A resultant force

Combining multiple forces to give a single force

To get to a single resultant force you need to be able to add forces. The rules are the same as for adding any other vectors, and are particularly easy to apply if you are strict about keeping the action of all the forces along a single line. Just place one vector, then align the tail of the second on the tip of the first by sliding the second vector across, without rotating it. Repeat for as many vectors as there are. The resultant is calculated by drawing in a vector from the tail of the first to the tip of the last.

The process is identical if carried out with forces that are not along one line. The principle is the same – you can translate, but not rotate, the vectors (because it's both magnitude and direction that are important). And it doesn't matter in which order you add them.

A number of quantities are best described using vectors, so knowing how to perform this addition will be useful throughout this topic (for example, velocity and momentum are both most straightforwardly dealt with as vectors).

Here you're clearly dealing with a very abstract set of representations, carefully developed through several steps from the original messy physical interactions. It's a good idea to start a new diagram on which to carry out these kinds of manipulations, and not to try to do all of the reasoning with a near photo-realistic depiction of the original situation.

How forces are combined, and the combination used

Teacher Tip: We'd suggest always modelling a situation using resultant force as a stepping stone to finding the acceleration.