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Homework Help: Calc 3: Motion in xy plane question

  1. Oct 1, 2009 #1
    1. The problem statement, all variables and given/known data

    In the xy plane, where distances are measured in feet, a 96 lb object is moving from left to right on the curve y=e^-x. At t-0 its speed is 6ft/s and is speeding up at (square root of 8) ft/s^2. what is the total force on it at that point? Give floating point values for the magnitude and angle of inclination of this force.

    2. Relevant equations


    3. The attempt at a solution

    I just don't really know where to begin. i'm sure once i get started on the right track, i can finish it. we know that the point in question is (0,1), and we know v(0)=6 ft/s and a(0)=sqrt8 ft/s^s. and we know y=e^-x, dy/dx= -e^-x, and second derivative= e^-x. the unit tangent is i-j and the unit normal is i+j. Now i'm stuck. do i need to use the breakdown of a into componets equation with the curvature and whatnot?
  2. jcsd
  3. Oct 1, 2009 #2


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    Science Advisor

    F= ma is a very good place to start! You know the object is moving on the curve [itex]y= e^{-x}[/itex] so its velocity vector must be tangent to that curve. And you have already calculated that the derivative is [itex]y'= -e^{-x}[/itex] so you know a vector tangent to that is [itex]x\vec{i}- e^{-x}\vec{j}[/itex] for each x. Further you are told that the speed (length of the velocity vector) is 6 ft/sec at t= t_0 and increases at the constant rate of [itex]2\sqrt{2}[/itex]: the speed at time t is [itex]6+2\sqrt{2}(t- t_0)[/itex]. That means that the velocity vector at time t is parallel to [itex]x\vec{i}- e^{-x}\vec{j}[/itex] (and so is of the form [itex]xv\vec{i}- ve^{-x}\vec{j}[/itex] which has length [itex]v\sqrt{x^2- e^{-2x}})= 2\sqrt{2}[/itex]).
  4. Oct 1, 2009 #3
    Alright, thanks! i think i got my answer. i ended up getting an acceleration vector of 11sqrt2 i + 7sqrt2 j. now i just need to multiply that by the mass to get the vector of the force. do i need to convert pounds to slugs? then my total force will be in pounds?
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