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A 30.6 kg crate initially at rest on a horizontal floor requires a 100 N 30° with the horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor

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The frictional force opposes the forward motion of the crate. The coefficient of static friction is 0.2.

Using the formula;

Fa = - Ff + mgsinθ

but Ff = μsFN and N = mgcosθ

Hence;

Fa = mgsinθ - μsmgcosθ

μsmgcosθ = mgsinθ - Fa

μk =  mgsinθ - Fa/mgcosθ

μk =  coefficient of static friction = ?

Fa = horizontal force = 100N

m = mass = 30.6 kg

θ = angle = 30°

g = acceleration due to gravity = 10 m/s^2

Substituting values;

μk =  [(30.6 × 10) sin 30°] - 100 / (30.6 kg × 10) cos 30°

μk = 153 - 100/265

μk = 0.2

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