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26 November, 22:39

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?

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  1. 26 November, 23:46
    0
    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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