Resultant Force

What is Resultant Force?

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

Download Formulas for GATE Mechanical Engineering - Machine Design

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 = F₁+F₂+F₃

Where,

Three forces acting in the same direction on an object are F₁, F₂, and F₃.

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 "tends 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.

Download Formulas for GATE Mechanical Engineering - Manufacturing Engineering and Materials

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:

F₁ = 80 N

F₂ = 100 N

F₃ = -30 N

F₃ has a negative value Because it acts in opposition to the other two forces.

The formula for resultant force is

F_R = F₁+F₂+F₃

F_R = 80 + 100 – 30

F_R = 150 N