Resultant Force I

1. Resultant force for two parallel forces

How to find the resultant force for two parallel forces?

If the forces are moving in the same direction. The resultant force is also in the direction of both forces. you have to ADD the magnitude of the two forces.



If the forces are moving in opposite direction, The direction of the resultant force is the same as the larger force. Subtract the magnitude of the lesser force by the larger force.


In the above example the resultant force is 1N in the direction of the larger force which is the 4N.

2. Resultant force of Two Non-Parallel Forces

When there are forces that moves in a non-parallel manner, simple calculation cannot be done to find the resultant force. What we can do is draw a scaled diagram.

Either by using the Triangle method



or the Parallelogram method



or more specifically



In the example above, let say if we put 100N = 2 cm.

F2 = 8 cm
F1 = 10 cm

You have to measure the angle carefully using a protractor to measure the angle between the two forces. The resultant force is the R which you can measure using a ruler and convert it back to the actual magnitude (e.g. if the resultant force is 12 cm then it would convert to 600 N)! The angle is the angle between R and F1.

Can you find the resultant force for this one?

Forces in Equilibrium II

As we have learnt, when forces are in a state of equilibrium, the net force (or also known as resultant force) is zero. The object is either at rest or in a motion with constant velocity (hence zero acceleration).

Examples of two forces in equilibrium are a plate resting on a table or a skydiver falling at a constant velocity which is also known as terminal velocity.

An object that  is resting on a tilted or inclined plane also can be in equilibrium with each other. In this case three forces are in equilibrium.



N is the normal reaction.
Weight is represented by mg where m = mass of the object and g is the gravitational constant.

Addition of forces and Resultant Force

In this example, you can see that there are three different ways on how a 40N force and a 30N force can react. In the first example both forces react in the same direction.

In the second example, both forces react in opposite direction. Hence the resultant force will be 10N in the direction of the greater force (40N).

In the third example, The two forces are in perpendicular with each other. If you are using the parallelogram method ( Or Phythagoras theorem!) you can easily find that the resultant force is 50N.




So if it helps, resultant forces can be categorised in three situations:

1. Two parallel forces
2. Two non-parallel forces
3. Two perpendicular forces

at GCE-O level, you may be asked to find the resultant force for only two forces. But in reality or more complex situations there are many forces that act on an object.