A block is placed on an inclined plane with an angle of inclination θ (in degrees) with respect to horizontal. The coefficient of static friction between the block and the inclined plane is 0.4. For what maximum value of θ will the block remain stationary on the inclined surface?

The maximum value of θ that will cause the block to remain stationary on the inclined surface is 21.8°

Explanation:

Given;

coefficient of static friction, μ = 0.4

for the block to remain stationary on the inclined plane, force pushing the block upward must be equal to the force acting downwards.

μR = mgsinθ

μmgcosθ = mgsinθ

μcosθ = sinθ

μ = sinθ/cosθ

μ = tanθ

θ = tan⁻¹ (0.4) = 21.8°

Therefore, the maximum value of θ that will cause the block to remain stationary on the inclined surface is 21.8°