancel{ft}}" data-semantic-owns="54 63" data-semantic-level-number="6" data-speech-node="true"><mrow data-latex="0.3048\; m" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="50,52" data-semantic-content="53" data-semantic-parent="64" data-semantic-attributes="latex:0.3048\\0003B m" data-semantic-owns="50 53 52" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="0.3048" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="54" data-semantic-attributes="latex:0.3048" data-semantic-level-number="8" data-speech-node="true">0.3048</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="54" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="54" data-semantic-attributes="latex:m" data-semantic-level-number="8" data-speech-node="true">m</mi></mrow><mrow data-latex="1 \;\cancel{ft}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="55,61" data-semantic-content="62" data-semantic-parent="64" data-semantic-attributes="latex:1 \\0003B\cancel{ft}" data-semantic-owns="55 62 61" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="63" data-semantic-attributes="latex:1" data-semantic-level-number="8" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="63" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{ft}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-children="60" data-semantic-parent="63" data-semantic-attributes="latex:\cancel{ft}" data-semantic-owns="60" data-semantic-level-number="8" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-children="57,58" data-semantic-content="59,57" data-semantic-parent="61" data-semantic-owns="57 59 58" data-semantic-level-number="9" data-speech-node="true"><mi data-latex="f" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:11" data-semantic-="" data-semantic-parent="60" data-semantic-attributes="latex:f" data-semantic-operator="appl" data-semantic-level-number="10" data-speech-node="true">f</mi><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:11" data-semantic-="" data-semantic-parent="60" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="10" data-speech-node="true">⁡</mo><mi data-latex="t" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:11" data-semantic-="" data-semantic-parent="60" data-semantic-attributes="latex:t" data-semantic-level-number="10" data-speech-node="true">t</mi></mrow></menclose></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="66" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="104" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="68,72" data-semantic-content="69" data-semantic-parent="104" data-semantic-owns="68 69 72" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="1.10" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="103" data-semantic-attributes="latex:1.10" data-semantic-level-number="5" data-speech-node="true">1.10</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="103" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="5" data-speech-node="true">×</mo><msup data-latex="10^2" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="70,71" data-semantic-parent="103" data-semantic-attributes="latex:10^2" data-semantic-owns="70 71" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="72" data-semantic-attributes="latex:10" data-semantic-level-number="6" data-speech-node="true">10</mn><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="72" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true">2</mn></msup></mrow></mrow><mo data-semantic-type="text" data-semantic-role="space" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="111" data-semantic-level-number="3" data-speech-node="true"> </mo><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="86,107" data-semantic-content="87" data-semantic-parent="111" data-semantic-owns="86 87 107" data-semantic-level-number="3" data-speech-node="true"><mfrac data-latex="\dfrac{kg⋅m^2}{s^2}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="82,85" data-semantic-parent="108" data-semantic-attributes="latex:\dfrac{kg⋅m^2}{s^2}" data-semantic-owns="82 85" data-semantic-level-number="4" data-speech-node="true"><mrow data-latex="kg⋅m^2" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="81,79" data-semantic-content="76" data-semantic-parent="86" data-semantic-attributes="latex:kg⋅m^2" data-semantic-owns="81 76 79" data-semantic-level-number="5" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="74,75" data-semantic-content="80" data-semantic-parent="82" data-semantic-owns="74 80 75" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="81" data-semantic-attributes="latex:k" data-semantic-level-number="7" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="81" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="81" data-semantic-attributes="latex:g" data-semantic-level-number="7" data-speech-node="true">g</mi></mrow><mo data-latex="⋅" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="82" data-semantic-attributes="latex:⋅" data-semantic-operator="infixop,⋅" data-semantic-level-number="6" data-speech-node="true">⋅</mo><msup data-latex="m^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="77,78" data-semantic-parent="82" data-semantic-attributes="latex:m^2" data-semantic-owns="77 78" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="79" data-semantic-attributes="latex:m" data-semantic-level-number="7" data-speech-node="true">m</mi><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="79" data-semantic-attributes="latex:2" data-semantic-level-number="7" data-speech-node="true">2</mn></msup></mrow><msup data-latex="s^2" data-semantic-type="superscript" data-semantic-role="latinletter" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="83,84" data-semantic-parent="86" data-semantic-attributes="latex:s^2" data-semantic-owns="83 84" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="85" data-semantic-attributes="latex:s" data-semantic-level-number="6" data-speech-node="true">s</mi><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="85" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true">2</mn></msup></mfrac><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="108" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="88,106" data-semantic-content="89" data-semantic-parent="108" data-semantic-owns="88 89 106" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="1.10" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="107" data-semantic-attributes="latex:1.10" data-semantic-level-number="5" data-speech-node="true">1.10</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="107" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="5" data-speech-node="true">×</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="92,94" data-semantic-content="105" data-semantic-parent="107" data-semantic-owns="92 105 94" data-semantic-level-number="5" data-speech-node="true"><msup data-latex="10^2" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="90,91" data-semantic-parent="106" data-semantic-attributes="latex:10^2" data-semantic-owns="90 91" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="92" data-semantic-attributes="latex:10" data-semantic-level-number="7" data-speech-node="true">10</mn><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="92" data-semantic-attributes="latex:2" data-semantic-level-number="7" data-speech-node="true">2</mn></msup><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="106" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="106" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true">J</mi></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></li> </ol> </div> <div class="box-exercise"> <span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C)"></span><span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C)"></span><h5 class="box-legend"><span class="lt-icon-default">Exercise <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="122" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-123-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-123-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-123-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use data-c="35" href="#MJX-123-NCM-N-35"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(500,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-123-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="31" href="#MJX-123-NCM-N-31"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-123-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-123-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container></span></h5> <ol start="1" style="list-style-type: lower-alpha;"> <li class="lt-chem-21720" style="background-color: unset;">In a bowling alley, the distance from the foul line to the head pin is 59 ft, 10 13/16 in. (18.26 m). If a 16 lb (7.3 kg) bowling ball takes 2.0 s to reach the head pin, what is its kinetic energy at impact? (Assume its speed is constant.)</li> <li class="lt-chem-21720" style="background-color: unset;">What is the potential energy of a 16 lb bowling ball held 3.0 ft above your foot?</li> </ol> <dl> <dt><strong class="emphasis bold">Answer a</strong></dt> <dd> <p class="lt-chem-21720" style="background-color: unset;">3.10 × 10<sup>2</sup> J</p> </dd> <dt><strong class="emphasis bold">Answer b</strong></dt> <dd> <p class="lt-chem-21720" style="background-color: unset;">65 J</p> </dd> </dl> </div> <span id="Summary"></span><span id="Summary"></span><h2 style="background-color: unset;" class="lt-chem-21720">Summary</h2> <p class="lt-chem-21720" style="background-color: unset;">All forms of energy can be interconverted. Three things can change the energy of an object: the transfer of heat, work performed on or by an object, or some combination of heat and work. <em>Thermochemistry</em> is a branch of chemistry that qualitatively and quantitatively describes the energy changes that occur during chemical reactions. <strong class="emphasis bold">Energy</strong> is the capacity to do work. <strong class="emphasis bold">Mechanical work</strong> is the amount of energy required to move an object a given distance when opposed by a force. <strong class="emphasis bold">Thermal energy</strong> is due to the random motions of atoms, molecules, or ions in a substance. The <strong class="emphasis bold">temperature</strong> of an object is a measure of the amount of thermal energy it contains. <strong class="emphasis bold">Heat (</strong><em class="emphasis bolditalic">q</em><strong class="emphasis bold">)</strong> is the transfer of thermal energy from a hotter object to a cooler one. Energy can take many forms; most are different varieties of <strong class="emphasis bold">potential energy (<em class="emphasis bolditalic"><abbr title="potential energy">PE</abbr></em>)</strong>, energy caused by the relative position or orientation of an object. <strong class="emphasis bold">Kinetic energy (<em class="emphasis bolditalic"><abbr title="kinetic energy">KE</abbr></em>)</strong> is the energy an object possesses due to its motion. The most common units of energy are the <strong class="emphasis bold">joule (J)</strong>, defined as 1 (kg·m<sup>2</sup>)/s<sup>2</sup>, and the <strong class="emphasis bold">calorie</strong>, defined as the amount of energy needed to raise the temperature of 1 g of water by 1°C (1 cal = 4.184 J). </p> <footer class="mt-content-footer"> <style>/*<![CDATA[*/#mt-toc-container {display: none !important;}/*]]>*/</style><script type="text/javascript">/*<![CDATA[*/ $(function() { if(!window['autoDefinitionList']){ window['autoDefinitionList'] = true; $('dl').find('dt').on('click', function() { $(this).next().toggle('350'); }); } });/*]]>*/</script> <script defer="true" src="https://static.cloudflareinsights.com/beacon.min.js" data-cf-beacon="{"token": "483ec2414e274209a7e93c253192df0b"}"></script><script src="https://cdn.libretexts.net/github/LibreTextsMain/Miscellaneous/h5p-resizer.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/iframe-resizer/4.2.11/iframeResizer.contentWindow.min.js" integrity="sha512-FOf4suFgz7OrWmBiyyWW48u/+6GaaAFSDHagh2EBu/GH/1+OQSYc0NFGeGeZK0gZ3vuU1ovmzVzD6bxmT4vayg==" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/iframe-resizer/4.2.11/iframeResizer.min.js" integrity="sha512-HY1lApSG7xxx8mYzs/lxRs+c5AaDThRaa3pvQB6puiswvf2lWqMJVf+8qSGiL4ZXfHQoPIqbd1TlpqfycPo3cQ==" crossorigin="anonymous"></script><script>/*<![CDATA[*/window.addEventListener('load', function(){$('iframe').iFrameResize({warningTimeout:0, scrolling: 'omit'});})/*]]>*/</script><script>/*<![CDATA[*/ window.PageNum = "auto"; 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