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# How to Find Resultant Force of Two Forces at an Angle

## Introduction

The formula below will help you understand how to find resultant force of two forces

R2 = F12+ F22

When two forces are acting at an angle, we will use the formula

R2 = F12+ F22 – 2 F1 F2 Cos ( 1800 – θ )

Where Forces F1 and F2 are acting at each other at an angle

## Explanation

Therefore, when you have two forces say 5N and 7N heading towards north ( the same ) direction and you are required to find the resultant of the two forces ( total force ). What you need to do is to add the two forces together to get the resultant force.

Forces F1 and F2 in the same direction where F1 = 5N and F2 = 7N

R = F1 + F2 = 5N + 7N = 12N

Forces F1, and F2 in the Same Direction While F3 is in Opposite Direction and F1 = 5N, F2 = 10N and F3 = 3N

R = F1 + F2 + F3 = 5N + (-3N) = 12N

F3 is in opposite direction and this is the reason we have (-3N) which shows that any force that is in negative direction is to be subtracted.

## Problem

An object is acted upon by two forces of 5N and 12N. Calculate the resultant of the forces acting at an angle of 1200 to each other.

[UTME 2019]

Solution

To calculate the resultant of the two forces, we need to extract our data from the above question

Data:

From the question above

We have two forces and they are as follows

F1 = 5N

F2 = 12N

The resultant ( R ) = ?

Angle between the two forces ( θ ) = 1200

Now, if we apply the formula

R2 = F12+ F22 – 2 F1 F2 Cos ( 1800 – θ )

Now, substitute the values of F1, F2 and θ into the above equation.

We now haveR2 = 52 + 122 – 2 x 5 x 12 Cos ( 1800 – 1200 )

which shows that R2 = 25 + 144 – 120 Cos 600

Hence, R2 = 169 – ( 120 x 0.5 )

We will now arrive at R2 = 169 – 60

After subtraction, we will have R2 = 109

By taking square root of each side we will have R = √109

And our final answer is R = 10.44N

Therefore, the resultant of the two forces acting between an angle of 1200 is Ten ( 10N ) newton.

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