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Applications of Newton's Laws

  1. Apr 26, 2005 #1
    Hello all,

    I never really had a great deal of trouble with physics until just recently and this place looks like a great place to learn. I am having problems with the following question:

    A frictionless track is to be built as shown, with L=3.20 m and H=2.90 m. In order to get the cart to slide from the top to the end of the track in the minimum time, how long should the distance D be? Assume that the speed of the cart on the horizontal surface is the same as at the bottom of the ramp.
    Hint: A minimum or maximum value can be found using derivatives.
    A picture to go along with the question

    How would I go about in setting this problem up? I am just clueless one where to start. I believe that I have to set up some type of formula, take the derivative of it and solve for D?

    Thank you for your time and help.
    Last edited: Apr 26, 2005
  2. jcsd
  3. Apr 26, 2005 #2


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    Science Advisor
    Homework Helper

    Some hints:

    No friction means energy is conserved.
    Acceleration for frictionless inclines is constant
    Average velocity is easy to calculate when acceleration is constant
    Average velocity is distance divided by time.
    Total path length is a fairly easy trig problem

    Tell us what you think needs to be done
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