# Homework Help: Double atwood machine

1. Oct 26, 2014

### hitemup

1. The problem statement, all variables and given/known data

The double Atwood machine has frictionless, massless pulleys and cords. Determine the acceleration of masses mA,mB,mC, and the tensions in the cords.

2. Relevant equations

F=ma

3. The attempt at a solution

First I looked down the bottom section. Assuming mB> mA

mB*g - FTA = mB*a
FTA - mA*g = mA*a

I got the following from the equations above, so I think this must be the acceleration for the masses A and B.

aA,B = g* (mB - mA)/(mB + mA)

Now Assuming mC*g>FTC

mC*g - FTC = mC*a

This is where I choked. What should be the second equation for this pulley? FTC = 2FTA?
If I were to find FTA in terms of mA, mB, and aA,B, would that be enough for aC's equation?

2. Oct 26, 2014

### ehild

A and B hang from the rope around the hanging pulley. Their accelerations are equal with respect to the pulley, but not with respect to the ground.
I suggest to write the acceleration of C first. It will be the same (with opposite sign) as the acceleration of the hanging pulley. It has no mass, so 2FTA=FTC.

3. Oct 26, 2014

### hitemup

What confuses me here is that there are too many possibilities, especially for A and B.

To write correct equations with respect to ground, I think I should consider the effect of FTC on A and B like you said. But what are their directions?
I mean if we assume C is going down, no problem. But either A or B could be going down or up in this situation. Should I just assume their directions too?

4. Oct 26, 2014

### ehild

Assume the directions, and solve.

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