Force vector A has a length of 5 N and an angle of 30 $\circ$ with respect to the positive x-axis.Force vector B has a length of 5 N and an angle of 150 $\circ$ with respect to the positive x-axis.What is the direction of a third force vector which must be added to A and B in order to make the net force equal to zero? (All three forces act on the same object). A)0^o B)90^o C)180^o D)270^o E)None of the above are correct.

Question

Quizplus · Accepted Answer

To make the net force equal to zero, the third force vector must be equal in magnitude but opposite in direction to the vector sum of A and B.

First, we find the x and y components of A and B:

Ax = 5 cos 30° = 4.33 N 
Ay = 5 sin 30° = 2.50 N 
Bx = 5 cos 150° = -4.33 N 
By = 5 sin 150° =  -2.50 N

Next, we add the x and y components separately to find the vector sum:

Rx = Ax + Bx = 0 
Ry = Ay + By = 0

This means that the vector sum of A and B is in the negative y direction (180° from the positive y-axis). Therefore, the third force vector must be in the opposite direction, which is in the positive y direction. The angle between this vector and the positive x-axis is 270°, so the answer is (D) 270°.

Force Vector a Has a Length of 5 N and an Angle