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Forces with direction and magnitude

  1. Jul 13, 2006 #1
    A 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


    i got F[1] as:
    y= 3*(root5)*sin(theta)

    i got F[2] as:
    y= (root5)*sin(theta)

    and then F[1] + F[2] as:
    F[x] = 4*(root5)*cos(theta)
    F[y] = 4*(root5)*sin(theta)

    i was just wondering if i have done it right ???

    from there i need to show the couple of the total force about the point with position vector i is zero..................does any understand this part or know how to do it ??????
  2. jcsd
  3. Jul 13, 2006 #2


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    Science Advisor

    But you don't know theta, do you? So those formulas a pretty much useless. Yes, you could calculate theta from the vectors they give you but that would be like going east around the world to get to a destination 1 mile west of you!

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

    For the second question I recommend that you first look up the definition of "couple of a force about a point".
  4. Jul 14, 2006 #3
    need my answer checked!!

    i've looked at the definition n various examples..but they are not similar to the one im doing so i cant really figure out how to show the couple of the total force about the point with position vector i is zero...

    im assuming that it is a single force...but a couple cannot be put in equilibrium by a single force!

    can some help me with this question...by showing me how to do it or telling me the steps to sove it ....thankz
    Last edited: Jul 14, 2006
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