diploma applied physics1

Two forces of 3N and 2N are acting at an angle of 45 to each other. Find the magnitude and direction of the resultant force?

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  1. 3 in x direction

    2 /sqrt 2 in x and 2/sqrt2 in y

    x force = 3 + 2/sqrt2
    y force = 2/sqrt 2

    }F} = sqrt [ (3 + 2/sqrt2)^2 + 9 ]

    tan angle above x axis = [ (2/sqt2)/(3 +2/sqrt2)]

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  2. or

    complete the parallelogram
    r^2 = 3^2 + 2^2 - 2(3)(2)cos135°
    = 13 - 12(-1/√2)
    r = appr 4.6 N

    or

    direction vector = (3,0) + (2cos45, 2sin45)
    = (3,0) + (1.414, 1.414) = (4.414 , 1.414)
    magnitude = √(4.414^2 + 1.414^2) = appr 4.6

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