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Lect13-Phys172s11-(7.1-7.9-Energy_macroscopic)

# Lect13-Phys172s11-(7.1-7.9-Energy_macroscopic) - PHYS 172...

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Spring 2011 PHYS 172: Modern Mechanics Lecture 13 – Energy in Macroscopic System Read 7.1– 7.8 Homeworks: It is expected that a student works on a a homework # x shortly after lecture # x , since HWx is on material of LECx. While the due dates for HWs are typically set to about a week after the respective lectures, this extra time should be considered as a grace period for emergencies and not as a suggestion to work on the assignment on that last day. Potential energy of a spring , s x s F k x = - x , s s x U F x = - 2 1 2 s s U k x = 2 1 2 s s U k s = Potential energy of a spring: 2 1 2 s k s s U Assume U s = 0 for relaxed spring y

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Energy of an oscillating spring-mass system x Neglect friction: ( ) 2 0 Δ = Δ + + = sys s E mc K U 2 2 1 0 2 2 s mv k x ° ± Δ + = ² ³ ´ µ 2 max 0 1 2 s K U k x = = y 2 max 2 0 mv K U = = 2 2 max max 1 2 2 s mv k x = x max -x max Maximum speed: Speed at any point: 2 2 2 max 1 1 2 2 2 s s mv k x k x + = ( ) ( ) 2 2 max / s v k m x x = - v c << 1 γ = HOME STUDY: Example, “a rebounding block” k s = 2000 N/m System: block, spring, Earth Assume: no interaction with surroundings γ = 1 i f E E = ( ) 2 2 0 1 1 2 2 i i f s f mgy mv mgy k L y + = + - 1. What is the lowest point reached by the block?
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Lect13-Phys172s11-(7.1-7.9-Energy_macroscopic) - PHYS 172...

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