The end of a chain, coiled near the edge of a horizontal surface, falls over the edge.

Question:

The end of a chain, coiled near the edge of a horizontal surface, falls over the edge. If the friction between the chain and the horizontal surface is negligible and the chain is inextensible then, when a length x of chain has fallen, the equation of motion is

d -(mxv) = mgx dt

where m is the mass per unit length of the chain, g is gravitational acceleration and v is the velocity of the falling length of the chain. If the mass per unit length of the chain is constant, show that this equation can be expressed as

dv xv + v = gx d.x

and, by putting y = v2, show that v = √(2gx/3).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question
Question Posted: