Acceleration of Two Blocks Connected by a Pulley on a Frictionless Ramp

[I_Auditor]

Homework Statement

Two blocks are of the same mass M. One lies on a frictionless ramp with slope θ, while the other one, connected by a rope, hangs by a pulley with a moment of inertia of I and a radius of r. Find the acceleration of the two blocks.

I don't have an actual picture, but this one might help:

Assuming m=M and that the pulley has a moment of inertia = I and a radius = r

Homework Equations

F = ma
Torque = F_tangential * r
Tension = Mg(1-sinθ)
2Ma should (?) be the total force on the blocks.

The Attempt at a Solution

I drew an FBD for the masses and got Mg(1-sinθ), but I'm unsure as to where I am supposed to go after this. I assumed that torque factored in, but I'm shaky on that aspect of the problem.

The answer given was (Mg(1-sinθ))/(2M-(I/r²)).

 

[BvU]

Hello I_A,

You sense there is more to this, but can't pinpoint it, is my impression.

I drew an FBD for the masses and got Mg(1-sinθ), but I'm unsure as to where I am supposed to go after this. I assumed that torque factored in, but I'm shaky on that aspect of the problem.

Did you draw one for each of the two ? Draw something equivalent for the pulley too.
You may assume that the rope does not slip on the pulley.

From the m diagram you should conclude that Tension $\ne$ Mg(1-sinθ) on the left side of the pulley.
From the pulley diagram you should conclude that the Tension on the left side of the pulley is not equal to the Tension on the right side of the pulley

By the time you have digested all that, you are well under way towards the book solution. Good luck !