Question

A chain hangs over a nail with 2.0 m on one side and 6.0 m on the other side. If the

force of friction is equal to the weight of 1.0 m of the chain, calculate the time required

for the chain to slide off the nail.

Answer 1

$\lambda=m/L$

Equation of motion

$\lambda y(t)g-\lambda(L-y(t))g-\lambda g=L\lambda\frac{d^2y(t)}{dt^2}\to$

$y(t)=\frac{L+1}{2}+Ae^{\sqrt{2g/L}\cdot t}$

$L=8\ m$

$y(0)=6\ m$ . So, we have $A=1.5$

$y(t)=\frac{L+1}{2}+1.5e^{\sqrt{2g/L}\cdot t}=4.5+1.5e^{1.581t}$

For $y(t)=8\ m\to t\approx0.54\ (s)$ . Answer