A block weighing 11.05 N rests on a 28 degree incline.

(a) Find the normal force exerted by the plane on the block out of the plane

(b) Find the frictional force exerted by the plane on the block up the slope.
c) Find the magnitude of the total force exerted by the plane on the block

(d)Find the normal force and the frictional force exerted by the block on the plane.

(d) is for this

normal force into the plane
and the frictional force down the slope

To find the answers to these questions, we need to understand the forces acting on the block on an inclined plane.

1. The weight of the block (W) is the force exerted by gravity on the block, and it acts downward vertically. Given that the block weighs 11.05 N, we can calculate the weight as W = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).

2. The normal force (N) is the force exerted by the inclined plane perpendicular to the plane's surface. It acts perpendicular to the surface of the plane and opposes the force of gravity. On an inclined plane, the normal force is less than the weight of the object.

3. The frictional force (f) is the force that opposes the motion of the block on the inclined plane. It acts parallel to the surface of the plane. In this case, it is going to act up the slope since the block is at rest.

Now, let's answer each part of the question:

(a) To find the normal force exerted by the plane on the block out of the plane, we need to use trigonometry. The normal force can be calculated using the formula N = W * cos(theta), where theta is the angle of inclination. In this case, the angle of inclination is 28 degrees. So, N = 11.05 N * cos(28 degrees).

(b) To find the frictional force exerted by the plane on the block up the slope, we can use the formula f = N * sin(theta), where theta is the angle of inclination. In this case, the angle of inclination is still 28 degrees. So, f = N * sin(28 degrees).

(c) To find the magnitude of the total force exerted by the plane on the block, we need to consider both the normal force and the frictional force. Since they act perpendicularly to each other, we can use the Pythagorean theorem to calculate the magnitude. The total force can be calculated as the square root of (N^2 + f^2).

(d) To find the normal force and the frictional force exerted by the block on the plane, we need to consider the equal and opposite nature of forces. The normal force exerted by the block on the plane is the same as the normal force exerted by the plane on the block. Similarly, the frictional force exerted by the block on the plane is equal in magnitude and opposite in direction to the frictional force exerted by the plane on the block. So, the normal force and the frictional force exerted by the block on the plane are the same as the values calculated in parts (a) and (b) respectively.