{"id":739,"date":"2023-08-18T14:29:59","date_gmt":"2023-08-18T21:29:59","guid":{"rendered":"https:\/\/dornsife.usc.edu\/lecture-support-lab\/?page_id=739"},"modified":"2023-09-18T10:12:22","modified_gmt":"2023-09-18T17:12:22","slug":"conservation-of-mechanical-energy","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/lecture-support-lab\/conservation-of-mechanical-energy\/","title":{"rendered":"Conservation of Mechanical Energy"},"content":{"rendered":"\n\n\n\n            \n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--accordions \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--accordions\"\n    \n      >\n\n    \n  \n      <ul>\n              <li>\n          <button type=\"button\" class=\"accordion-trigger \" id=\"heading-1-1-ieZGBKrbQe\" aria-controls=\"section-1-1-ieZGBKrbQe\" aria-expanded=\"false\" aria-disabled=\"false\">\n                          <span class=\"item-title\">M.9(1) &#8211; Bowling Ball Pendulum<\/span>\n            \n                      <\/button>\n\n          <div id=\"section-1-1-ieZGBKrbQe\" role=\"region\" aria-labelledby=\"heading-1-1-ieZGBKrbQe\" class=\"accordion-panel\">\n\n                            \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>A bowling ball fastened at the end of a cord hanging from the ceiling of the classroom demonstrates the exchange between potential and kinetic energies.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-740 aligncenter\" src=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_1.jpg\" alt=\"Bowling Ball Pendulum\" width=\"225\" height=\"300\" \/><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n            \n                      <\/div>\n        <\/li>\n\n              <li>\n          <button type=\"button\" class=\"accordion-trigger \" id=\"heading-1-2-ieZGBKrbQe\" aria-controls=\"section-1-2-ieZGBKrbQe\" aria-expanded=\"false\" aria-disabled=\"false\">\n                          <span class=\"item-title\">M.9(2) Loop-the-Loop<\/span>\n            \n                      <\/button>\n\n          <div id=\"section-1-2-ieZGBKrbQe\" role=\"region\" aria-labelledby=\"heading-1-2-ieZGBKrbQe\" class=\"accordion-panel\">\n\n                            \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>A ball rolling on this track demonstrates the relationship among potential, kinetic and rotational energies. Loop-the-loop is a circular section of track with rails of metal tubing held together by metal cross ties. It is attached to two straight sections of similar track. The ends of the cross ties have threads that fit short support rods for use in supporting the track. Release the ball from one end of the track. The ball will orbit the track without losing contact and will reach the other end at the same height as it began.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-723 aligncenter\" src=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m12_3-300x198.jpg\" alt=\"Loop-the-Loop\" width=\"300\" height=\"198\" srcset=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m12_3-300x198.jpg 300w, https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m12_3.jpg 398w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n            \n                      <\/div>\n        <\/li>\n\n              <li>\n          <button type=\"button\" class=\"accordion-trigger \" id=\"heading-1-3-ieZGBKrbQe\" aria-controls=\"section-1-3-ieZGBKrbQe\" aria-expanded=\"false\" aria-disabled=\"false\">\n                          <span class=\"item-title\">M.9(3) &#8211; Energy of Rotation<\/span>\n            \n                      <\/button>\n\n          <div id=\"section-1-3-ieZGBKrbQe\" role=\"region\" aria-labelledby=\"heading-1-3-ieZGBKrbQe\" class=\"accordion-panel\">\n\n                            \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>The track used in this demonstration is mounted on a wooden board. It consists of an aluminum wide strip covering the board and two parallel sides a little wider than the ball used. One end of the track is clamped to heavy stands forming an inclined plane and it is set on the edge of a table. The ball is released twice from the top of the track. First, it is allowed to rotate. On the second time, it slides down the plane &#8211; the rotational movement can be inhibited by pulling out two small rods mounted on the sides of the ball, like wings, and setting it on the track. The &#8220;wings&#8221; should hold to the sides of the track. The whole class will see that when the ball does not rotate, it jumps further away from the table than when it rotates down the track.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-742 size-full\" src=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_3.jpg\" alt=\"Energy of Rotation\" width=\"400\" height=\"200\" srcset=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_3.jpg 400w, https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_3-300x150.jpg 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n            \n                      <\/div>\n        <\/li>\n\n              <li>\n          <button type=\"button\" class=\"accordion-trigger \" id=\"heading-1-4-ieZGBKrbQe\" aria-controls=\"section-1-4-ieZGBKrbQe\" aria-expanded=\"false\" aria-disabled=\"false\">\n                          <span class=\"item-title\">M.9(4) &#8211; Ballistic Pendulum<\/span>\n            \n                      <\/button>\n\n          <div id=\"section-1-4-ieZGBKrbQe\" role=\"region\" aria-labelledby=\"heading-1-4-ieZGBKrbQe\" class=\"accordion-panel\">\n\n                            \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>This apparatus can be used to demonstrate topics of conservation of momentum and projectile motion. The pendulum swings freely at one end. When the ball hits the bob and swings it up, the bob is held at its highest point of the swing by a ratchet system. A protrusion at the base of the bob catches the ratchet which has a scale for measurement of height changes. For experiments on the range of the projectile, the pendulum can be swung out of the way so that the spring gun can fire the projectile horizontally into the air. The projectile can be fired at different velocites by the spring-gun, adjusting the spring&#8217;s tension. It also shows conservation of energy since potential energy is stored in the spring-loaded gun which becomes kinetic energy when the massive bob is fired, and is converted back to potential energy when it catches the ratchet.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-743 size-full\" src=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_4.jpg\" alt=\"Ballistic Pendulum\" width=\"398\" height=\"262\" srcset=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_4.jpg 398w, https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_4-300x197.jpg 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n            \n                      <\/div>\n        <\/li>\n\n              <li>\n          <button type=\"button\" class=\"accordion-trigger \" id=\"heading-1-5-ieZGBKrbQe\" aria-controls=\"section-1-5-ieZGBKrbQe\" aria-expanded=\"false\" aria-disabled=\"false\">\n                          <span class=\"item-title\">M.9(5) &#8211; High Road-Low Road<\/span>\n            \n                      <\/button>\n\n          <div id=\"section-1-5-ieZGBKrbQe\" role=\"region\" aria-labelledby=\"heading-1-5-ieZGBKrbQe\" class=\"accordion-panel\">\n\n                            \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>It shows the conversion of potential energy into kinetic energy. Although the low road ball must travel a longer distance, it will be faster than the high road ball due to the conversion of gravitational potential energy into kinetic energy.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-744 aligncenter\" src=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_5-300x210.jpg\" alt=\"High Road-Low Road\" width=\"300\" height=\"210\" srcset=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_5-300x210.jpg 300w, https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_5.jpg 398w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n            \n                      <\/div>\n        <\/li>\n\n              <li>\n          <button type=\"button\" class=\"accordion-trigger \" id=\"heading-1-6-ieZGBKrbQe\" aria-controls=\"section-1-6-ieZGBKrbQe\" aria-expanded=\"false\" aria-disabled=\"false\">\n                          <span class=\"item-title\">M.9(6) &#8211; Interrupted Pendulum<\/span>\n            \n                      <\/button>\n\n          <div id=\"section-1-6-ieZGBKrbQe\" role=\"region\" aria-labelledby=\"heading-1-6-ieZGBKrbQe\" class=\"accordion-panel\">\n\n                            \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>In a simple pendulum, the ball swings to the same height on each side of its rest position. If a bar interrupts its motion on one side, making the pendulum shorter, the ball still reaches the same height.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-745 aligncenter\" src=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/m9_6_000.jpg\" alt=\"Interrupted Pendulum\" width=\"167\" height=\"298\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-746 aligncenter\" src=\"https:\/\/dornsife.usc.edu\/lecture-support-lab\/wp-content\/uploads\/sites\/280\/2023\/08\/mechanic1-56.gif\" alt=\"Interrupted Pendulum\" width=\"271\" height=\"265\" \/><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n            \n                      <\/div>\n        <\/li>\n\n          <\/ul>\n  \n  \n\n  <\/div><\/div>\n\n\n\n  \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--two-column-ctas \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--two-column-ctas\"\n    \n      >\n\n    \n      <div class=\"group\">\n\n                  \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Back to Mechanics\n      <\/h2>\n\n\n<\/div>\n      \n              <ul>\n                      <li>\n                  \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/dornsife.usc.edu\/lecture-support-lab\/mechanics\/\n    aria-label=\"Read more about Mechanics\"  \n>\n    Mechanics \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#000\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n            <\/li>\n                  <\/ul>\n      \n    <\/div>\n      <div class=\"group\">\n\n                  \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Back to Home\n      <\/h2>\n\n\n<\/div>\n      \n              <ul>\n                      <li>\n                  \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/dornsife.usc.edu\/lecture-support-lab\/\n    aria-label=\"Read more about Home\"  \n>\n    Home \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#000\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n            <\/li>\n                  <\/ul>\n      \n    <\/div>\n  \n\n  <\/div><\/div>\n\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--spacer \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--spacer\"\n    \n      >\n\n    \n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":354,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-content-detail.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-739","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - 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