Question

A uniform rope of length L and mass M lying on a smooth table is pulled by a constant force F. What is the tension in the rope at a distance l from the end where the force is applied?

Answer 1

Acceleration of rope a = \(\frac FM\)

Now to find tension at point C, a distance \(\ell\) from point B, we can write equation of motion of any one part (AC or CB), both moving with acceleration a.

Equation of motion of part AC is

Answer 2

The tension in the rope at a distance l from the end is F(1-l/L).