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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)
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
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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