# Lect_15 - Potential energy Basic energy You are speeding...

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Potential energy Kinetic energy Basic energy Lecture 15 Energy Conservation; Potential Energy 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 ) 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 m g A B r 3 2 1 () mg W = = + + = + + = 3 2 1 3 2 1 G G G G G G G G G G G G = = G G Work by gravity does not depend on the path Gravitational potential energy Gravitational potential energy The work done by gravity does not depend on the path, it only depends on the vertical displacement , or on the initial and final y: = U = potential energy We can ALWAYS write this work as (minus) the change in some function ( ) that depends on position (not on path): ( ) i f WU = −−= constant Umgy =+ Gravitational potential energy: There is always room for an arbitrary constant, because what matters is

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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 1 to 2 ?
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Lect_15 - Potential energy Basic energy You are speeding...

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