L10F11 - P123F11Lecture104Nov2011 ELASTICPOTENTIALENERGYAND

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1 P123 F11 Lecture 10 4 Nov 2011 ELASTIC POTENTIAL ENERGY AND ENERGY CONSERVATION t W P av • Power: dt dW P • 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: • Curved path in gravity: 1 2 E E W other 0 other W then 0 1 2 E E 2 1 g g g U U W Review of last lecture • Path in gravity: 1 Watt = 1 Joule/Sec
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2 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 Clicker  i f i f mgy mgy mv mv 2 2 2 1 2 1
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3 ELASTIC POTENTIAL ENERGY x = Displacement from equilibrium ) 0 ( 0 1 2 2 1 2 1 2 1 2 2 2 1 x kx kx kx W W W el Work done on spring by force F to create displacement x : BUT 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 Spring at equilibrium If 0 2 1 el W x x When spring retracts: ! 0 2 2 2 1 2 1 2 1 kx kx W el x s F x 1 x 2 F
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4 As with gravity, work done by spring can be characterized as change in potential energy: 2 2 1 kx U 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 force of gravity does not) So, if a spring acts on a body: 2 1 el el el TOT U U W W 1 2 K K K [Elastic Force Only] x
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L10F11 - P123F11Lecture104Nov2011 ELASTICPOTENTIALENERGYAND

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