# Why does every cable have 2 different tensions?

## Homework Statement

I was recently introduced to the concept of non-massless cables. I am used to solving problems where the cable is massless, and therefore tension on both ends of the cable are the same.

However, my TA mentioned that this is only true in 3 instances.
1. If the cable is massless.
2. If there is no acceleration on the cables (that is Fnet=0)
3. (Actually a special case of 2) When the cable is in free-fall.

The reason for this is never explained however. When I was doing a problem, with a cable in between two blocks, I initially tried to make tensions on both ends of the cable to be the same. Yet, I was told this was incorrect, because the cable has mass.

Can someone clarify the reason why cables always have two different tensions, even massless ones (where t1=t2)?

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Chestermiller
Mentor
A cable with mass doesn't just have two different tensions. The tension in the cable varies with location along the entire cable, in order for each small section of the cable to be accelerated. Draw a free body diagram on a small section of cable and use Newton's second law to predict how the tension changes with position if the mass per unit length of the cable is ρ.

PhanthomJay