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Math Help - rollercoaster question about force & postion

  1. #1
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    Lightbulb rollercoaster question about force & postion

    Hi there,

    A rollercoaster car has mass m and it has the postion vector given below when it moves along a certain section of track.

    r(t) = cos(2t)i + sin(2t)j + (15t -3.5t^2)k where i,j & k are cartesian unit vectors and r is postion with respect to time, t (0 < t < 4π)

    show that over the interval avobe that the magnitude of the force exerted on the car is constant.
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  2. #2
    A Plied Mathematician
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    Newton's Law

    Well, I would take two derivatives to obtain the acceleration vector, and then take the magnitude of that resulting vector. If \vec{F}=m\vec{A}, then |\vec{F}|=m|\vec{a}|, since, as Landau proved, mass must be positive. I think you'll find that the magnitude of the force is constant for all time, not just the interval specified.

    Hope this helps.
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