Constraint relation in a pulley spring system

[Shivang kohlii]

Homework Statement

How to apply constraints in the system to get a relationship between the displacements of block of mass m and pulley of mass M.?

Homework Equations

∑T.a= 0

The Attempt at a Solution

Assuming tension in both strings to be T .
-T × a1 ( for the block) + 2T × a2 ( for the strings attached to sides of pulley) + for the string attached from the centre = 0

I can't understand how to proceed

 

[Chestermiller]

The place to start on a pulley problem is this the kinematics, not the dynamics. If the center of the pulley moves downward a distance y, and the string is of constant length, how much does the mass move downward relative to the center of the pulley? Relative to the table?

 

[haruspex]

Assuming tension in both strings to be T .

If that were true, why would the pulley rotate?

 

[Shivang kohlii]

If that were true, why would the pulley rotate?

Why should it rotate ? It's fixed to a table so the tension in both strings should be same

 

[Shivang kohlii]

The place to start on a pulley problem is this the kinematics, not the dynamics. If the center of the pulley moves downward a distance y, and the string is of constant length, how much does the mass move downward relative to the center of the pulley? Relative to the table?

That's the issue .. I don't know how to establish a relation..

 

[haruspex]

Why should it rotate ? It's fixed to a table so the tension in both strings should be same

The pulley doesn't know what the string is attached to. This is not a massless pulley. If the pulley has accelerating rotation, some net torque must cause it. Where is that coming from?

 

[Chestermiller]

That's the issue .. I don't know how to establish a relation..

Establishing the kinematic relation is a math problem. The length of the rope is constant. This is the constraint you need to use.