A playground merry-go-round made in the shape of a solid disk, hasa diameter of

Question

A playground merry-go-round made in the shape of a solid disk, hasa diameter of 2.74 m and a mass of353.7 kg. Two children, each of mass30.2 kg, sit on opposite sides at the edgeof the platform. Approximate the children as point masses. (a) What torque is required to bring themerry-go-round from rest to 26 rpm in19.7 s? ___N · m

(b) If two other bigger children are going to push on themerry-go-round rim to produce this acceleration, with what forcemagnitude must each child push? ___N
(a) What torque is required to bring themerry-go-round from rest to 26 rpm in19.7 s? ___N · m

(b) If two other bigger children are going to push on themerry-go-round rim to produce this acceleration, with what forcemagnitude must each child push? ___N

Explanation / Answer

a) What torque is required to bring the merry-go-round fromrest to 26 rpm in 19.7 s? ___N · m
Since torque is given in terms of moment of inertia Iand acceleration as = I = (2 - 1)/t = [26 x 2 / 60 -0]/ 19.7 = 8.30 rad/s I= Id + I c1 +Ic2using parallel axis theoremfor   I c1 and  Ic2   as I c1 =mc1R2 + mc1R2 =2mc1R2 wehave I= 0.5mdR2 + mc1R2 + mc2R2
I= (0.5md + 2mc1 +2mc2)R2 I= ( 0.5x 353.7 + 2x30.2 + 2x30.2)2.742/4 I= 559 kg m2   = 559 x 8.30 = = 4,640 N m (b) If two other bigger children are going to push on themerry-go-round rim to produce this acceleration, with what forcemagnitude must each child push? ___N
F= /R F= 4,640 / (2.74/2) F= 3,348 N

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