A block is projected upward along a rough incline of angle θ. Coefficient of kinetic friction is μ, with tanθ > μ. Let a₁ be the magnitude of acceleration while moving upward and a₂ the magnitude while sliding downward. Then a₁/a₂ is:
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Question

A block is projected upward along a rough incline of angle θ. Coefficient of kinetic friction is μ, with tanθ > μ. Let a₁ be the magnitude of acceleration while moving upward and a₂ the magnitude while sliding downward. Then a₁/a₂ is:

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G1 Physics · Accepted Answer

While the block moves upward, gravity and friction both act down the plane: a₁ = g(sinθ + μcosθ). While it moves downward, friction acts up the plane: a₂ = g(sinθ - μcosθ). Hence a₁/a₂ = (sinθ + μcosθ)/(sinθ - μcosθ).