Consider a block kept on an inclined plane (inclined at 45°) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and

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Solution

Q.
Consider a block kept on an inclined plane (inclined at 45°) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and the inclined plane ( $μ$ ) is equal to [2023]

1 0.50

2 0.33

3 0.25

4 0.60

Ans.
(2)

$F_{1} = m g \sin 45 ° + f = m g \sin 45 ° + μ N$

$F_{1} = \frac{m g}{\sqrt{2}} + μ m g \cos 45 °$

$F_{1} = \frac{m g}{\sqrt{2}} (1 + μ)$

$F_{2} = m g \sin 45 ° - f = m g \sin 45 ° - μ N$

$= \frac{m g}{\sqrt{2}} (1 - μ)$

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

$\frac{m g}{\sqrt{2}} (1 + μ) = 2 \frac{m g}{\sqrt{2}} (1 - μ)$

$1 + μ = 2 - 2 μ$

$μ = \frac{1}{3} \approx 0.33$

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