Two forces A and B act at a point O. A=30 N at 60 degree and B= 40 N at 120 degree, relative to x-axis. Calculate the magnitude and direction of the resultant force using the method of perpendicular components.
Fx = 30 cos 60 - 40 cos 60
Fy = 30 sin 60 + 40 sin 60
F = sqrt (Fx^2 + Fy^2)
Tan theta = Fy/Fx
Note - Theta is in quadrant 2 because 40>30
Use 180 - the magnitude of the angle
To calculate the magnitude and direction of the resultant force using the method of perpendicular components, we need to resolve each force into its x and y components.
First, let's find the x and y components of force A:
Fx(A) = A * cos(60°)
= 30 N * cos(60°)
= 15 N
Fy(A) = A * sin(60°)
= 30 N * sin(60°)
= 25.98 N
Next, let's find the x and y components of force B:
Fx(B) = B * cos(120°)
= 40 N * cos(120°)
= -20 N
Fy(B) = B * sin(120°)
= 40 N * sin(120°)
= 34.64 N
Now we can find the x and y components of the resultant force by adding the corresponding components of A and B:
Fx(Resultant) = Fx(A) + Fx(B)
= 15 N - 20 N
= -5 N
Fy(Resultant) = Fy(A) + Fy(B)
= 25.98 N + 34.64 N
= 60.62 N
The magnitude of the resultant force can be found using the Pythagorean theorem:
Magnitude = sqrt((Fx(Resultant))^2 + (Fy(Resultant))^2)
= sqrt((-5 N)^2 + (60.62 N)^2)
= sqrt(25 N^2 + 3682.1444 N^2)
= sqrt(3707.1444 N^2)
= 60.90 N
Finally, we can find the direction of the resultant force using trigonometry:
Direction = arctan(Fy(Resultant) / Fx(Resultant))
= arctan(60.62 N / -5 N)
≈ -85.56°
Therefore, the magnitude of the resultant force is approximately 60.90 N, and its direction is approximately -85.56° relative to the x-axis.