For the situation in which a block on a rough horizontal surface is pulled by a force F at an adjustable angle θ above horizontal, the angle θ for which the force needed to just start motion is minimum satisfies:
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Question

For the situation in which a block on a rough horizontal surface is pulled by a force F at an adjustable angle θ above horizontal, the angle θ for which the force needed to just start motion is minimum satisfies:

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G1 Physics · Accepted Answer

From F = μmg/(cosθ + μ sinθ), the denominator must be maximum. Differentiate: -sinθ + μ cosθ = 0. Hence tanθ = μ.