Question

A wooden block of mass 2 kg rests on a rough inclined plane of angel of inclination 30°, then frictional force bet
inclined plane is (g = 10 m3-2) (mk = 0.2)
(A) 0.2 x 2 x 10 x sin 30°
(B) 2 x 10 x sin
30°
(C) 0.2 X 2 X 10 X cos 30°
(D) zero​

Answer 1

Answer:

The answer is a option B

Answer 2

If the block is resting with out slipping on the inclined surface, it means that the frictional force is greater than the gravitational pull down the plane. we calculate the minimum value of static friction at the surface of the block.

Friction force Ff = coeff of static friction * Normal force

Ff = Mu * N

Normal force N = mg cos Ф as the block is in equilibrium. and net force in the direction of perpendicular to plane is zero. Ф is the angle of inclination of plane.

Ff = Mu * m g Cos Ф = 0.7 * 2 kg * 9.8m/s² * cos 30 = 11.88 Newtons

Suppose we calculate the component of weight along the inclined plane:

= m g Sin Ф = 2 kg * 9.8m/s² * sin 30 = 9.8 Newtons

So we see that the static frictional force is higher than the gravity along the inclined plane, so the block rests.

If Ф is increased, cos Ф reduces and sin Ф increases, and then there will be a point when the block starts to slide.