A student of mass m = 50 kg wants to measure the mass of a playground merry-go-r
ID: 1699440 • Letter: A
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.
Explanation / Answer
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
I11 = I22
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
(b) The time taken to comes to rest t = 39s
from rotational dynamics
f = i + 2t
then the angular acceleration
= - i/2 = - (1.3)/2(39)
= - 0.0167 rad/s^2
therefore the torque
= I = (1/2 MR^2)
= (0.5)(260.355)(1.5)^2 (0.0167)
= 4.89 N
(c) from rotational dynamics
f^2 = i^2 + 2
therefore = -i^2 / -2
= (1.3)^2 /2(0.0167)
= 50.6 rad or 8.05 rev
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