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Math Help - Mechanics - Help?

  1. #1
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    Mechanics - Help?

    A couple of mechanics questions I jsut cant get my head around;

    1) A light rod of 50cm lies on a horizontal table. A person holds the end of the rod. The rod is subjected to a couple, of moment 40Nm, causing it to rotate upon the table. What force perpendicular to the rod must the person exert through each hand in order to prevent rotation?

    2) A uniform beam AB of mass 10kg and length 4m rests horizontally on two supports, one at A and the other 1m from B. Where must a body of mass 50kg be placed on the beam if it wished to make the reactions at the supports equal?
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  2. #2
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    2) An upward reaction occurs at both supports, Fa and Fb.

    A downward weight force of Fw = 10(9.81) = 98.1 N occurs at the center of the beam.

    Assume the body of mass is placed to the left of the beams center.
    It has a downward force of Fm = 50(9.81) = 490.5 N

    The sum of the forces in the Y (vertical) direction is 0.
    Therefore we have, Fa + Fb = 490.5 N + 98.1 N = 588.6 N
    For Fa = Fb, we have 2 Fa = 588.6N
    Therefore Fa = Fb = 294.3 N

    The sum of the moments about the beams center is 0 (CCW is positive).
    Therefore we have, Fm(x) - Fa(2m) + Fb(1m) = 0
    Subbing in values for Fa, Fb, and Fm and solving for x, we get x = 0.6 m
    Thus the mass should be placed 0.6 meters to the left of the beams center so that the reaction forces can equal eachother.
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