Question

If the chain is lowered at a constant speed $v=1.2$ m/s, determine the normal reaction exerted on the floor as a function of time (The chain has a mass of $80$ kg and a total length of $6$ m).

Answer 1

Linear density $=\frac{80}{6}=\frac{40}{3}\frac{kg}{m}$

mass come to rest in 1 second $\frac{dm}{dt}=\frac{40}{3}\times 1.2\frac{kg}{m}$

$F=\frac{dp}{dt}=v\frac{dm}{dt}=1.2\times 16=19.2N$

normal reaction $=1.2\times \frac{40}{3}t+19.2=16t+19.2$