find the net force produced by a 40 newton force and a 50 newton force in each of the following cases:

both forces act in the same direction.

both forces act in opposite directions.

To find the Resultant vector in any direction,

add the magnitudes in that direction
call your direction along the + x axis, or EAST
then you have
case A:
40 East + 50 East = 90 East
case B
40 East - 50 East = - 10 East (which is + 10 West)

Case 1: Both forces act in the same direction.

When two forces act in the same direction, the net force is simply the sum of the individual forces. Therefore, to find the net force, you need to add the magnitudes of the forces.

Net force = Force1 + Force2

Given:
Force1 = 40 Newtons
Force2 = 50 Newtons

Net force = 40 N + 50 N
Net force = 90 Newtons

Therefore, when both forces act in the same direction, the net force is 90 Newtons.

Case 2: Both forces act in opposite directions.

When two forces act in opposite directions, the net force can be found by subtracting the magnitude of the smaller force from the magnitude of the larger force. The direction of the net force is determined by the direction of the larger force.

Net force = Larger force - Smaller force

Given:
Force1 = 40 Newtons
Force2 = 50 Newtons

Since Force2 is the larger force, the net force will have the same direction as Force2.

Net force = 50 N - 40 N
Net force = 10 Newtons

Therefore, when both forces act in opposite directions, the net force is 10 Newtons in the direction of the larger force.

To find the net force produced by the given forces, you need to consider their magnitudes and directions.

1. If both forces act in the same direction:
In this case, you can simply add the magnitudes of the forces to find the net force. The net force will have the same direction as the individual forces.
Net Force = 40 N + 50 N = 90 N (in the same direction)

2. If both forces act in opposite directions:
When forces act in opposite directions, you need to subtract the smaller magnitude force from the larger magnitude force to find the net force. The net force will have the direction of the larger force.
Net Force = Larger force - Smaller force
Net Force = 50 N - 40 N = 10 N (in the direction of the larger force)

Therefore, the net force produced by a 40 N force and a 50 N force would be:
- 90 N (in the same direction) if the forces act in the same direction.
- 10 N (in the direction of the larger force) if the forces act in opposite directions.