A student of mass m = 50 kg wants to measure the mass of a playground merry-go-r

Question

A student of mass m = 50 kg wants to measure the mass of a playground merry-go-round, which consists of a solid metal disk of radius R = 1.5 m that is mounted in a horizontal position on a low-friction axle. She tries an experiment: She runs with speed v = 7.1 m/s toward the outer rim of the merry-go-round and jumps on to the outer rim, as shown in the figure. The merry-go-round is initially at rest before the student jumps on and rotates at 1.3 rad/s immediately after she jumps on. You may assume that the student's mass is concentrated at a point. (a) What is the mass of the merry-go-round? 314 kg Incorrect: Your answer is incorrect. (b) If it takes 39 s for the merry-go-round to come to a stop after the student has jumped on, what is the average torque due to friction in the axle? (c) How many times does the merry-go-round rotate before it stops, assuming that the torque due to friction is constant? rev

Explanation / Answer

(a)
M = 2mv/(wr)..........................(conservation of angular momentum)
M = 2*50 * 7.5 / 1.3*1.5
M = 384.6 kg

(b)
Torque, T = I*?
? = w/t = 1.3 / 39
? = 0.0333 rad/sec

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