First slide

Angle of repose

Question

A block of mass 1kg is kept on a rough inclined plane at θ = 30º with horizontal. The block is connected with a string as shown. Between the block and inclined plane µ_s = 3 / 4 = tan37º .Then tension in the string is (g = 10ms^–2)

Moderate

A

< 5N but not equal to zero
B

> 5N
C

5√3N
D

zero

Solution

$mg\sin \theta = (1)(10) \times \frac{1}{2} = 5N$
${f_2} = \mu mg\cos \theta = \frac{3}{4} \times 1 \times 10 \times \frac{{\sqrt 3 }}{2} = \frac{{15\sqrt 3 }}{4} = 6.495N$
$clearly\;{f_2} > mg\sin \theta$
so body at rest and T = 0

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