Question

There are two inclined surfaces of equal length (L) and same angle of inclination 45° with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down, on rough surface than on the smooth surface. The coefficient of kinetic friction (μ) between the object and the rough surface is close to ______.

Options

• 0.25

• 0.40

• 0.5

• 0.75

Answer 1

There are two inclined surfaces of equal length (L) and same angle of inclination 45° with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down, on rough surface than on the smooth surface. The coefficient of kinetic friction (μ) between the object and the rough surface is close to 0.75.

Explanation:

Given: t₂ = 2t₁

a₁ = g sin 45°

= `g/sqrt2`

L = `1/2 a_1t_1^2`

a₂ = g(sin 45° − μ cos 45°)

= `g/sqrt2(1 - μ)`

L = `1/2 a_1t_2^2`

t₂ = 2t₁

`1/2 g/sqrt2 t_1^2 = 1/2g/sqrt2(1 - μ)4t_1^2`

1 = 4(1 − μ)

μ = `3/4`

= 0.75