Question

A force vector F1 points due east and has a magnitude of 200 Newtons, A second force F2 is added to F1. The resultant of the two vectors has a magnitude of 400 newtons and points along the due east/west line. Find the magnitude and direction of F2. Note that there are two answers.

Answer 1

To find the magnitude and direction of F2, we use vector addition. F2 can either be 200N due east to add up to the resultant force, or 600N due west to cancel out F1 and still end up with the 400N resultant force due east.

Step-by-step explanation:

To find the magnitude and direction of F2, we can use vector addition. Since the resultant force is 400 Newtons due east and F1 is 200 Newtons due east, F2 can have two possible orientations based on vector addition. In one scenario, F2 is also acting due east, and in the second scenario, it is acting due west.

For F2 acting due east, the magnitude of F2 is simply the difference between the resultant force and F1, so:

F2 = 400N (resultant force) - 200N (F1) = 200N (due east)

For F2 acting due west, it must be larger than the resultant force to still end up with a net 400N due east. So, the magnitude of F2 is:

F2 = 400N (resultant force) + 200N (F1) = 600N (due west)

Thus, the two possible magnitudes and directions for F2 are 200N due east or 600N due west.

Answer 2

A force vector F1 points due east and has a magnitude of 200 Newtons, A second force F2 is added to F1. The resultant of the two vectors has a magnitude of 400 newtons and points along the due east/west line. Find the magnitude and direction of F2. Note that there are two answers. The given values are
F1 = 200 N F2 =? Total = 400 N

Solution: F1 + F2 = T 200 N + F2 = 400N
F2 = 400 - 200
F2 = 200 N