Calculations involving forces

The resultant force is the single force that has the same effect as two or more forces acting together.

Two forces in the same direction

Two forces that act in the same direction produce a resultant force that is larger than either individual force.

You can easily calculate the resultant force of two forces that act in a straight line in the same direction by adding their sizes together.

Example

Two forces, 3 N and 2 N, act to the right. Calculate the resultant force.

Two arrows, one above the other, both pointing to the right, one labelled 2 N and one labelled 3 N. Then an equals sign and then another arrow to the right labelled 5 N.Two forces acting in the same direction

Resultant force F = 3 N + 2 N = 5 N to the right.

The resultant force is 5 N to the right.

Two forces in opposite directions

Two forces that act in opposite directions produce a resultant force that is smaller than either individual force.

To find the resultant force subtract the magnitude of the smaller force from the magnitude of the larger force.

The direction of the resultant force is in the same direction as the larger force.

Example

A force of 5 N acts to the right, and a force of 3 N act to the left.

Calculate the resultant force.

Two arrows, one above the other, one pointing to the left, labelled 2 N, the other pointing to the right labelled 3 N. Then an equals sign, with an arrow to the right labelled 1 N.Two forces acting in opposite directions

Resultant force F

Resultant force F = 5 N - 3 N = 2 N to the right.

The resultant force is 2 N to the right.