CHAPTER 8 PHYS195 NOTES (part two)

# CHAPTER 8 PHYS195 NOTES (part two) - CHAPTER EIGHT NOTES...

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CHAPTER EIGHT NOTES Physics 195 Lecture (part one)

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Conservation of Energy If only conservative forces are present, the total kinetic plus potential energy of a system is conserved, i.e. the total “mechanical energy” is conserved. E = K + U is constant constant Both K and U can change, but E = K + U remains constant. E = K + U E = K + U = W + U = W + (-W) = 0 using K = W using U = -W
Dennis and Carmen are standing on the edge of a cliff. Dennis throws a basketball vertically upward, and at the same time Carmen throws a basketball vertically downward with the same initial speed. You are standing below the cliff observing this strange behavior. Whose ball is moving fastest when it hits the ground? viD viC Dennis Dennis Carmen Carmen h vfC vfD F=-mg U g = 0 U g =mgh K=- U g =mgh Gain in kinetic energy = Loss in potential energy K=1/2m(v f C ) 2 -1/2m(v i C ) 2 =1/2m(v f D ) 2 -1/2m(v i D ) 2 = mgh

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Question : Work & Energy A box sliding on a horizontal frictionless surface runs into a fixed spring, compressing it a distance x 1 from its relaxed position while momentarily coming to rest. If the initial speed of the box were doubled and its mass were halved , how far x 2 would the spring compress ? x
Solution Again, use the fact that Energy is conserved k m v x 1 1 1 = k m v x = x 1 v 1 so kx 2 = mv 2 m 1 m 1 Initially E = 1 / 2 mv 2 only kinetic energy Finally E = ½ kx 2 only potential energy Gain in potential energy = Loss in kinetic energy

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x 2 v 2 m 2 m 2 So if v 2 = 2v 1 and m 2 = m 1 /2 x 2 = 2v 1 m 1 2 k = v 1 2m 1 k x 2 = 2 x 1 k m v x 1 1 1 = k m v x 2 2 2 = k m v x 2 2 2 =
Example: Airtrack & Glider A glider of mass M is initially at rest on a horizontal frictionless track. A mass m is attached to it with a massless string hung over a massless pulley as shown. What is the speed v of M after m has fallen a distance d ?

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CHAPTER 8 PHYS195 NOTES (part two) - CHAPTER EIGHT NOTES...

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