Question

Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 200 N and b = 400 N. Round your answers to one decimal place.)

Answer 1

Answer: R = 346.4N and angle 30° to the horizontal negative axis

Explanation:

To find the resultant force, we need to sum up the forces on the vertical and horizontal axis.

For the horizontal axis;

Rx = -b + acos60

Rx = -400N +200cos60

Rx = -400N +100N

Rx = -300N

For the vertical axis;

Ry = asin60 = 200sin60

Ry = 173.2N

The resultant force R can be given as;

R = √(Rx^2 +Ry^2)

R = √((-300)^2 + 173.2^2)

R = 346.4N

Angle z can be written as

Tanz = Ry/Rx

z = taninverse (Ry/Rx)

z = taninverse (173.2/300)

z = 30°