Lect10 - Physics 211 Lecture 10 Todays Agenda Review of Work Work done by gravity near the Earths surface Examples pendulum inclined plane free

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Physics 211: Lecture 10, Pg 1 Physics 211: Lecture 10 Physics 211: Lecture 10 Today Today ’s Agenda s Agenda z Review of Work z Work done by gravity near the Earth’s surface z Examples: Î pendulum, inclined plane, free fall z Work done by variable force Î Spring z z Work done by variable force in 3-D Î Newton’s gravitational force z Conservative forces & potential energy
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Physics 211: Lecture 10, Pg 2 Review: Constant Force Review: Constant Force θ F r d i s p l a c e m n t F r Work, W , of a constant force F acting through a displacement r is: W = F r r = F r cos( θ ) = F r r
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Physics 211: Lecture 10, Pg 3 Review: Sum of Constant Forces Review: Sum of Constant Forces Suppose F NET = F 1 + F 2 and the displacement is S . The work done by each force is: W 1 = F 1 i r r W 2 = F 2 r F TOT r F 1 F 2 W NET = W 1 + W 2 = F 1 r r + F 2 r = ( F 1 + F 2 ) r W NET = F NET r
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Physics 211: Lecture 10, Pg 4 Review: Constant Force. .. Review: Constant Force. .. W = F i r z No work done if θ = 90 o . Î No work done by T . Î No work done by N . v N T v v
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Physics 211: Lecture 10, Pg 5 Work/Kinetic Energy Theorem: Work/Kinetic Energy Theorem: { Net Net Work Work done on object } = { change change in kinetic energy kinetic energy of object } W F = K = 1 / 2 mv 2 2 - 1 / 2 mv 1 2 x F v 1 v 2 m W F = F x
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Physics 211: Lecture 10, Pg 6 Work done by gravity: Work done by gravity: z W g = F i r = mg r cos θ = - mg y (remember y = y f -y i ) W g = - mg y Depends only on y ! j j m r m g g y θ m
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Physics 211: Lecture 10, Pg 7 Work done by gravity. .. Work done by gravity. .. z Depends only on y, not on path taken ! m m g g y j j W NET = W 1 + W 2 + . . .+ W n r = F i r = F y r 1 r 2 r 3 r n = F r 1 + F r 2 + . . . + F r n = F ( r 1 + r 2 + . . .+ r n ) W g = - mg y
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Physics 211: Lecture 10, Pg 8 Lecture 10, Lecture 10, Act 1 Act 1 Falling Objects Falling objects Falling Objects z Three objects of mass m begin at height h with velocity 0 . One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a pendulum. What is the relationship between their velocities when they have fallen to height 0 ? v=0 v i H v=0 v p v=0 v f Free Fall Frictionless incline Pendulum (a) (a) V f > V i > V p (b) (b) V f > V p > V i (c) (c) V f = V p = V i
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Physics 211: Lecture 10, Pg 9 Lecture 10, Lecture 10, Act 1 Act 1 Solution Solution v = 0 v 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 gH 2 v v v p i f = = = does not depend on path !!
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This note was uploaded on 02/10/2009 for the course PHYS 211 taught by Professor Tonyliss during the Spring '09 term at University of Illinois, Urbana Champaign.

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Lect10 - Physics 211 Lecture 10 Todays Agenda Review of Work Work done by gravity near the Earths surface Examples pendulum inclined plane free

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