(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. A horizontal force F is applied to one end of the rope. (a) Show that the rope must sag, even if only by an imperceptible amount. Then, assuming that the sag is negligible, find (b) the acceleration of rope and block, (c) the force on the block from the rope, and (d) the tension in the rope at its midpoint.

2. Relevant equations

F=ma

3. The attempt at a solution

For (a), it is because the rope has mass so gravity acts on it. Since no other vertical force acts on the rope, it's net force is downwards and therefore must sag.

For (b): From force = mass * acceleration:

[tex] a = \dfrac{F}{m+M} [/tex]

For (c), the pull of the rope is the only force acting on the block. It is also accelerating with the block:

[tex] F = M\cdot a = \dfrac{M\cdot F}{m+M}[/tex]

So far, everything makes sense to me. However, I am not sure how to approach part (d) because this is the first problem where the rope has mass, so I don't know how to deal with it. Can anyone help?

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# Homework Help: Force problem with non-massless rope

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