# Kleppner and Kolenkow 5.10 – Falling Chain

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

A chain of mass M and length ##\ell## is suspended vertically with its lowest end touching a scale. The chain is released and falls onto the scale. What is the reading of the scale when a length of chain, ##x##, has fallen? (Neglect the size of individual links.)

http://ift.tt/1eLuXm3 <—– Image

2. Relevant equations

$$M_{dx}=M\frac{x}{\ell}$$
$$K_i=0$$
$$U_i=Mg\frac{x}{\ell}(\ell-x)$$
$$K_f=\frac{Mxv^2}{2\ell}$$
$$U_i=0$$

3. The attempt at a solution

When I equate the initial potential energy and the final kinetic energy, it is not possible to solve for M without cancelling it; I need to find ##M(x)##. Also, energy methods must be used.
Am I missing something?

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