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Thread: Mechanics Vector Assessment

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    Default Mechanics Vector Assessment

    Ann and Beryl are both pushing a piano. Ann pushes in the direction 4i + 3j and Beryl in the direction 12i + 5j, where i and j are the standard unit vectors. Together they produce a force of (68i + 33j) N so that p(4i + 3j) + q(12i + 5j) = 68i + 33j, where p and q are constants. Calculate the force with which Beryl pushes.

    Thanks in advance

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    4pi + 3pj + 12qi + 5qj = 68i + 33j

    equate vector components:
    4p + 12q = 68 (1)
    3p + 5q = 33 (2)'

    Solve simultaneously for p,q

    So then Beryl's force = (12qi + 5qj) Newton

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    Quote Originally Posted by ZephyrsFury View Post
    4pi + 3pj + 12qi + 5qj = 68i + 33j

    equate vector components:
    4p + 12q = 68 (1)
    3p + 5q = 33 (2)'

    Solve simultaneously for p,q

    So then Beryl's force = (12qi + 5qj) Newton
    Never thought of that!! Thanks man

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    Usually if force is the final answer, you might want to just give the magnitude
    |F| = sqrt(x^2 + y^2)

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    Quote Originally Posted by marpis View Post
    Usually if force is the final answer, you might want to just give the magnitude
    |F| = sqrt(x^2 + y^2)
    Force is a vector; unless specifically stated otherwise, you should provide a direction too.

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    Quote Originally Posted by ZephyrsFury View Post
    Force is a vector; unless specifically stated otherwise, you should provide a direction too.
    If Ann and Beryl pull the piano, I think 500N is better answer than 244Nx4/3i + 333Nx5j
    I know those won't give the same answer.

    An exception is if the plane is 2-dimensional, so there are only + and - directions.

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    Quote Originally Posted by marpis View Post
    If Ann and Beryl pull the piano, I think 500N is better answer than 244Nx4/3i + 333Nx5j
    I know those won't give the same answer.

    An exception is if the plane is 2-dimensional, so there are only + and - directions.
    Vector form is the more correct answer, especially since you're given the direction of the force in the question. If it were 1D then yeah a sign is usually sufficient as long as you define which direction is positive.

    Besides in this case, its easier just to write the answer in vector component form. Why bother doing anything extra?
    Last edited by ZephyrsFury; 11-18-2010 at 01:24 PM.

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