Falling Chain (3.11)

1. The problem statement, all variables and given/known data

A chain with length ℓ is held stretched out on a frictionless horizontal table, with a length y0 hanging down through a hole in the table. The chain is released. As a function of time, find the length that hangs down through the hole (don’t bother with t after the chain loses contact with the table). Also, find the speed of the chain right when it loses contact with the table.

2. Relevant equations

[tex]y_0\ge y\ge l[/tex]

3. The attempt at a solution

Conceptually, more of the chain must be through the hole so that y-naught is greater than y (initially). To cause an acceleration to the left (or towards the hole; however you picture the scenario), the tension T must be equal to mg (correct?). What I’m having trouble with is setting up an appropriate differential equation; should I just do the old: [tex]\ddot{y}=-g[/tex] because this would (should) hold true if I claim that the tension T is equal to mg. This means that something fundamental is getting past me, I just don’t know what. Also this doesn’t have to do with the question, but is K&K harder than the book I already have (Morin)?


Leave a comment

Your email address will not be published.


Show Buttons
Hide Buttons