Question

A body is sliding down an inclined plane having coefficient of friction 0.5 the normal reaction is twice that of resultant downward force along the inclined plane then find the angle between the inclined plane and the normal

Answer 1

Answer:

A body is sliding down an inclined plane having coefficient of friction 0.5. If the normal reaction is twice that of the resultant downward force along the incline, the angle between the inclined plane and the horizontal is [EAMCET (Engg.) 2000]

Answer 2

◆ Answer -

Angle of inclination = 45°

● Explanation -

For a body sliding at inclination α, normal reaction is given as -

N = mg.sinα

Also, resultant force along the inclined plane will be -

R = mg (sinα-μ.cosα)

Given that normal reaction is twice the resultant force.

N = 2R

mg.sinα = 2mg (sinα-μ.cosα)

sinα = 2sinα - 2μ.cosα

sinα = 2 × μ × cosα

tanα = 2 × 0.5

tanα = 1

Taking tan inverse,

α = arctan(1)

α = 45°

Therefore, angle of inclination is 45°.

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