the diagram show a cylinder of mass 8kg lying at rest on two smooth planes inclined at angles 40 degrees and 50 degrees to the horizontal.

Calculate the reaction exerted by each plane on the cylinder

Thanks in advance

To calculate the reaction exerted by each plane on the cylinder, we need to consider the forces acting on the cylinder. Since the cylinder is at rest, the net force acting on it must be zero.

Let's consider the forces:

1. Weight: The weight of an object is given by the formula weight = mass * gravity. In this case, the weight of the cylinder is 8 kg * 9.8 m/s^2 (acceleration due to gravity) = 78.4 N. The weight acts vertically downwards.

2. Normal force: The normal force is the force exerted by a surface to support the weight of an object in contact with it. Since the cylinder is in contact with two inclined planes, there will be two normal forces, one from each plane.

Now, let's calculate the normal forces exerted by each plane:

For the first inclined plane (with an angle of 40 degrees to the horizontal):

- Resolve the weight of the cylinder into components:
- Perpendicular component: weight * cos(angle) = 78.4 N * cos(40) = 59.90 N
- Parallel component: weight * sin(angle) = 78.4 N * sin(40) = 50.53 N

The normal force on the first inclined plane (N1) will be equal to the perpendicular component of the weight, which is 59.90 N.

For the second inclined plane (with an angle of 50 degrees to the horizontal):

- Resolve the weight of the cylinder into components:
- Perpendicular component: weight * cos(angle) = 78.4 N * cos(50) = 50.53 N
- Parallel component: weight * sin(angle) = 78.4 N * sin(50) = 59.90 N

The normal force on the second inclined plane (N2) will be equal to the perpendicular component of the weight, which is 50.53 N.

Therefore, the reactions exerted by each plane on the cylinder are as follows:

- The first inclined plane exerts a reaction of 59.90 N on the cylinder.
- The second inclined plane exerts a reaction of 50.53 N on the cylinder.