Item 11 A 35-kg child stands on the edge of a 370-kg playground merry-go-round t

Question

Item 11 A 35-kg child stands on the edge of a 370-kg playground merry-go-round that is turning at the rate of 1 rev every 2.2 s. He then walks to the center of the platform. Part A If the radius of the platform is 1.5 m, what is its rotational speed once he arrives at the center? Assume that the platform is a uniform disk, and the child is ''point-like'', that is, his dimensions are so small compared to the platform size, that he can be considered to be a point-mass. Item 13 A frictionless pulley has the shape of a uniform solid disk of mass 2.10 kg and radius 10 cm. A 1.20 kg stone is attached to a very light wire that is wrapped around the rim of the pulley (the figure (Figure 1 ) ), and the system is released from rest. Part A How far must the stone fall so that the pulley has 4.50 J of kinetic energy? Part B What percent of the total kinetic energy does the pulley have? Enter the answer as a percent, not as a fraction. For instance, if the ratio is 0.75, enter this as 75.

Explanation / Answer

1) angular speed is w = 2 pi / 2.2 = 0.2893 rad/s

The angular momentum is

[(35) (1.5)^2 + (0.5)(370)(1.5)^2 ] (0.2893) = [ (0.5)(370)(1.5)^2 ] W

W= 0.344 rad/s

b)

The gravitational potenital energy should be equal to rotational kinetic energy

m g h - (1/2) m v^2 = 4.5 J

(1.2 )(9.8) h + (1/2) m v^2 = 4.5 J

h = (4.5)[ 2 m+ M / Mmg]

h = (4.5 ) (0.1822) = 0.82m

c)

Speed is V = 4 m gh / 2m + M = 8.571

Total energy is (1/2) (1.2)(8.571)^2 + 4.5 = 48.9 J

fraction of energy = 4.5 /48.9 = 9.3 %

K/Kt = 9.3

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