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 = 6.6 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?

1676 kg my answer is incorrect.

238 kg is correct

Explanation / Answer

Note: My calculations maybe off because of significant digits The mass of the student m = 50kg the linear speed of the student v = 6.6m/s the radius of the disk r = 1.5m the angular speed of the platform and student ? = 1.3 rad/s from law of conservation of angular momentum I1?1 = I2?2 mR^2(v/R) = ( 1/2MR^2)(?2) 2m(v/R)/ ?^2 = M therefore the mass M = 2(50)(6.6/1.5) / 1.3^2 = 260.355 kg

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