# Effect of friction on the tension in a pulley

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1. Nov 26, 2014

### rasen58

I measure the tension in a pulley system with two masses (one smaller, one larger) where I pull the small mass down and let it go so that the system accelerates in the direction of the larger mass. This is without friction.

Then, I try to consider friction. Does the tension in the string change?

How I tried to think about it was on either side of the pulley. So on the side with the smaller mass, which goes upward after letting go, if there is friction, then the friction force points downward and adds with the gravitational force. So therefore, I think that the tension force pointing upwards has to increase as well to balance the new friction force pointing downward.
But if you look on the other side, with the large mass, you see that it is going down. So the gravitational force points down and the tension force points up. The new friction force also points up, but because the gravitational force can't change, I think that the tension force would have to decrease to match the increase in friction force upwards, so that the net force stays the same.

But the tension can't increase on one side and decrease on the other, so I'm confused. Did I think about it in the wrong way?

2. Nov 26, 2014

### Staff: Mentor

Does the string slide over the surface of the pulley? Does the pulley have mass? Is there friction in the bearings of the pulley?

Chet

3. Nov 26, 2014

### rasen58

I would think the string slides over the surface of the pulley?
Massless pulley
There is friction everywhere on the pulley that there can be friction, I don't think it would matter where in order to analyze the problem

4. Nov 27, 2014

### A.T.

Really? Usually a pulley is meant to rotate, so the string doesn't have to slide.
If you want to analyze it quantitatively, then it does matter if the friction force is at the pulley axle (no sliding) or the string directly (sliding).

5. Nov 27, 2014

### rasen58

Oh right, well the pulley actually does rotate, my fault.

Then I guess the friction is at the pulley axl

6. Nov 27, 2014

### Staff: Mentor

Why not? If you're assuming that the tensions on the two sides have to be equal, this is true only if there is no friction in the pulley and the pulley is massless. To see this, apply the rotational form of Newton's Second Law to the pulley: $$\sum \tau = I \alpha$$

Last edited: Nov 27, 2014
7. Nov 27, 2014

### rasen58

@jtbell So I was right? It actually does increase on one and decrease on the other? Thanks