Question

A Uniform chain with mass per unit length L is lifted upwards with a constant speed by a force F. Find out the force in terms of time

Answer 1

Chain has a constant speed. Therefore, net force on it should be zero.

$F=F_t+W$

$F_t=\frac{dm}{dt}(v_0-0)=\frac{dm}{dl}\frac{dl}{dt}v_0=\rho v_0^2$

$W=(y\cdot\rho)\cdot g$

$F=\rho v_0^2+\rho gy=\rho(v_0^2+gy)=\rho(v_0^2+g\cdot (v_0t))=\rho v_0(v_0+gt)$ . Answer