First slide

Friction on horizontal surface

Question

A block of mass 4 kg rests on rough horizontal surface. A vertically downward force P is applied on the block. The block just starts sliding when horizontal force P is applied on the block. If $P = \frac{1}{2} mg$ , find the coefficient of friction between the block and the surface.

Moderate

A

3/4
B

1/2
C

2/3
D

1/3

Solution

Normal reaction N = mg + P
$∴ f_{\max} = μN = μ (mg + P)$
$∴ P = μ (mg + P) \Rightarrow μ = \frac{\frac{1}{2} mg}{mg + p} = \frac{\frac{1}{2} mg}{mg + \frac{1}{2} mg} = \frac{1}{3}$

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