Resultant Force II

For the resultant force of two perpendicular forces, we need to consider other methods.

In this situation, two non-parallel forces are acting on an object at a right angle to each other.



So with the example above, there is Force a (Sometimes called component a) and Force b (sometimes called component b).

The resultant force is named as F.

The resultant force can be obtained through Phytogras theorem

F^2 = a^2 + b^2

F = Square root of (a^2+b^2)




Example of question:

What is the resultant force if Force a,70N  and Force b, 90N act on an object and both for the forces are perpendicular to each other. What is the direction of the force?

i. Resultant force, Fr = Square root of (70^2 + 90^2)
                                  = 114N

ii. Direction, Tan (theta) = 70 / 90
                                        = 0.7778
                                        = 37.9 degree

So the resultant force is 114N and the direction is 37.9 degree from the original 90N force.

If you have known the basic principle.
The questions can be manipulated but you can still know how to work out the question.

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?