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15 September, 14:34

Two 20 Newton forces act concurrently on an object what angle between these forces produce a resultant force with the greatest magnitude

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  1. 15 September, 15:01
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    Let θ₁ and θ₂ be the angles between the two forces and the direction of motion.

    To produce motion in the indicated direction, the net force is

    F = 20 cos θ₁ + 20 cos θ₂

    = 20 (cos θ₁ + cos θ₂)

    = 40 cos [ (θ₁+θ₂) / 2] cos[ (θ₁-θ₂) / 2]

    The maximum value of the cosine function is 1, and it occurs when its argument is zero.

    Therefore the maximum value of F occurs when

    θ₁ + θ₂ = 0

    or

    θ₁ - θ₂ = 0

    Add the two equations to obtain

    2 θ₁ = 0 = > θ₁ = 0

    Also, θ₂ = θ₁ = 0

    Answer: The angle between the two forces is zero.
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