Question

Three forces act on a particle that moves with a constant velocity. Two of these forces are: F1 = 2.0i + 4.0j - 2.0k and F2 = -8.0i + 9.0j - 8.0k, all components expressed in N.
What is the magnitude of the third force?

Answer 1

Answer:

17 N

Explanation:

Constant velocity means acceleration is 0.

If acceleration is 0, then the net force is 0.  Which means the i components add up to 0, the j components add up to 0, and the k components add up to 0.

0 = 2.0 N − 8.0 N + Fi

Fi = 6.0 N

0 = 4.0 N + 9.0 N + Fj

Fj = -13 N

0 = -2.0 N − 8.0 N + Fk

Fk = 10. N

The magnitude of the force is:

F² = Fi² + Fj² + Fk²

F² = (6.0 N)² + (-13 N)² + (10. N)²

F = √305 N

F ≈ 17 N