The minimum force required to move a body up an inclined plane is three times the minimum force required to prevent it from sliding down the plane. If the coefficient of friction between the body and

Question

The minimum force required to move a body up a rough inclined plane

$F_{1} = mg (sin θ + μ cos θ)$

The minimum force required to prevent the body from sliding down the rough inclined plane.

$F_{2} = mg sinθ - μ mg cosθ$

$F_{1} = 3 F_{2}$

$mg (sinθ + μcosθ) = 3 mg (\sin - μcosθ)$

$4 μcosθ = 2 sinθ$

$tanθ = 2 μ = \frac{1}{\sqrt{3}}$

$\Rightarrow θ = 30 °$

TestHub · Accepted Answer

The minimum force required to move a body up a rough inclined plane

$F_{1} = mg (sin θ + μ cos θ)$

The minimum force required to prevent the body from sliding down the rough inclined plane.

$F_{2} = mg sinθ - μ mg cosθ$

$F_{1} = 3 F_{2}$

$mg (sinθ + μcosθ) = 3 mg (\sin - μcosθ)$

$4 μcosθ = 2 sinθ$

$tanθ = 2 μ = \frac{1}{\sqrt{3}}$

$\Rightarrow θ = 30 °$

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