A puck of mass M = 02 kg is tied to string of length 1 m, with the other end nai

Question

A puck of mass M = 02 kg is tied to string of length 1 m, with the other end nailed to the top of a rough horizontal surface. The puck is given an initial speed of 5 m/s and begins to move in a circle, as shown below. If the puck comes to rest after making 15 revolutions, what is the coefficient of kinetic friction between the puck and the surface? (Using g = 9.8 m/s^2 mu_k = 0.135) A block of mass, m = 200 g is pressed against a spring with a spring constant k = 1400 N/m until the block compresses the spring 10 cm. The spring rests at the bottom of a ramp inclined at 60degree to the horizontal. Determine how far up the incline the block moves from the point of release before momentarily coming to rest, if there is no friction (4.12 m) if the coefficient of kinetic friction is 0.4 (3.35 m) The blocks in the Atwood machine shown below are released from rest. Assuming no friction in the pulley, what is the speed of the masses when they are at the same height?

Explanation / Answer

4. Number of revolutions = 15
distance = 15*2pi*1 = 30pi
work done by friction = mu*0.2*9.8*30pi = 0.5*0.2*5^2 [ conservation of energy]
mu = 0.01354
5. a) PE stored in spring = 0.5*1400*(0.1)^2 = 7 J
Net gain in hieght = h
mgh = 7 [conservation of energy]
h = 7/0.2*9.8 = 3.5714 m
distance up the incline, l = h/sin(60) = 4.1239 m
b) with friction
let the distance up the incline be x
PE in spring = 7J
Work done by friction = mu*mgcos(60)*x = 0.4*0.2*9.8*cos(60)*x = 0.392x
PE gained = mgh = mgxsin(60) = 0.2*9.8xsin(60) = 1.6974x
by energy conservation
7 = 1.6974x + 0.392x
x = 3.35 m
6. When they are at the same hieght, means 2 kg mass moved up by 0.5m, the 3 kg block came down by 0.5m
Gain in PE by 2kg block = 2*9.8*0.5 = 9.8J
Loss in PE by 3 kg block = 3*9.8(0.5) = 14.7 J
Net Energy gain = 14.7-9.8 = 4.9 J = 0.5mv^2
4.9*2/(3+2) = v^2
v = 1.4 m/s

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