A vertical chain hangs just above a balance. It
dropped. What is the force read by the balance? [1,2]
At any time, the force registered is 3 times weight of chain on the balance = 3ρxg
Here is the way this problem has
been solved in most of the textbooks, under the category of 'variable mass' problems.
Consider an increment
of chain dx going from speed v to a stop in time dt.
Force on table
= weight of chain on table + impulsive force of increment dx colliding
with the table
= ρxg + (mass) (change in
speed) / (time taken)
= ρxg + (ρdx) (v) / (dt)
= ρxg + ρv2
= ρxg + ρ (2gx) (Assume:
chain's part in air has fallen freely with g over
a distance x, so v2 =
something missing in this analysis.
Love, An Introductory Treatise on
Principles of Dynamics (Cambridge Univ. Press, Cambridge,
1897). Page 301-304.
 H. Lamb, Dynamics, 2nd Ed
(Cambridge Univ. Press, London
1929). Page 149.
This page was
updated on March 13, 2011