Motion on an Inclined Plane:

When a body is kept on an inclined plane, it experiences a force of gravity that acts downwards and a normal force that acts perpendicular to the plane. If the plane is rough, then a frictional force also acts on the body in the direction opposite to the motion. The angle of the plane with the horizontal is known as the angle of inclination.

Calculating the Force Required to Prevent Motion:

To calculate the force required to prevent motion of a block on a rough incline plane, we need to consider the forces acting on the block. These forces are:

1. Force of gravity (Fg) = m*g, where m is the mass of the block and g is the acceleration due to gravity.
2. Normal force (N) = m*g*cos(theta), where theta is the angle of inclination.
3. Frictional force (Ff) = mu*m*g*cos(theta), where mu is the coefficient of friction.

The force required to prevent motion is given by:

F = N + Ff

If the block is not moving, then the force of friction is equal to the force applied on the block. Therefore,

Ff = mu*N

Substituting the value of N in terms of m and theta, we get:

Ff = mu*m*g*cos(theta)

Substituting the value of Ff in the equation of force required to prevent motion, we get:

F = m*g*cos(theta)*(mu + sin(theta))

To prevent the block from moving, the force applied (F) must be equal to or greater than the force required to prevent motion.

Calculating the Force Required in this Case:

Given that the mass of the block (m) is 20 kg and the angle of repose (theta) is 30 degrees. The angle of repose is the maximum angle at which a block can be placed on an inclined plane without sliding down.

To calculate the force required to prevent motion, we need to know the coefficient of friction (mu). The coefficient of friction depends on the nature of the surfaces in contact. Let's assume that the coefficient of friction between the block and the plane is 0.4.

Substituting the values in the equation of force required to prevent motion, we get:

F = m*g*cos(theta)*(mu + sin(theta))
F = 20*9.8*cos(30)*(0.4 + sin(30))
F = 196.04 N

Therefore, the force required to prevent the block from sliding down the plane is 196.04 N.