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17 February, 11:37

Two forces with magnitudes of 200 and 100 pounds act on an object at angles of 60° and 170° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

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  1. 17 February, 12:20
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    First force F1 = 200 N

    Second force, F2 = 100 N

    θ1 = 60°

    θ2 = 170°

    Take Summation of Forces Horizontal and vertical

    ΣFx = 200cos60° - 100cos (180-170°)

    =200cos60° - 100cos (10°)

    = 1.519 N

    ΣFy = 200sin60° + 100sin (180-170°)

    = 200sin60° + 100sin10°

    = 190.57

    Resultant/Magnitude

    R = √[ (ΣFx) ² + (ΣFy) ²]

    =√[1.519² + (190.57) ²]

    R = 190.576 N

    Direction of resultant force

    θ = arctan [ΣFy / ΣFx]

    θ = 89.54°
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