A 3-kg block slides along a horizontal surface with an initial speed of 7 m/s. T

Question

A 3-kg block slides along a horizontal surface with an initial speed of 7 m/s. The coefficient of friction between the block and the surface is n = 0.5. After sliding a distance ol 4 m. the block makes a smooth transition on a friction less ramp inclined at an angle of 40" to the horizontal, (a) Find the velocity of the block at the bottom of the ramp, (b) 1 low far up on the ramp docs the block slide before coming to rest? (c) Find the final position on the block. A 1-kg steel ball is connected to a 2 m string as shown in the figure. the ball is released from rest in a horizontal position, and at the lowest point strikes a 4-kg block sitting at rest on rough shelf. After collision, the ball bounces back at 1.565 m/s. (a) Find the velocity of the ball just before the collision, (b) Find the velocity of the block just after collision, (c) Decide if the collision is elastic, (d) After collision, the block slides 2.2 m before coming to rest. What is the coefficient of kinetic friction between the block and the shelf?

Explanation / Answer

5 . a) friction force, f = ukN = uk m g = 0.5 * 3 * 9.8 = 14.7 N

Work done by fritction = change in KE

- 14.7 * 4 = 3 v^2 /2 - 3(7^2)/2

v = 3.13 m/s

b) Work done by gravity = change in KE

- m g L sin40 = 0 - 3(3.13^2)/2

9.8 * L * sin40 = 3.13^2 / 2

L = 0.778 m

c) height of final osition = Lsin40 = 0.5 m

horizontal distance from bottom of incline = Lcos40 = 0.6 m

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