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# Resultant Force

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Let’s first understand the force to understand the resultant force better. A force is a push or a pull that may cause an object’s velocity to change. Since forces are vectors, they have both a magnitude and a direction. There are several examples of forces in daily life, such as weight force (the weight of something), the force of a bat on a ball, and the force used by a hair brush to brush hair.

But what exactly is Resultant Force? The resultant force refers to the net force acting on an object when it is subjected to several forces acting in various directions. To put it another way, the definition of the resultant force is the force that would have the same impact on an object as all of the other forces combined. Forces acting in the same direction add up, whereas those acting in the opposite direction cancel out.

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Table of content

## What is Resultant Force?

The total effective force exerted on a body in all directions is known as the

esulting force. The resultant force must also be zero when the object is resting or moving at the same speed. Because all forces act in the same direction, the resulting force should be the same.

The Pythagorean Theorem can also calculate the resultant force if one force is perpendicular to another or if two forces act in opposite directions. The formula below is used to calculate the resultant force.

### Resultant Force Definition

The difference between the forces exerted on an object when a system of forces is at work is known as the Resultant force.

It is possible to combine forces applied to the same body part to produce the same result. However, it is impossible to combine forces with different places of application and keep the same impact on the body. A system of forces acting on a rigid body is combined by relocating the forces to the same point of application and calculating the related torques. The resultant force torque is obtained by adding these forces and torques.

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## Resultant Force Formula

The Pythagorean theorem calculates the resultant force when two forces act perpendicularly. The formula for Resultant Force is as follows:

**F _{R} = F_{1}+F_{2}+F_{3}**

Where,

Three forces acting in the same direction on an object are F_{1}, F_{2}, and F_{3}.

## How to Find the Resultant Force?

Using Newton’s Second Law, we can determine the resultant force if we know the mass ‘m’ of an object and the acceleration ‘a’ caused by the forces acting on it. Indeed, Newton’s Second Law states that the force F alone is what causes an object with mass ‘m’ to accelerate.

F = ma

This is our resultant force, F. Thus, we can write:

R = ma

This implies that the resultant force R has the same direction as a and an amount equal to the product of ma.

## Newton’s First Law of Motion

The first law of motion states that an object at rest ends to stay at rest, and an object in motion tends to stay in motion unless acted upon by an imbalanced force.

If there is an uneven force, there will also be a resulting force, which will cause the object to accelerate. Newton’s Second Law states that the magnitude and direction of the unbalanced force, as well as the mass of the object, will determine the magnitude and direction of the acceleration.

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## Newton’s Second Law of Motion

According to Newton’s second law of motion, an object’s force equals its mass times its acceleration (a). It can be expressed mathematically as

F = ma

This can also be applied as a formula for resultant force. This formula can determine how a resultant force will impact an object’s motion.

## Resultant Force Example

**Question:** When three forces are exerted on an item simultaneously—for example, 80 N, 100 N, and 30 N, and the 30 N force is opposite to the other two forces, what is the F_{R}?

**Solution:**

Given:

F_{1} = 80 N

F_{2} = 100 N

F_{3} = -30 N

F_{3} has a negative value Because it acts in opposition to the other two forces.

The formula for resultant force is

F_{R} = F_{1}+F_{2}+F_{3}

F_{R} = 80 + 100 – 30

**F _{R} = 150 N**