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

In the system shown in the figure (see attachment), the pulleys on the left and right are fixed, but the pulley in the center can move to the left or right. The two masses are identical. Show that the mass on the left will have an upward acceleration equal to g/5. Assume all the ropes and pulleys are massless and frictionless.

2. Relevant equations

F=ma

3. The attempt at a solution

I will call the left rope's tension T1 and the right rope's tension T2. The left weight will be called "a" and the right weight will be called "b".

Net force on a = T1 - mg

Net force on b = T2 - mg

acceleration of a = T1/m - g

acceleration of b = T2/m - g

Forces on middle pulley = T2*2 - T1

I have approached this problem from many angles and I just can't come up with an equation that uses both tensions because the middle pulley being massless makes it impossible to find an acceleration for it.

Since F=ma, when mass is 1/infinity, acceleration becomes infinity. So I can't find the acceleration of the middle pulley that way.

Furthermore, despite every other approach I've used, I just can't get "g/5" for the left weight's acceleration.

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# Homework Help: Pulley system with a weight's acceleration of g/5

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