Question

A body whose weight is P slides down a rough inclined plane. The angle of inclination is 30°, the length of the inclined plane, 160 cm, and the coefficient of friction, 0.2. The initial velocity of the body is zero. How long does it take the body to slide down the inclined plane? 

Answer 1

Answer: t ≅ 1sec.

Explanation:

The force exerted by the body on the plane is N = P cosα. The force of friction is F₁ = kN = kP cos a and the component of the weight acting along the inclined plane is F = P sinα. According to Newton's second law,

(F - F₁)t = Pvlg, (1)

where v is the velocity of the body at the bottom of the plane and t is the time of descent. 

Since the initial velocity was zero, then

l = 1/2(at²) = 1/2(vt).

Hence v is equal to 2l/t. Inserting the value of v in equation (1), we have