# Homework Help: Momentum Problem on a chain

1. Jan 20, 2009

### cordyceps

1. The problem statement, all variables and given/known data
A chain of length L and total mass M is released from rest with its lower end just touching the top of a table. Find the force exerted by the table on the chain after the chain has fallen through a distance x. (Assume each link comes to rest the instant it reaches the table.)

2. Relevant equations
p= mv
ek= (1/2)mv^2

3. The attempt at a solution
First, I tried to find the force by taking the derivative of kinetic energy:
ek= (1/2)mv^2
m= M(L-x)/L, v^2= 2xg
ek= Mxg(L-x)/L
d/dt(ek)= Mgv-2Mgxv/L

F= [d/dt(ek)]/v= Mg-2Mgx/L
But this turns out to be the wrong answer. Any advice? Thanks.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 20, 2009

### Carid

Assuming that the mass is distributed equally along the chain, what proportion of the mass M is on the table when a length x out of a total length L is on the table?

3. Jan 20, 2009

### cordyceps

mass= M(x/L)
But I don't think its as simple as the normal force of the mass on the table: Mg(x/L).

4. Jan 21, 2009

### Carid

Well the answer does seem a bit simple and obvious. But I think it is right.
Let's ask ourselves what force, if any, does the table exert on the part of the chain which is falling?

5. Jan 21, 2009

### cordyceps

In addition to the normal force, I think there is also a force somehow related to the motion of the part of the chain that is in the air. Mg(x/L) is not the right answer according to the book.

6. Jan 22, 2009

### Carid

OK a force is characterised by a change in momentum.

At the beginning the momentum of the chain is zero.

After the chain has fallen X the part of the chain in motion has a certain momentum.

Maybe they want you to express the instantaneous change in momentum.

7. Jan 25, 2009

### cordyceps

Thanks for the help.
So d/dt[ (M(L-X)/L) * sqrt(sgX) ] = ... Mg - 3Mgx/L
-> Force= 3Mgx/L - Mg
This is fairly close to the answer = 3Mgx/L. Why is there the Mg?