# lec19 - Lecture19 P112 March3,2008 ReviewofWork

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Lecture 19 P112 March 3, 2008

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Review of Work When a constant force F acts on a particle that undergoes a straight-line displacement s , the work done by the force on the particle is defined as Units: 1 Joule = 1 Newton x Meter Work done by the net force on a particle equals the change in the particle’s kinetic energy W net = K 2 - K 1 = D K
New definition: Power Rate of doing work or transferring energy v : velocity of particle on which force F acts Units: watts(W) 1W = 1 J / s kilowatt (kW)  =  10 3  W megawatt (MW)  =  10 6  W milliwatt (mW)  =  10 -3  W horsepower (hp)  =  746 W  = 0.746 kW P = dW dt = r F · d r r dt = r F · d r r dt = r F · r v P = r F · r v

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1 2 3 4 5 A ball swings back-and- forth as a pendulum  without friction nor drag.   At which locations is the  net power due to all forces  acting on the ball equal to  zero?
Variable Force: (1D) Constant force: W = F x area under F vs. x plot: For variable force, we find the area by integrating: dW = F(x) dx . F x W g x F(x) x 1 x 2 dx W = F ( x ) dx x 1 x 2 ò

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Variable Force: (3D)
Examples Gravity: m m g g y 2 y r r 4 r 2 r 1 y Springs (1D): F(x) x 2 W s x x 1 -kx

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Falling Objects Three objects of mass m begin at height H with velocity v=0. How do their velocities compare when they have fallen to height 0? (1) (1) V f > V i > V p (2) (2) V f > V p > V i (3) (3) V f = V p = V i v=0 i H v=0 v p v=0 v f Free Fall Frictionless incline Pendulum
solution (a) (a) V f > V i > V p (b) (b) V f > V p > V i (c) (c) V f = V p = V i v=0 i H v=0 v p v=0 v f Free Fall Frictionless incline Pendulum Only gravity will do work: W g = mgH = 1 / 2 mv 2 2 - 1 / 2 mv 1 2 = 1 / 2 mv 2 2 v f = v i = v p = 2 gH does not depend on path !!

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Conservative Forces Gravity Mass on spring Both cases: Work only depends on initial and final position
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## This note was uploaded on 04/16/2009 for the course PHYS 1112 taught by Professor Leclair,a during the Fall '07 term at Cornell University (Engineering School).

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lec19 - Lecture19 P112 March3,2008 ReviewofWork

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