# Pulleys with Strings Having Mass

Suppose there is a pulley (a disc) of mass m1 and a string passes over the pulley with masses m2 and m3 hanging on both ends of the string with m3 > m2. I know that the acceleration should be (m3 - m2)g/(1/2m1 + m2 + m3) and I know how to get there.

However, since the pulley rotates and has mass, the tensions are different on the two ends of the string. That would mean that the string is not massless because there would be an infinite acceleration if the string was massless. However, the mass of the string appears nowhere in the final answer. Why is this so?

Bystander
Homework Helper
Gold Member
should be (m3 - m2)g/(1/2m1 + m2 + m3) and I know how to get there.
I(m1), since m1 is going to be rotating.
infinite acceleration if the string was massless.
The problem statement has attached masses to the ends of the string.

I don't think I made myself clear. An identical problem is here: http://physics.bu.edu/~duffy/semester1/c14_atwood2.html. My question is how we can assume the string is massless because it is clear that the tension of the two sides of the string is different (the pulley would not rotate if the tensions were the same.) Since the tensions are different, there is a net force somewhere on the string and that would yield infinite acceleration on the string if the string was massless.

Doc Al
Mentor
Since the tensions are different, there is a net force somewhere on the string
Why do you think that?

ehild
Homework Helper
Suppose there is a pulley (a disc) of mass m1 and a string passes over the pulley with masses m2 and m3 hanging on both ends of the string with m3 > m2. I know that the acceleration should be (m3 - m2)g/(1/2m1 + m2 + m3) and I know how to get there.

However, since the pulley rotates and has mass, the tensions are different on the two ends of the string. That would mean that the string is not massless because there would be an infinite acceleration if the string was massless. However, the mass of the string appears nowhere in the final answer. Why is this so?
The tensions are different in the two hanging parts of the string, but do not change along the length, if the string is massless. The tensions are the same at both ends of a string.