- #1

PhizKid

- 477

- 1

## Homework Statement

A block of mass M is attached to a rope of mass m and length l, and the rope is being pulled with a force F on a frictionless surface and there is no gravity. Find the tension in the rope.

## Homework Equations

F = ma

## The Attempt at a Solution

A friend has been trying to help me with this, but I don't understand his explanations. As he explained it, I need to take a small segment of the rope to find a differential equation to integrate. I don't really see the logic or reasoning behind this, but I guess if I want to integrate an equation, the equation has to be a differential and I need to somehow obtain that equation with the information I'm given. I can't use a point on the rope because a derivative is a slope and you can't find a slope with a point, so I need to take a very small segment of the rope.

So here is my force diagram of the forces acting on the rope:

So we have: [tex]T_M(x + \Delta x) - T_F(x + \Delta x) = \Delta m \cdot a[/tex]

There are 2 different tensions so I'm not sure how to combine them into a single tension..