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Math Help - forces/couple

  1. #1
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    Question forces/couple

    particle of mass m kilograms is acted on by two forces F[1] and F[2] with magnitudes 3*sqr-root 5 newtons and sqr-root 5 newtons and directions parallel to the vectors i+2j and i-2j respectively.
    The particle is initially at a position given by the vector 2i+j

    i was told to calculate the cartesian components of F[1] and F[2] and hence calculate the total force F[1] + F[2], acting on the particle in component form

    MY SOLUTION

    The vector i+ 2j has length sqrt{1^2+ 2^2}= sqrt{5}[
    A vector in that direction, with length is just 3 times that: 3i+ 6j. That's the first force vector.
    Similarly, the vector i- 2j also has length root5 so that is the second force vector. The total force, then, is F1+ F2= (3i+ 6j)+ (i- 2j)= 4i+4j

    from there i need to show the couple of the total force about the point with position vector i is zero.....so the total force is 4i+4j ............................

    I would appreaciate a explanation to how to tackle this Q, so I can do it myself................but im assuming that it is a single force and a couple cannot be put in equilibrium by a single force so it must be zero? is that correct???????
    Last edited by dopi; July 14th 2006 at 03:12 PM.
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  2. #2
    Super Member malaygoel's Avatar
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    Couple is given by : r X F, where r is a vector from the position of particle to the point of application
    and F is the force vector.
    Couple can be zero (if any of following conditions arise):
    1)magnitude of r is zero
    2)magnitude of F is zero
    3)F and r are parallel or antiparallael

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