# Calculate the initial acceleration of this pulley system

#### Phantoful

1. The problem statement, all variables and given/known data 2. Relevant equations
W=mg
F=ma
3. The attempt at a solution
I'm not sure how I should be answering this problem, and the diagram itself looks odd. I was thinking about how it would work in real life, since the biggest pulley is attached to the leftmost pulley, by the same string that m1 is on, wouldn't acceleration all be zero? Since the biggest pulley is attached to the roof...

Also, looking at it from FBD, The masses seem simple (m1*g, T1 and m2*g, T2) but when I try to do the pulleys, it's like a recursion happens because the whole system loops.

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#### BvU

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the whole system loops
not the whole sytem. Only the wire and it has a fixed length!

Sort out equations and knowns/unknowns....

#### BvU

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Did you notice the first item in the template also asks for 'all variables and given/known data'?

Make free-body diagrams

#### haruspex

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(m1*g, T1 and m2*g, T2)
What do you mean by that? Are you suggesting that there are two different tensions, that one equals m1g and the other equals m2g? None of those statements are true.

#### Chestermiller

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This is a very tricky problem. The force balance on the left massless pulley, has a force of T upwards and 2T downwards. So, for equilibrium, the tension in the rope must be zero.

Last edited:

#### tnich

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The force balance on the left massless pulley, has a force of T upwards and 2T downwards.
Not only that, but a net force acting on a massless pulley doesn't get you any closer to determining its acceleration. It seems like force balance equations will not work for this problem.
Here is another way to look at it. Since the pulley on the left is massless, it will move either up or down to compensate for the motions of $m_1$ and $m_2$ without any opposing or assisting force at all. Are the motions of the two masses affected by any force other than gravity?

#### Chestermiller

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Not only that, but a net force acting on a massless pulley doesn't get you any closer to determining its acceleration. It seems like force balance equations will not work for this problem.
Here is another way to look at it. Since the pulley on the left is massless, it will move either up or down to compensate for the motions of $m_1$ and $m_2$ without any opposing or assisting force at all. Are the motions of the two masses affected by any force other than gravity?
no. If the tension in the rope is zero, the acceleration of each mass is g.

#### tnich

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no. If the tension in the rope is zero, the acceleration of each mass is g.
Sounds like you have just solved the problem.

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