First slide

Friction on inclined plane of angle more than angle of repose

Question

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^{0}$ , the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively

Moderate

A

0.4 and 0.3
B

0.6 and 0.6
C

0.6 and 0.5
D

0.5 and 0.6

Solution

Coefficient of static friction,
$μ_{s} = \tan 30^{0} = \frac{1}{\sqrt{3}} = 0.6$
Acceleration of the box, $a = g \sin 30^{0} - μ_{K} g \cos 30^{0}$
Using, S = ut + $\frac{1}{2} {at}^{2}$
$\Rightarrow 4 = \frac{1}{2} [\frac{g}{2} - \frac{μ_{k} g \sqrt{3}}{2}] \times 16 \Rightarrow μ_{K} = 0.5$

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