Question

A block starts moving up an inclined plane of inclination $30^\circ $ with an initial velocity of $v_{0}$ . It comes back to its initial position with velocity $\frac{v_{0}}{2}$ . The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I}{1000}.$ The nearest integer to $I$ is _____.

Answer 1

$a=gsin30+\mu gcos30$
$V_{0}^{2}=2ad$
$d=\frac{V_{0}^{2}}{2 a}$
$W_{f}=k_{f}-k_{i}$
$-2\mu mgcos30\frac{V_{0}^{2}}{2 a}=\frac{1}{2}m\frac{V_{0}^{2}}{4}-\frac{1}{2}mV_{0}^{2}$
$\frac{+ 2 μg cos 30}{a}=+\frac{3}{4}$
$8\mu gcos30=3gsin30+3\mu gcos30$
$5μgcos30=3gsin30$
$\mu =\frac{3 tan 30}{5}=\frac{\sqrt{3}}{5}$
$\frac{\sqrt{3}}{5}=\frac{I}{1000}$
$I=346$