 # Resultant Force Formula

## Resultant Force Formula

The Resultant force is defined as the total force acting on a body along with their directions. When the object is at rest or travelling with the same velocity, the resultant force has to be zero. Since all the forces are acting towards the same direction, the resultant force should be same for all the forces.

If one force is acting perpendicular to another, the resultant force is determined by using Pythagorean theorem.The Resultant force formula is given by,

FR = F1 + F2 + F3

Where,

F1, F2, F3 are the forces acting in the same direction on a body.

If force F2 is perpendicular to force F1, the resultant force formula is given as,

Problem 1

If three forces 50N, 60N and 20N are acting on a body simultaneously and 20N is opposite to the direction of other two. Determine the resultant force.

Solution:

Given:

F1 = 50N,

F2 = 60N

F3 = 20N

(F3 is opposite to the other two, therefore F3 = -20N)

Resultant force formula is given by,

FR = F1+F2+F3

= 50+60-20

= 90N

Example 2

If 4N and 9N forces act perpendicular to an object, determine the resultant force.

Solution:

Given:

F1 = 4N

F2 = 9N

Because they are perpendicular to each other, the resultant force formula is given by,

FR = F12+F22

FR = 16+81

FR = 97

= 9.84N