Posted by **Priyanka** on Sunday, March 25, 2012 at 2:18am.

A bucket of water with a mass of 4.0 kg is attached to a rope that is wound around a cylinder. The cylinder has a mass of 8.0 kg and is mounted horizontally on frictionless bearings. The bucket is released from rest.

(a) Find its speed after it has fallen through a distance of 0.90 m?

(b) What is the tension in the rope?

(c) What is the acceleration of the bucket?

m/s^2

Sorry but I have no idea how to do this, so please help! Thank you.

- Physics -
**Damon**, Sunday, March 25, 2012 at 7:38am
Is the cylinder solid and what is its radius? We need to know its moment of inertia if we are to find its angular acceleration and therefore the tension in the line.

- Physics -
**bobpursley**, Sunday, March 25, 2012 at 7:39am
you have a tension on the rope, twirling a cylinder. THe tension produces torque, which moves the cylinder.and , it is the cylinder which retards the bucket mass.

bucketweight*radius=MomentInertia*angularacceeration.

moment of inertia for a cylinder. Look it up.

so folve for angular acceleartion from the above.

final speed?

speed=wf*r=I*angacceleration

tension? mg-m(angularacc*r)

acceleration?

m*r*angacceleration

- Physics -
**Damon**, Sunday, March 25, 2012 at 7:45am
Assume you can calculate I

alpha = angular acceleration

T r = I alpha

alpha = T r/I

a = alpha r = T r^2/I

so

T = a I/r^2

then the mass

m a = mg-T

m a = m g - (I/r^2)a

a [ m+(I/r^2)] = m g

a = m g /[ m+(I/r^2)]

- Physics -
**Priyanka**, Sunday, March 25, 2012 at 2:06pm
Sorry, but this is still confusing there is no radius given besides the info I have provided earlier!

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