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?
1 answer:
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
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