Question

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 the inclined plane is 1/2√3 the angle of the inclined plane is

A. 60°
B. 45°
C. 30°
D. 15°

Answer 1

The angle of inclination of the plane is determined as 30° (Option C).

How to calculate the angle of inclination?

The angle of inclination of the plane is calculated as follows;

The given condition is that the minimum force required to move the body up is three times the minimum force required to prevent it from sliding down.

F(up) = 3 F(down)

Wsinθ + μWcosθ = 3 (Wsinθ - μWcosθ)

If we simplify the equation further, we will have;

Wsinθ + μWcosθ = 3Wsinθ - 3μWcosθ

μWcosθ + 3μWcosθ = 3Wsinθ - Wsinθ

4μWcosθ = 2Wsinθ

2μcosθ = sinθ

2μ = sinθ / cosθ

2μ = tanθ

The value of coefficient of friction μ is given as
`(1)/(2√(3) )`

`2 * (1)/(2√(3) ) = tan \theta \\\\(1)/(√(3) ) = tan \theta`

`\theta = tan ^(-1) ((1)/(√(3) )) }\\\\\theta = 30^0`