physics

A uniform pole 7m long and weighing 10kg is supported by a boy 2m from one end and a man 3m from the other end.At what point must a 20kg weight be attached so that the man would support thrice as much weight as the boy?

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  1. from left end where x = 0
    b up at x = 2.0
    10 down at x = 3.5
    m up at x = 4.0
    20 down at x = x
    and
    m = 3 b
    ===================
    forces up = forces down
    b + m = 10 + 20 = 30
    moments clockwise = moments counterclockwise about x = 0
    10*3.5 + 20 x = b * 2 + m *4
    so
    20 x = 2 b + 4 m -35
    b + m = 30
    m = 3 b
    -----------------------------
    b + 3 b = 30
    b = 30/4 = 15/2 = 7.5
    m = 3 b = 22.5
    then
    20 x = 2 b + 4 m -35
    20 x = 15 + 90 - 35 = 70
    x = 7/2 = 3.5

    LOL right at the middle
    check
    now we have 22.5+ 10 = 32.5 down at the middle
    b*distance to middle = 22.5 * m's distance to middle ?
    7.5 * (3.5-2) = 22.5 * (4.0 - 3.5)?
    7.5 * 1.5 = 22.5 * .5 ?
    YES ! Caramba :)
    (should have seen it right from the start though)

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  2. thanks but is this answer correct

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