Force exerted by the wedge on the block in an inclined plane system

To determine the force exerted by the wedge on the block in the inclined plane system, we need to consider the forces acting on the block and the wedge separately.

Forces acting on the block:
1. Weight (mg): The weight of the block acts vertically downwards with a magnitude equal to the mass of the block (m) multiplied by the acceleration due to gravity (g).

Forces acting on the wedge:
1. Normal force (N): The normal force exerted by the inclined plane on the wedge acts perpendicular to the surface of the wedge. It counteracts the component of the weight of the wedge that is perpendicular to the inclined plane.

Now, let's consider the forces that affect the motion of the block on the inclined plane:

1. Weight of the block (mg): This force acts vertically downwards and can be resolved into two components - one parallel to the inclined plane (mg*sin(theta)) and the other perpendicular to the inclined plane (mg*cos(theta)).
2. Normal force exerted by the wedge (N): This force acts perpendicular to the inclined plane and counteracts the component of the weight of the block that is perpendicular to the inclined plane.
3. Force of friction (f): The force of friction between the block and the inclined plane acts parallel to the inclined plane and opposes the motion of the block.

To prevent the block from slipping on the wedge, the force of friction should be equal to or greater than the maximum possible value of the frictional force, which is given by:

f_max = μ*N

where μ is the coefficient of friction between the block and the inclined plane, and N is the normal force exerted by the wedge.

Since the block is not slipping, the force of friction can be determined as:

f = μ*N

The force exerted by the wedge on the block is equal to the frictional force, which is equal to μ*N.

In summary, the force exerted by the wedge on the block is equal to the force of friction between the block and the inclined plane, which can be determined using the equation f = μ*N, where μ is the coefficient of friction and N is the normal force exerted by the wedge.