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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