A crate weighing 400N rests on aplane inclined at an angle of 20 degrees to the horizontal. there is a force of friction of 120N acting up the ramp. Determine (i) the resultant force acting on the crate, (ii) the contact,or normal force between the ramp and the crate.

Wc = 400 N. = Wt. of crate.

Fc = 400N @ 20o. = Force of crate.
Fp = 400*sin20 = 136.8 N. = Force parallel to incline.
Fv = 400*cos20 = 376 N. = Normal =
Force perpendicular to incline.

Fr = Fp-Ff = 136.8-120 = 16.8 N. = Resultant force.

To solve this problem, we need to use the concepts of force components and equilibrium. Here's how you can determine the resultant force and the contact or normal force:

(i) Calculating the Resultant Force:
The resultant force can be calculated by considering the forces acting along the inclined plane. We'll break down the weight of the crate and the force of friction into their respective components.

1. Resolve the weight of the crate: The weight of the crate is acting vertically downward. We can resolve it into two components:
- The component perpendicular to the inclined plane is given by W⊥ = mg * cos(θ), where m is the mass of the crate and g is the acceleration due to gravity (9.8 m/s^2).
- The component parallel to the inclined plane is given by W∥ = mg * sin(θ).

2. Calculate the net force along the plane: It can be determined by summing up the forces acting parallel to the plane.
- Net force along the plane, F∥ = W∥ - frictional force = W∥ - Ffriction

3. Calculate the magnitude of the resultant force: The resultant force is the vector sum of the net force along the plane and the perpendicular component of the weight.
- Resultant force, Fresultant = √(F∥² + W⊥²)

(ii) Determining the Contact or Normal Force:
The contact force or normal force is the perpendicular force exerted by the inclined plane on the crate. It is equal in magnitude but opposite in direction to the perpendicular component of the weight.

1. Calculate the contact force: The contact force is given by the perpendicular component of the weight.
- Contact force, Fcontact = W⊥

Now, let's calculate the values:

Given:
Weight of the crate (W) = 400 N
Angle of inclination (θ) = 20 degrees
Frictional force (Ffriction) = 120 N
Acceleration due to gravity (g) = 9.8 m/s²

(i) Calculating the Resultant Force:
1. Resolve the weight of the crate:
W⊥ = 400 N * cos(20°)
W∥ = 400 N * sin(20°)

2. Calculate the net force along the plane:
F∥ = W∥ - Ffriction

3. Calculate the resultant force:
Fresultant = √(F∥² + W⊥²)

(ii) Determining the Contact or Normal Force:
1. Calculate the contact force:
Fcontact = W⊥

Keep in mind that to get the final numerical values for Fresultant and Fcontact, you need to perform the calculations using appropriate units and values from the given problem.