Mechanics - massive pulley, Atwood machine or similar

[iloveannaw]

hi,

why does a massive pulley cause different tensions in a length of cable? I've looked for answers but got only that "the pulley needs to be lifted". Couldn't really picture it. Some maths would be nice

cheers!

 

[rcgldr]

It would seem that differences in tension would require friction in the wheels in a constant velocity situation. You could also have differences in tension during periods of jerk where the rate of force change travels as the speed of sound through the cable.

In the case of acceleration, imagine that the cable is a single length of cable in space, and being pulled at one end to accelerate it. The amount of tension will be highest at the pulled end and lowest at the free end. If you ignore the mass of the cable, then this effect does not exist.