First slide

Friction on inclined plane of angle more than angle of repose

Question

A block takes twice as much time to slide down a 45° rough inclined plane as it takes to slide down a similar smooth plane. The coefficient of friction is:

Easy

A

$\frac{3}{4}$
B

$\frac{\sqrt{3}}{2}$
C

$\frac{1}{4}$
D

$\frac{1}{3}$

Solution

By using 2^nd equation of motion s = ut + (½) at²
For smooth inclined plane : $s = 0 + \frac{1}{2} (gsin θ) t_{1}^{2}$
For sough inclined plane : $s = 0 + \frac{1}{2} (gsin θ - μgcos θ) t_{2}^{2}$
$But t_{2} = 2 t_{1} so μ = \frac{3}{4}$

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