- #1

Raphael30

- 12

- 4

## Homework Statement

A rope of length L and mass m is attached to the ceiling and folded at mid length. The free end of the rope is held against the ceiling, then dropped at time t=0.

a) Calculate the velocity of the free end as a function of y, its distance from the ceiling.

b) Calculate R, the reaction force exerted by the ceiling as a function of y.

## Homework Equations

Free fall: a=g, v=gt, y=0.5gt^2, therefore v^2=2gy; R=-Fg

## The Attempt at a Solution

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I couldn't find a way the free end was subject to any rope tension, so I supposed its fall was free, therefore v=sqrt(2gy)

However, at y=L, v has to become 0 because the rope is extensible.

Following the logic that the folded part didn't pull on the rope, I interpreted the reaction force as the tension in the rope, of magnitude mg/2 at the start and gaining mgy/2L as the free end drops (because the folded part loses y/2 in legth as it drops)

The goal of this exercise is supposed to be an introduction to whip dynamics, but I feel like my results are far too simple and don't really enlighten me on that subject. Can anyone verify my results and point out the flaws in my logic?