A 50.0 kg child is on a 200 kg merry-go-round with a radius of 1.50 m. The child

Question

A 50.0 kg child is on a 200 kg merry-go-round with a radius of 1.50 m. The child starts at .5m from the center and moves to the edge. The child's parent accelerates the merry-go-round from the rest at .75 rad/s^2 to a speed of 1.5 rad/s.

a) How long did the parent push the merry-go-round?

b) how much force is required to hold the child when at .5 m from the center? (This centripetal force could be from friction, holding on, or both)

c) Determine the kinetic energy of the system (child and merry0go0round) when moving at 1.5 rad/s.

d) Determine the final angular velocity when the child is at the edge (1.50 m from the center).

Explanation / Answer

angular acceleration a = 0.75 rad/s^2

initial velocity wi = 0 rad/s

final velocity wf = 1.5 rad/s

wf = wi + at

t = wf - wi / a

t = 1.5 / 0.75

t = 2 s

b)

force required = cenrtripetal force = mw^2r = 50 x 1.5 x 1.5 x 0.5 = 56.25 N

c)

KE = 0.5 x I x w^2

I of the merry go round = mr^2 = 200 x 1.5^2 = 450 kgm^2

I of the boy = 0.5 mr^2 = 0.5 x 50 x 1.5 x 1.5 = 56.25 kgm^2

w = 1.5 rad/s

KE = 0.5 x (450 + 56.25) x 1.5^2 = 569.53 J

d)

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