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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

How to Find Resultant Force of Two Forces 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.

How do you find the resultant force of two forces at an angle?
How do you find the resultant force of two forces at an angle?

[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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