 1. Calculating resultant force

A resultant force is the force obtained when two or more forces are acting on a body. To find the resultant force in one direction, sum forces acting in the same direction and subtract forces acting in an opposite direction. When forces are acting perpendicularly to each other, the Pythagoras' theorem can be used to find the resultant force. # 1

Jane tries to push a box forward horizontally by exerting a force of 45 N on it. The box does not move, thus she calls her friend, Mary, to help her. Jane pushes again with a force of 45 N and Mary pushes with a force of 38 N, both horizontally. If the frictional force exerted on the box by the ground is 47 N, what is the magnitude of the resultant force acting on the box?

The direction in which they are pushing can be considered to be positive.
resultant force = 45 N + 38 N − 47 N = 36 N in the direction they are pushing in

36 N # 2

The diagram provided shows a free-body force diagram of an object. Calculate the magnitude of the resultant force acting on the object.

resolving vertically: 5 N − 3 N = 2 N
resolving horizontally: 8 N − 6 N = 2 N
magnitude of resultant force = √(2² + 2²) = 2.8 N (2 s. f.)

2.8 N # 3

A swimmer is providing a thrust of 600 N and the water exerts a drag force on the swimmer of 180 N. What is the resultant force experienced by the swimmer?

The swimmer's direction of motion may be taken to be positive.
resultant force = 600 N − 180 N = 420 N in the direction of the swimmer's motion

420 N forwards # 4

Two propellers that create perpendicular thrusts of 3 N and 4 N are mounted on a boat. Find the magnitude of the overall thrust that these two propellers create.

When forces are acting perpendicularly to each other, the Pythagoras' theorem can be used to find the resultant force.
|F| = √(3² + 4²) = √25 = 5 N

5 N # 5

A car is travelling on a rough road. If the thrust provided by the car's engine is 1500 N and the friction on the car due to the road is 450 N, what is the magnitude of the horizontal resultant force acting on the car?

The direction of car's motion can be taken to be positive
resultant force = 1500 N − 450 N = 1050 N in the direction of the car's motion

1050 N End of page