(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

P is a pulley with neglectable mass which is being affected by an external force F. Determine the accelerations of P, m and M.

I've got a picture, but it goes something like this:

There's a pulley and from it (on each side) there are two masses hanging. On the left is m and on the right is M. The force F is from the centre of the pulley and is pointing straight up. (I hope you understand what I mean.)

And it's also assumed that the rope is massless.

2. Relevant equations

F = ma

3. The attempt at a solution

There are only forces in the y-direction and I'm using up as the positive axis.

m: T - mg = ma_{m}

M: T - Mg = Ma_{M}

And I know that since the pulley is massless (or can be considered as such) the forces on it need to balance out or it'd be accelerating with infinite acceleration. The forces acting on it are F and 2T, tension from each of the sides.

That means that T = ½F and:

½F - mg = ma_{m}

a_{m}= ½(F/m) - g

and doing the same for M I get:

a_{M}= ½(F/M) - g

This is stated as correct in my book. My problem is the acceleration of the pulley - I think I'm not seeing something.

Because for some reason (this I can see from the answer that is supposed to be correct) a_{P}= ½a_{m}+ ½a_{M}

Why exactly is that? Is it because the tension from the rope is half that of the force? I'm a bit confused and I don't want to guess a reason, because that's not going to be so good if I'm not right..

Ah, I'll be thankful for any help :)

- Hanna

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# Homework Help: Acceleration of two masses and a pulley

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