# Lect11 - Physics 211: Lecture 11 Conservative Forces:...

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Page 1 Physics 211: Lecture 11, Pg 1 Physics 211: Lecture 11 Today Today ’s Agenda s Agenda z Conservative forces & potential energy - review z Conservation of “total mechanical energy” ¾ Example: pendulum z Non-conservative forces ¾ friction z General work/energy theorem z Example problem Physics 211: Lecture 11, Pg 2 Conservative Forces: Conservative Forces: z We have seen that the work done by gravity does not depend on the path taken. R 1 R 2 M m h m W g = -mgh = 1 2 g R 1 R 1 GMm W Physics 211: Lecture 11, Pg 3 Lecture 11, Act 1 Work & Energy Work & Energy z A rock is dropped from a distance R E above the surface of the earth, and is observed to have kinetic energy K 1 when it hits the ground. An identical rock is dropped from twice the height ( 2R E ) above the earth’s surface and has kinetic energy K 2 when it hits. R E is the radius of the earth. ¾ What is K 2 / K 1 ? (a) (a) (b) (b) (c) (c) 3 2 4 3 2 R E R E 2R E Physics 211: Lecture 11, Pg 4 Lecture 11, Act 1 Solution Solution z Since energy is conserved, K = W G . R E R E 2R E 1 2 G R 1 R 1 GMm = W 1 2 R 1 R 1 c = K Where c = GMm is the same for both rocks Physics 211: Lecture 11, Pg 5 Lecture 11, Act 1 Solution Solution z For the first rock: R E R E E E E 1 R 1 2 1 c 2R 1 R 1 c = K = 1 2 R 1 R 1 c = K 2R E E E E 2 R 1 3 2 c 3R 1 R 1 c = K = z For the second rock: So: 3 4 2 1 3 2 = K K 1 2 = Physics 211: Lecture 11, Pg 6 Conservative Forces: z We have seen that the work done by a conservative force does not depend on the path taken. W 1 W 2 W 1 W 2 W 1 = W 2 W NET = W 1 -W 2 = W 1 1 = 0 z Therefore the work done in a closed path is 0.

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Page 2 Physics 211: Lecture 11, Pg 7 Lecture 11, Act 2 Conservative Forces Conservative Forces z The pictures below show force vectors at different points in space for two forces. Which one is conservative ? (a) (a) 1 (b) (b) 2 (c) both (1) (2) y x y x Physics 211: Lecture 11, Pg 8 Lecture 11, Act 2 Solution Solution z Consider the work done by force when moving along different paths in each case: (1) (2) W A = W B W A > W B Physics 211: Lecture 11, Pg 9 Lecture 11, Act 2 z In fact, you could make money on type (2) if it ever existed: ¾ Work done by this force in a “round trip” is > 0 ! ¾ Free kinetic energy!! W = 15 J W = 0 W = -5 J W = 0 W NET = 10 J = K Physics 211: Lecture 11, Pg 10 Potential Energy Recap: Potential Energy Recap: z For any conservative force we can define a potential energy function U such that: z The potential energy function U is always defined only up to an additive constant. ¾ You can choose the location where U = 0 to be anywhere convenient. U = U 2 -U 1 = -W =- F .
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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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Lect11 - Physics 211: Lecture 11 Conservative Forces:...

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