What will be the acceleration of an Atwood machine with a frictional pulley with the following mass values?

Question

What will be the acceleration of an Atwood machine with a frictional pulley with the following mass values?

Pulley: 3.6 kg

Mass A: 1.4 kg

Mass B: 4.1 kg

Answer 1

Because there is friction at the pulley, you know that there are T_A and T_B on both sides of the pulley. Unfortunately, there is not enough information to do this problem: You need to know the friction at the pulley or the moment of inertia of the pulley or the mass and it's shape (disk or ring). The normal way to do this problem is to do force balances for MA, for MB, and around the pulley. If you sum these equations, the tensions drop out and you can solve for the acceleration. (Since you give a mass for the pulley, it is unlikely to be frictional, so much as having a moment of inertia.

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