# Why is tension in a rope the same at every point?

So, I had this lecture where it was explained that if the pulley is friction-less, then the tension on any point of the rope is going to be same.

I can understand the friction-less part, as pulley is not applying any resistive forces that change the magnitude of the tension force.

But even then, how can the force of tension be same at any point on the rope?

## 1 Answer

If the tension changed throughout the rope, there would be a piece of the rope experiencing different tension forces on its ends, and hence experiencing a net force.

Newton's second law says that $F = m a$, and the acceleration of the rope is the same as the acceleration of the blocks. Since the rope is light, that means the net force on each piece of the rope has to be very small. That means the change in the tension must be very small. Usually the rope is so light compared to the blocks that we can neglect the change in tension along it entirely, so the tension is the same at every point.

• so we treat the rope like a system? – Daksh Miglani Sep 1 '18 at 5:32
• @DakshMiglani Yes, I am applying $F=ma$ to the system of the rope. – knzhou Sep 1 '18 at 5:33