To find the resultant of two forces, we can apply the law of cosines which is used in physics to calculate the resultant vector of two forces not acting in the same direction:
The formula of the law of cosines is as follows:
R = sqrt(F1^2 + F2^2 + 2*F1*F2*cos(Theta))
Let me break it down for you:
Step 1: We substitute the known values into the equation.
Here,the forces F1 and F2 are given as 50 Newton and 30 Newton, respectively, and the angle θ is given as 60°. However, we first need to convert this angle from degrees to radians. In one circle, there are 2π radians, which is equal to 360°. This implies that 1° equals π/180 radians. So 60° would be π/3 radians.
Step 2: Calculate respective forces and angle values.
Force F1 squared is (50^2) = 2500 N².
Force F2 squared is (30^2) = 900 N².
Step 3: To find the component 2*F1*F2*cos(Theta), we plug in the known values and get 2*50*30*cos(π/3) = 1500 N².
Step 4: We now plug everything back into the Law of Cosines and simplify:
R = sqrt(2500 + 900 + 1500)
R = sqrt(4900)
Therefore, the magnitude or resultant of the two forces when they're at a 60° angle from each other is 70.0 Newtons.