A dad pushes tangentially on a small hand-driven merry-go- round and is able to

Question

A dad pushes tangentially on a small hand-driven merry-go- round and is able to accelerate it from rest to a frequency of 17 rpm in 11.0 s .Assume the merry-go-round is a uniform disk of radius 2.9 m and has a mass of 770 kg and two children (each with a mass of 21 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. Express your answer using two significant figures. What force is required at the edge? Express your answer using two significant figures.

Explanation / Answer

(A) wi = 0

wf = 17 rpm = 17 x 2pi rad / 60 sec = 1.78 rad/s

wf = wi + alpha t

1.78 = 0 + 11 alpha

alpha = 0.162 rad/s^2

I = ( M R^2 / 2) + (2 m R^2)

= (770 x 2.9^2 / 2) + (2 x 21 x 2.9^2)

= 3591.07 kg m^2

Net torque = I alpha = 3591.07 x 0.162 = 581.1 N m .........Ans

(B) torque = r F

581.1 = (2.9) (F)

F = 200.4 N

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