An 95.0-N crate of apples sits at rest on a ramp that runs from the ground to the bed of a truck. The ramp is inclined at 29.0° to the ground.

(a) What is the normal force exerted on the crate by the ramp?

95 cos29 = 83.1 N

To find the normal force exerted on the crate by the ramp, we need to consider the forces acting on the crate. The normal force is the force exerted by a surface perpendicular to the surface. In this case, the ramp is the surface that is perpendicular to the ground.

First, let's identify the forces acting on the crate:
1. Weight (mg): This is the force exerted on the crate due to gravity. It is given by the mass of the crate (m) multiplied by the acceleration due to gravity (g).
2. Normal force (N): This is the force exerted by the surface perpendicular to the crate (the ramp). This is the force we are trying to find.
3. Frictional force (f): This is the force opposing the motion of the crate along the ramp. However, since the crate is at rest, this force can be ignored for now.

Since the crate is at rest, both the vertical and horizontal forces must be balanced. In the vertical direction, the weight (mg) is balanced by the normal force (N).

To find the normal force, we can use the following equation:

N = mg * cos(θ)

where:
N is the normal force
m is the mass of the crate
g is the acceleration due to gravity (approximately 9.8 m/s^2)
θ is the angle of inclination of the ramp (given as 29.0°)

Now, let's calculate the normal force:

N = 95.0 N * cos(29.0°)

To find the cosine of 29.0°, you can use a scientific calculator or trigonometric table. The result will be the value of N, which represents the normal force exerted on the crate by the ramp.