A chain of mass M and length L is suspended vertically with its lower end touching a scale. The chain is released and falls onto the scale. What is the reading of the scale when a length x of the chain has fallen? Neglect the size of the individual links.

There are two quantities which effect the reading on the scale. The weight of the chain that has accumulated on the scale after falling a distance x and the impulse per unit time imparted by the chain colliding with the scale. The total force is the sum of these two contributions.
http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html