# Kinetic energy, force, rotation

## Homework Statement

A light, flexible rope is wrapped several times around a hollow cylinder with a weight of 49.0 N and a radius of 0.27 m. The cylinder is attached by spokes of a negligible moment of inertia to a fixed horizontal axle coincident with the axis of the cylinder; the cylinder is free to rotate without friction about this axle. The cylinder is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 4.95 m, at which point the end of the rope is moving at 6.25 m/s; the rope does not slip on the cylinder.

A)What is the change in kinetic energy of the hollow cylinder as a result of the rope having been pulled?

B) For the situation as described in the introduction, what is the value of P?

## Homework Equations

v=rw

k = 1/2mv2 + 1/2Iw2

w = omega

ki + ui + Work = kf + uf

## The Attempt at a Solution

i didnt know how to do part a so i just skipped to part B)

W = FD ----> W = P(4.95m)

W = kf

P(4.95m) = 1/2(5kg)(6.252) + 1/2(1/2(5kg)(.27m)2(6.25/.27)2)

P = 29.59 N

This is wrong though and i am not sure why. Also if i could get some help on part A that would be great.

Thank you :)

vela
Staff Emeritus
Homework Helper

## Homework Statement

A light, flexible rope is wrapped several times around a hollow cylinder with a weight of 49.0 N and a radius of 0.27 m. The cylinder is attached by spokes of a negligible moment of inertia to a fixed horizontal axle coincident with the axis of the cylinder; the cylinder is free to rotate without friction about this axle. The cylinder is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 4.95 m, at which point the end of the rope is moving at 6.25 m/s; the rope does not slip on the cylinder.

A)What is the change in kinetic energy of the hollow cylinder as a result of the rope having been pulled?

B) For the situation as described in the introduction, what is the value of P?

## Homework Equations

v=rw

k = 1/2mv2 + 1/2Iw2

w = omega

ki + ui + Work = kf + uf
In the equation

$$K=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2$$

what does $v$ stand for? Don't just say velocity. The velocity of what?

## The Attempt at a Solution

i didnt know how to do part a so i just skipped to part B)

W = FD ----> W = P(4.95m)

W = kf

P(4.95m) = 1/2(5kg)(6.252) + 1/2(1/2(5kg)(.27m)2(6.25/.27)2)

P = 29.59 N

This is wrong though and i am not sure why. Also if i could get some help on part A that would be great.

Thank you :)
Also, you're using the wrong moment of inertia. The key word is hollow.

V should be the velocity of the center of mass v_cm

i am not sure what moment of inertia to use then? would it be

I = mr^2

should i just be using K = 1/2Iw^2 instead of what i have?

thanks for the help :)

vela
Staff Emeritus
Homework Helper
V should be the velocity of the center of mass v_cm
Right. So what is the velocity of the cylinder's center of mass?
i am not sure what moment of inertia to use then? would it be

I = mr^2
Yes, all of the mass of the hollow cylinder is at a distance r away from the axis of rotation, so I=mr2.
should i just be using K = 1/2Iw^2 instead of what i have?

thanks for the help :)