Calculating Acceleration of a Falling Bucket Attached to a Pulley System

[the whizz]

Homework Statement

1.A bucket of mass m is connected by a rope to a frictionless pulley of mass M. Use Newton’s 2nd law for torques and Newton’s 2nd law to find an equation for the acceleration of the bucket if it is released from rest and allowed to fall.

Homework Equations

The Attempt at a Solution

so i need we need to find Normal force in both direction. i know that

sum of Force in X direction is that o= N- Tcos(theta)

From the problem i am not sure how to find the Tension and where the normal force in the Y direction would come from.

 

[LowlyPion]

Isn't what you have is a F = m*g being retarded by an I*a/R where I is the moment of inertia?

Apparently the frictionless part refers to the rotation of the pulley and not the friction of the rope on the pulley because if the rope is free to slip, what torque would there be?

 

[djeitnstine]

Take the tension T to be the reactant force

Hint...it is 90 degrees to the axis of rotation.

 

[rl.bhat]

Forces acting on the bucket are T and mg. Since bucket is moving downwards, net force acting on it is
ma = mg - T...(1)
The tangential force actin on pulley is T.
Therefore The torque on pulley is T*R = I* alpha = I*Ra ...(2)
Substituting the expression for I and solving eq. 1 and 2 , find the equation for the acceleration.