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 15 rpm in 11.0 s . Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 560 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge.

Part A Calculate the torque required to produce the acceleration, neglecting frictional torque. Express your answer to two significant figures and include the appropriate units. τ τ = SubmitPrevious AnswersRequest Answer Incorrect; Try Again; 4 attempts remaining Part B What force is required at the edge?

Answer 1

Time period = T = 11 sec

Initial angular speed of the merry-go-round = ₁ = 0 rad/s

Rotational speed of the merry-go-round after 11 sec = N₂ = 15 rpm

Angular speed of the merry-go-round after 11 sec = ₂

₂ = 1.571 rad/s

Angular acceleration of the merry-go-round =

₂ = ₁ + T

1.571 = 0 + (11)

= 0.1428 rad/s²

Mass of the merry-go-round = M = 560 kg

Radius of the merry-go-round = R = 2.5 m

Moment of inertia of the merry-go-round = I

I = MR²/2

I = (560)(2.5)²/2

I = 1750 kg.m²

Mass of each child = m = 25 kg

Number of children = n = 2

The children sit on the edge of the merry-go-round therefore the children are at a distance equal to the radius from the center.

Moment of inertia of the system = I₀

I₀ = I + nmR²

I₀ = 1750 + (2)(25)(2.5)²

I₀ = 2062.5 kg.m²

Torque applied by the dad =

I₀ =

(2062.5)(0.1428) =

= 294.525 N.m

Force required at the edge = F

= FR

294.525 = F(2.5)

F = 117.81 N

Rounding off the answers to two significant figures,

= 294.525 N.m

= 2.9 x 10² N.m

F = 117.81 N

F = 1.2 x 10² N

A) Torque required to produce the acceleration = 2.9 x 10² N.m

B) Force required at the edge = 1.2 x 10² N