- #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
[/B]
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?