Find the resultant R of the following forces all acting on the same point in the given directions: 30lb northeast; 70 lb to the south; and 5

Question

Find the resultant R of the following forces all acting on the same point in the given directions: 30lb northeast; 70 lb to the south; and 50 lb 20 degrees north of west.

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Bình An 3 weeks 2021-08-23T23:09:26+00:00 1 Answers 2 views 0

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    2021-08-23T23:11:17+00:00

    Answer:

    net force is 40.8 Lb in direction 50.8 degree South of West

    Explanation:

    As we know that the three forces are given as

    F1 = 30 lb North East

    F2 = 70 lb South

    F3 = 50 lb at 20 degree North of West

    Now we can write in vector form as

    F_1 = 30 sin45 \hat i + 30 cos45 \hat j

    F_1 = 21.2 \hat i + 21.2 \hat j

    F_2 = -70 \hat j

    F_3 = -50 cos20\hat i + 50 sin20 \hat j

    F_3 = -47\hat i + 17.1 \hat j

    now the net force due to above all

    F = F_1 + F_2 + F_3

    F = (21.2 - 47)\hat i + (21.2 - 70 + 17.1)\hat j

    F = -25.8 \hat i - 31.7 \hat j

    magnitude of net resultant force is

    F = \sqrt{25.8^2 + 31.7^2}

    F = 40.8 Lb

    direction of the force is along

    \theta = tan^{-1}(\frac{31.7}{25.8})

    \theta = 50.8 degree

    So net force is 40.8 Lb in direction 50.8 degree South of West

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