# Tension and Acceleration with a Pulley and Two Masses

## Homework Statement

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?

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

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.

haruspex
Homework Helper
Gold Member
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.
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.
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.
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.

Another possibility is that there may be friction in the pulley's axle
Yeah i missed that point.

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.
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!

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