Question

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Answer 1

Explanation:

Consider a plane is inclined to the horizontal at an angle Ɵ. Let the body placed on the inclined plane slide down with an acceleration a, then

The reaction R = mg cos Ɵ ------Eqn (1)

Net force on the body down the inclined plane = f = mg sin Ɵ – F

f = ma = mg sin Ɵ – μR as μ = F / R ---- Eqn (2)

Now substitute for R, from equation (1)

ma = mg sin Ɵ – μ mg cos Ɵ = mg( sin Ɵ - μ cos Ɵ )

a = mg( sin Ɵ - μ cos Ɵ )

The acceleration of the body down a rough inclined plane is always less than the acceleration due to gravity g. that is a < g

Thus, the minimum force required to push the body down the inclined plane is f (down) = mg( sin Ɵ + μ cos Ɵ )

The minimum force required to push the body down the inclined plane is

f (up) = mg( μ cos Ɵ - sin Ɵ )

Answer 2

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