Question

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.

Answer 1

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.

Answer 2

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

Answer 3

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)]

Answer 4

Sorry, but this is still confusing there is no radius given besides the info I have provided earlier!