Question

A playground merry-go-round has radius 2.40m and moment of inertia 2100kg?m2 about a vertical axle through...

A playground merry-go-round has radius 2.40m and moment of inertia 2100kg?m2 about a vertical axle through its center, and it turns with negligible friction.

A child applies an 22.5N force tangentially to the edge of the merry-go-round for 19.0s . If the merry-go-round is initially at rest, what is its angular speed after this 19.0s interval?

How much work did the child do on the merry-go-round?

What is the average power supplied by the child?

Homework Answers

Answer #1

Note that

Torque = F r

Thus, as F = 22.5 N, r = 2.40 m,

Torque = 54.0 m*N

As

Torque = I (alpha)

--> alpha = Torque / I

where I = moment of inertia = 2100 kg*m^2

alpha = angular acceleration

Thus,

alpha = 0.0257 rad/s^2


As

w = wo + alpha * t

and

wo = initial angular velocity = 0 rad/s
w = final angular velocity
t = time = 19.0 s

Then

w = 0.4886 rad/s   [ANSWER, PART A, angular speed]

******************

Note that

Work = Torque (delta theta)

Here,

delta theta = wo t + 1/2 (alpha) t^2

Thus,

delta theta = 4.64 rad

Thus,

Work = 250.6 J   [ANSWER, PART B]

********************

Note that

Power = Work/time

= 13.2 W   [ANSWER, PART C]

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A playground merry-go-round of radius R = 1.60 m has a moment of inertia I =...
A playground merry-go-round of radius R = 1.60 m has a moment of inertia I = 255 kg·m2 and is rotating at 11.0 rev/min about a frictionless vertical axle. Facing the axle, a 25.0 kg child hops onto the merry-go-round and manages to sit down on its edge. What is the new angular speed of the merry-go-round?​
A playground merry-go-round of radius 1.9 m has a moment of inertia 139 kg.m2 and is...
A playground merry-go-round of radius 1.9 m has a moment of inertia 139 kg.m2 and is rotating at 9 rev/min about a frictionless vertical axle. Facing the axle, a 27 kg child hops onto the merry-go-round, and manages to sit down on the edge. What is the new angular speed of the merry-go-round?
A merry-go-round has a radius of 3.12m and a moment of inertia of 2800kg m2 about...
A merry-go-round has a radius of 3.12m and a moment of inertia of 2800kg m2 about the vertical axis through the center. It hsd wd40 so it turns without friction. A child applied a tangential force of 14 N for 13 s. The merry-go-round starts at rest. What is the work done by the child during the 13s?
A playground merry-go-round of radius ? = 2.0 m has a moment of inertia ? =...
A playground merry-go-round of radius ? = 2.0 m has a moment of inertia ? = 250 kg ⋅ m^2 is rotating at 15 rpm about a frictionless, vertical axle. Facing the axle, a 25-kg child hops onto the merry-goround and manages to sit down on the edge. (a) (10 pts) What is the total angular momentum of the ‘merry-go-round-child’ system before and after the child hops on the the merry-go-round? (b) (10 pts) What is the new angular speed,...
A 24.5kg child is standing on the outer edge of the horizontal merry go round that has a moment of inertia 989 kg*m^2 about a vertical axis through its center and a radius of 2.40m.
A 24.5kg child is standing on the outer edge of the horizontal merry go round that has a moment of inertia 989 kg*m^2 about a vertical axis through its center and a radius of 2.40m. the entire system including the child is initially rotating at 0.180 rev/s . find the angular velocity if the child moves to a new position 1.10m from the center of the merry go round.
A playground merry-go-round of radius R = 2.6 m has a moment of inertia of I...
A playground merry-go-round of radius R = 2.6 m has a moment of inertia of I = 200 kg*m^2. and is rotating at a rate of ω = 11 rev/min around a frictionless vertical axis. Facing the axle, a 39 kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round (in rev/min)
A merry-go-round with a moment of inertia equal to 1250kg?m2 and a radius of 2.5 m...
A merry-go-round with a moment of inertia equal to 1250kg?m2 and a radius of 2.5 m rotates with negligible friction at 1.70 rad/s. A child initially standing still next to the merry-go-round jumps onto the edge of the platform straight toward the axis of rotation, causing the platform to slow to 1.35 rad/s.What is her mass?
A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely...
A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely with an angular speed of 3.0 rad/s. Two people, each having a mass of 60 kg are standing right outside the edge of the merry-go-round. One person radially steps on the edge merry-go-round with negligible speed and the angular speed changes to ?1. A few seconds later, the second person radially steps on the merry-go-round with negligible speed but at distance of 4.0 m...
A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely...
A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely with an angular speed of 3.0 rad/s. Two people, each having a mass of 60 kg are standing right outside the edge of the merry-go-round. One person radially steps on the edge merry-go-round with negligible speed and the angular speed changes to ?1. A few seconds later, the second person radially steps on the merry-go-round with negligible speed but at distance of 4.0 m...
A playground merry-go-round has a radius of 1.5 m and mass of 200 kg, and turns...
A playground merry-go-round has a radius of 1.5 m and mass of 200 kg, and turns with negligible friction about a vertical axle through its center. A child applies a constant force that produces a torque of 50 N·m to the merry-go-round. Its moment of inertia is given by I = ½MR2. The next four questions have to do with this rotating merry-go-round. Determine the angular acceleration of the merry-go-round in rad/s2. a. 0.047 rad/s2 b. 0.222 rad/s2 c. 0.965...