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6 March, 05:06

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?

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  1. 6 March, 07:21
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    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°
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