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 18 rpm, in 13.0 s. Assume the merry-go-round is a uniform disk of radius 2.7 m; and has a mass of 800 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge?

Answer 1

Answer:

F = 176.175 N

Explanation:

given,  

radius of merry - go - round = 2.7 m

mass of the disk = 800 kg  

speed of the merry- go-round = 18 rpm  

                                                 = 18 $\dfrac{2\pi }{60}$

                                                 = 1.88 rad/s

time = 13 s

mass of two children = 25 kg  

ω = ω₀ + α t

1.88 = 0 + α(13)

α = 0.145 rad/s²

we know

τ = I α

so,

$I = \dfrac{1}{2}MR^2+ 2 MR^2$  

$I = \dfrac{1}{2}\times 800 \times 2.7^2+ 2\times 25\times 2.7^2$

$I = 3280.5 kg.m^2$  

τ = I α

τ = 3280.5 x 0.145

τ = 475.67 N m

τ = F x r

475.67 = F x 2.7

F = 176.175 N