Question

A block placed on a rough inclined plane of inclination 30 can be pushed upward with force F .if the inclination is increased to 60 the same block can be prevented from sliding down find the coefficient of friction

Answer 1

The coefficient of friction between the two blocks is μ = √3 - 1/√3 +1

Explanation:

The friction force in the first case is in the downward direction and in the second case in the upward direction.

When θ = 30° , F - mgsin30° - μmgcos30° = 0 .....(1)

When θ = 60° , F + μmgcos60° - mgsin60° = 0 .....(2)

Using equation (1) and (2)

μ(cos60° + cos30°) = sin60° - sin30°

OR

μ (1/2 + √3/2) = √3/2 - 1/2

μ = √3 - 1/√3 +1

The coefficient of friction between the two blocks is μ = √3 - 1/√3 +1

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