Tension Equal in Pulley System w/ 2 Strings

[fk378]

This is a general question...

Given a pulley system that consists of one pulley and 2 strings--each with a mass hanging from it. One mass is 3kg, the other is 4kg. In class we concluded that the tension on each string was equal--why?

 

[Epsillon]

Arent they attached to the same string?

Can you have two different tension forces on one string?
(Hint)

 

[fk378]

Oh I see. What if you had one string along 2 pulleys? (So then the string is going upwards for 2 parts of the string, and downwards for 1 part of the string). Then is the tension along the whole string just T, or for 2 parts it is T, and the other part it is -T?

 

[Epsillon]

AS long as the same string is being used the tension force is the same