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**1. Homework Statement**

This is from Serway's book Prob 9.71...(busying preparing for GRE)

A chain of length L and total mass M is released from rest with its lower end just touching the top of a table, as in figure (a). Find the force exerted by the table on the chain after the chain has fallen through a distance x, as in figure (b).

Assume each link comes to rest the instant it reaches the table.

[PLAIN]http://img820.imageshack.us/img820/9648/971d.jpg [Broken]

**2. Homework Equations**

The solution given by the book is 3mgx/L, but I couldn't get it.

**3. The Attempt at a Solution**

My attempt is to consider the centre of mass of the chain.

The centre of mass is calculated to be

[tex]x_{CM}=\frac{(L-x)^{2}}{2L}[/tex]

Then differentiate twice to get an expression of [tex]a_{CM}[/tex]

and find the net force on the centre of mass, less the gravity Mg, should be the force to stop the chain.

Finally, the normal force acting on the chain already on the table is Mg(x/L)

Then add together.

But the problem is, I could not figure out the derivatives of [tex]x_{CM}[/tex]:

[tex]v_{CM}=\frac{-(L-x)}{L}\frac{dx}{dt}[/tex]

what should be dx/dt?

Anyone could give me some hints? Or my approach is not correct?

I know this is a challenging problem as it is a level 3 in the book. Thanks!!

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