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

Answer: 346

$a=gsin30+\mu gcos30$
$V_0^2=2ad$
$d=\frac{V_0^2}{2a}$
$W_f=k_f-k_i$
$-2\mu mgcos30\frac{V_0^2}{2a}=\frac{1}{2}m\frac{V_0^2}{4}-\frac{1}{2}m{V}_0^2$
$\frac{+2\mu gcos30}{a}=+\frac{3}{4}$
$8\mu gcos30=3gsin30+3\mu gcos30$
$5\mu gcos30=3gsin30$
$\mu =\frac{3tan30}{5}=\frac{\sqrt{3}}{5}$
$\frac{\sqrt{3}}{5}=\frac{I}{1000}$
$I=346$