Resultant Force Formula

Resultant Force Formula

When numerous forces act on an object, the resultant force is the force that creates the same acceleration as all of the other forces combined.

What is Resultant Force?

The entire effective force operating on a body, as well as their directions, is known as the resultant force. The resultant force must also be zero when the item is at rest or travelling at the same velocity.

Because all of the forces are acting in the same direction, the resultant force for all forces should be the same.

The Pythagorean Theorem can also be used to compute the resultant force if one force acts perpendicular to the others.

Resultant Force formula

The Resultant force formula is stated by

F_R=F₁+F₂+F₃

Where,  F₁,F₂,F₃ are the force acting in the same direction on a body

The resultant force formula is stated as, if F₂ is perpendicular to F₁.

It’s worth noting that this isn’t simply the sum of the forces’ magnitudes. However, the total of the forces as vectors is far more appropriate. This is due to the fact that vectors contain both magnitude and direction, which we must consider when calculating the sum.

As a result, if an item has no force, the resultant force will also be zero, according to the preceding equation. If an item is only subjected to one force, the resultant force will be the same as the original force. As a result, instead of performing the usual sum, we must conduct the vector sum of the forces.

Solved examples:

Question 1: Consider the following three forces: 50 N, 60 N, and 20 N. These are all acting on the same body at the same time. The direction of 20 N is diametrically opposed to the other two. Calculate the resulting force.

Solution:

F₁=90N

F₂=60N

F₃=-20N

Because it opposes the other two forces, force F₃is negative.

The following formula can be used to calculate the resultant force:

F_R=F₁+F₂+F₃

F_R=50+60-20

F_R=90N

Thus the resultant force is 90N

Question 2: If perpendicular forces of 4 N and 9 N act on an item. Then calculate the force as a result.

Solution:

F₁= 4N

F₂ = 9N

These two are perpendicular to each other. As a result, the resultant force will be calculated as follows:

=√97

=9.84

Thus, the resultant force will be 9.84 N

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