# Atwood's Machine, massive pulley and upwards force acting upon it.

1. Feb 19, 2013

### DavidDante

1. The problem statement, all variables and given/known data
The usual configuration of an Atwood's Machine.
Two masses: m1, m2
Accelerations (unknown): a1, a2, ap (Pulley)
Rope Tension: T (Unknown)
BUT:
Massive pulley: mp
Upwards force acting on pulley (i.e the pulley is not in equilibrium): F

NOTE: Consider that all the pulley's mass in concentrated at the center of the pulley, so as not to consider the moment of inertia. (Is this ok?)

Question: Find the tension T, and the accelerations a1, a2.

2. Relevant equations
Newton's Second Law

3. The attempt at a solution
So this is what I tried:
Analyzing the pulley.
F - 2T - mp . g = mp . ap............................................(I)

Analyzing the whole System as a unit:
F - (mp + m1 + m2) . g = (mp + m1 + m2) . ap.............(II)

Analyzing m1:
T - m1 . g = m1 . a1...................................................(III)

From (II) I derived ap in terms of known constants, then I replaced ap (in terms of the constants) in (I) and I found T in terms of known constants. Finally I replaced the equation for T in (III).

So this is what I've got. Did I miss anything? Any feedback would be greatly appreciated.

Thanks-

2. Feb 20, 2013

### Simon Bridge

That is only OK if the operation of the machine means that the pulley does not rotate.

The approach you want is to draw three free-body diagrams, one for each mass and another for the pulley. You need to relate the tensions to the torques on the pulley.