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(15) Energy Conservation and Potential Energy

(15) Energy Conservation and Potential Energy - Potential...

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Potential energy Kinetic energy Basic energy Lecture15 Energy Conservation; Potential Energy
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ACT: Car Accident? You arespeeding down theroad without a carein theworld and just as you areapproaching a sharp curvein theroad abovea scenic overlook you notice that your brakes aresoft dueto leaking brakefluid. From past experienceyou estimatethat you have about 2 s of braking left. Beforethedangerous curvethereis a dip in theroad. Which is thebest placeto useyour limited brake? You must slow down beforethecurveor you will becomepart of thescenery! Dip A B C D Not D!!!! DecreaseK as much as possible Need large| W | Apply forceduring long distance For fixed time(2 s), longest distance when largespeed Largest speed is at the dip (work by gravity increases K)
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Work done by gravity Work done by gravity A block of mass m is lifted from thefloor (A) to a table(B) through two different trajectories. Find thework doneby gravity. y Δ m g A B Δ r Δ r Δ r Δ r ( 29 y mg r g m r r r g m r g m r g m r g m W - = = + + = + + = 3 2 1 3 2 1 y mg r g m W - = = Work by gravity does not depend on thepath
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Gravitational potential energy Gravitational potential energy Thework doneby gravity does not depend on thepath, it only depends on the vertical displacement y Δ , or on the initial and final y: y mg W - = U = potential energy We can ALWAYS write this work as (minus) thechangein some function U( r) that depends on position (not on path): ( 29 i f W U U U = - - = -∆ const ant U mgy = + Gravitational potential energy: There is always room for an arbitrary constant, because what matters is U Δ
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Elastic Potential Energy (Spring) Elastic Potential Energy (Spring) What is the work doneby a spring as the tip is pulled from x 1 to x 2 ?
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