Calculating Acceleration and Tensions in a Blocks and Pulley System

[DragonZero]

Homework Statement

In the system shown below, there is a block of mass M = 4.4 kg resting on a horizontal ledge. The coefficient of kinetic friction between the ledge and the block is 0.25. The block is attached to a string that passes over a pulley, and the other end of the string is attached to a hanging block of mass m = 2.1 kg. The pulley is a uniform disk of radius 8.4 cm and mass 0.62 kg. Find the acceleration of each block and the tensions in the segments of string between each block and the pulley.

Homework Equations

T - Mg(coefficient of kinetic friction) = Ma
mg - T = ma
a = g((m-M)/(M+m))

torque = inertia * alpha
alpha = linear acceleration / radius

The Attempt at a Solution

inertia = 0.5 * 0.62 * 0.084^2 + 0.62 * 0.084^2 = 0.00656

For the acceleration, I think the main equation I'll need to use is torque = inertia * (linear acceleration / radius), but I'm not sure how to find torque.

 

[omoplata]

Assume the string to have two tensions. One for the region between the pulley and the hanging block. One for the region between the pulley and the resting block.

 

[DragonZero]

So would that be:

T - Mg(coefficient of kinetic friction) = mg - T

 

[omoplata]

There is only one T term there. And did you take into account the moment of inertia of the pulley?

Assume tension $T_{1}$ for the region of the string between the hanging block and the pulley. Assume tension $T_{2}$ for the region of the string between the resting block and the pulley.

Use Newton's 2nd law for the two blocks, and an equation connecting angular acceleration, torque and moment of inertia for the pulley.

 

[cupid.callin]

the FBD will be like:

note that tensions are different
and also linear acceleration of blocks will be (angular acc of pulley)*(radius of pulley)Now wrote eqn's