# 4 Pulleys, 2 Masses

1. Oct 27, 2009

### sjeddie

This isnt a hw question, I just thought of it but don't know how to model the situation
Given a pulley system like this
http://img101.imageshack.us/img101/2106/pulleys.png [Broken]
suppose the string is massless and the pulleys are massless and frictionless.
say m2 is greater than m1, each having 2*tension force pulling up, they will have different accelerations since f=ma?
But since the length of the string is conserved, shouldnt they both be moving up at the same speed, hence their acceleration should be the same?

I am very confused. Help please!

Last edited by a moderator: May 4, 2017
2. Oct 27, 2009

### Gear300

Not necessarily. For there to be a net movement of a rope/wire, there needs to be a net tensional force towards one end of the rope. The rope over a pulley is not going to move if one side doesn't have a greater tension. So for the 2nd pulley from the right, in order for the m2 to move up, the tension of the rope to the left of the pulley has to be greater than the right. Because of the possible of tensional imbalances, there is a possible situation for m1 to accelerate faster than m2.

3. Oct 27, 2009

### sjeddie

But if the string is massless, does that mean the tension will be the same everywhere, and the 2 masses will have the same acceleration?

4. Oct 27, 2009

### Gear300

Well...its been a while since I've done this...but even in the case of constant tension the 2 masses would experience a different acceleration --- F/m1 > F/m2 for a constant force F.