Calculating the tension of a rope that is attached to a block

A uniform rope of mass m and length l is attached to a block of mass M. The rope is pulled with force, F. Find the tension at distance x from the end of the rope. Neglect gravity.

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Consider a tiny differential portion of the rope of length dx, its mass is given by (m dx/l) and the forces acting on it are the tension of the nearby points on the rope, that is:
<br>T(x)-T(x+dx)
<br>Using Newton's 2nd law and ...

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