In the situation given, a force of 100 N is acting on a block placed on rough horizontal surface
as shown in the figure. The block does not slide. If the angle of friction is found to be ${tan}^{- 1} \frac{1}{n}$ .
Find the value of n. Take $g = {10 m/s}^{2}$ ____

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answer is 2.

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Detailed Solution

$∴ N = F \sin 37 ° + mg = 100 (\frac{3}{5}) + 100 = 160 (N) μ = \frac{F}{N} = \frac{F_{x}}{N} = \frac{100 \cos 37 °}{160} = \frac{80}{160} = \frac{1}{2} μ = T a n ϕ = \frac{1}{n} ∴ \frac{1}{n} = \frac{1}{2} \Rightarrow n = 2$

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