Lecture_10

Lecture_10 - P123Lecture105Nov2010 ELASTICPOTENTIALENERGYAND

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P123 Lecture 10 5 Nov 2010 ELASTIC POTENTIAL ENERGY AND ENERGY CONSERVATION Review of last lecture t W P av • Power : dt dW P 1 Watt = 1 Joule/Sec • Gravitational Potential Energy : mgy U g • Work – Energy Theorem : 1 2 1 2 g g other U U K K W • Let E = K + U (Total Energy) : If: 1 2 E E W other 0 other W then 0 1 2 E E • Curved path in gravity: 2 1 g g g U U W • Path in gravity: 1
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i Clicker Three identical balls are thrown with equals speeds from the top of a building at angles to the horizontal as shown. Neglect air resistance. What is the relationship between their speeds when the balls hit the ground? A) v 1 = v 2 = v 3 B) v 1 = v 2 < v 3 C) v 1 < v 2 < v 3 D) v 1 > v 2 > v 3  i f i f mgy mgy mv mv 2 2 2 1 2 1 2
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ELASTIC POTENTIAL ENERGY x = Displacement from equilibrium Spring at equilibrium Work done on spring by force F to create displacement x : x F ) 0 ( 0 1 2 2 1 2 1 2 1 2 2 2 1 x kx kx kx W BUT W W el As spring is stretched, it applies an equal and opposite force on whatever is causing the stretching. Where el W is work done by the spring. 2 2 2 1 2 1 2 1 kx kx W el If 0 2 1 el W x x When spring retracts: s F 3 ! 0 2 2 2 1 2 1 2 1 kx kx W el x 1 x 2
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As with gravity, work done by spring can be characterized as change in potential energy: 2 1 k U 2 kx el   el el el el el el U U U U U kx kx W 1 2 2 1 2 2 2 1 2 1 2 1 Recall Energy – Displacement diagram: Note: U ( x ) must be referenced to x = 0 ! (different from gravity) (This is because the elastic force depends on position while the (This is because the elastic force depends on position while the force of gravity does not) So, if a spring acts on a body: U U W W x 2 1 el el el TOT 1 2 K K K 4 [Elastic Force Only]
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If ONLY elastic force acts on body: 2 TOT U
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Lecture_10 - P123Lecture105Nov2010 ELASTICPOTENTIALENERGYAND

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