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 magnitude of the 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)-10 N
B)-5 N
C)0
D)5 N
E)10 N

Question

Quizplus · Accepted Answer

To make the net force equal to zero, the third force vector must be equal and opposite to the resultant force of force vectors A and B. Resultant force can be found by adding the two vectors together using vector addition.

Using the cosine law, we can find the x and y components of vector A and B:

Ax = 5 cos 30° = 4.33 N 
Ay = 5 sin 30° = 2.5 N

Bx = 5 cos 150° = -4.33 N 
By = 5 sin 150° = 2.5 N

Adding the x and y components separately:

Rx = Ax + Bx = 0 
Ry = Ay + By = 5 N

Thus, the magnitude of the third force vector must be 5 N, in the opposite direction of Ry. Therefore, the correct answer is D) 5 N.

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