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1. A crate of mass 10.0 kg slides down a ramp 30.0 m long that makes an angle of 15 with respect to the horizontal. The coefficient of kinetic friction between the crate and the ramp is f-LK - 0.1.

(A). How much work does the force of friction do on the crate from the top of the rt~'?pto ~le bcittom7

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(B). What is the speed of the crate when it reaches'the bottom of the ramp if it starts out at rest at the top?

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(C). A second ramp, identical to the first one (same angle \vith respect to the horizontal and same coefficient of kinetic friction with respect to the crate) is placed so that its bottom is touching the bottom of the first ramp, forming a V-shape. Thus, as the crate finishes sliding down the first ramp, it begins to slide up the second ramp. How far up the second ramp does it travel before it stops moving (and then afterward starts sliding down again)?

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2. Two equal masses of'm, = 5.0 kg are attached to either end of a spring with spring constant k = 50.0 N1m and zero rest length. Initially the masses are both at rest at x = 0 on a frictionless surface with the spring at its rest length.

At time t = 0 a force whose magnitude depends on time as

F = 10.0 N/s x t (pointing from left to right) is applied to horizontally on the left mass for a time f:::"t = 2 s. Before t = 0 and after t = 2 s, the force is zero.

(A). Determine the impulse applied to the system. from t = 0 s to t = 2 s.

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(B). Find VCM, the velocity of the center of mass of the system, at time t = 10 s.

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(C). \\Then the force is removed at t = 2 s, the positions of the blocks are measured to be at Xl = 0.3 111 and X2 = 0.5 m and at that instant they have velocities of VI = 5.5 m/s and V2 = 5.7 m/s. How much work did the force do on the system while it was acting?

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(C). When the force is removed at t = 2 s, the positions of the blocks are measured to be at Xl = 0.3 m and X2 = 0.5 m and at that instant they have velocities of VI = 5.5 m/s and V2 = 5.7 m/s. How much work did the force do on the system while it was acting?

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3. An electron of mass 'me = 9.1 X 10-31 kg n10ves with a speed of 1.0 x 107 m/s. It undergoes a collision with a second electron which is originally sitting rest. After the collision, one electron moves out with speed 6.0 x 106 TP/s and its path makes an angle with respect to the original axis of the collision and the other electron has a speed of 8.0 x 106 m/s and its path makes an angle ewith respect to the original collision axis. -

(A). Is this collision elastic or inelastic? Explain your answer. ~("'-o k E -\-c K~ = 1 yv-) V?

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(B). Find the angles and e. (If you need more space to work, continue on the back of this sheet).

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