# Tension and Acceleration with a Pulley and Two Masses

1. Jul 10, 2013

### rakeru

1. The problem statement, all variables and given/known data

If there is a mass on a frictionless table connected by a string to another mass hanging from a pulley off the side of the table, is the net force on the string zero? Is the force of tension equal on both sides if the system is accelerating? Would both objects accelerate equally?

2. Jul 10, 2013

### haruspex

3. Jul 10, 2013

### rakeru

I mean, I think it would be equal.. but I'm not sure. Apparently it would be zero if the string has negligible mass.

4. Jul 11, 2013

### projjal

If the string is light the net force on it is zero; or else it is accelerating and so there should be some force on it.If the pulley is also massless, the tension on both sides will be same.And obviously both the objects will have same acceleration,provided the string is rigid.

5. Jul 11, 2013

### haruspex

I would word that a little differently. If a section of the string has mass m and acceleration a then the net force on it is ma. If the string is massless then that must be 0.
Another possibility is that there may be friction in the pulley's axle. (We generally assume there is sufficient friction between the string and pulley to prevent slipping.) This would lead to a difference in tensions even if the pulley is massless.

6. Jul 12, 2013

### projjal

Yeah i missed that point.

7. Aug 23, 2013

### Vibhor

I do not understand the case when friction is present at the axle and the pulley is massless.

Writing torque equation,(T1-T2)R=Iα .But the R.H.S is zero as I=0.So,T1=T2 .

How is that there is difference in tensions,when the pulley is massless ?

Thanks!

8. Apr 28, 2014

### projjal

In the torque equation, there'll be torque due to the force of friction.