(15) Energy Conservation and Potential Energy

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

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Potential energy Kinetic energy Basic energy Lecture 15 Energy Conservation; Potential Energy
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ACT: Car Accident? You are speeding down the road without a care in the world and just as you are approaching a sharp curve in the road above a scenic overlook you notice that your brakes are soft due to leaking brake fluid. From past experience you estimate that you have about 2 s of braking left. Before the dangerous curve there is a dip in the road. Which is the best place to use your limited brake? You must slow down before the curve or you will become part of the scenery! Dip A B C D Not D!!!! Decrease K as much as possible Need large | W | Apply force during long distance For fixed time (2 s), longest distance when large speed 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 the floor (A) to a table (B) through two different trajectories. Find the work done by 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 the path
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Gravitational potential energy Gravitational potential energy The work done by gravity does not depend on the path, 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) the change in 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 done by a spring as the tip is pulled from x
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This note was uploaded on 03/27/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Fall '08 term at Iowa State.

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

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