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Car rolling down a track.

  1. Jul 21, 2012 #1
    1. The problem statement, all variables and given/known data
    A car on the frictionless track starts from rest at height h. The tracks valley and hill
    consists of a circular-shaped segments of radius R.
    What is the maximum height h from which the car can start so as not to fly off the track when going over the hill?
    Give your answer as a multiple of R.
    3. The attempt at a solution
    ok I know that its potential energy is mgh when we let it go. And we need to put it at least
    the height of R to make it the top of the hill on the other side.
    But im not sure how fast it can be going and not lift off the ground.
    I know that it would have to exceed its weight. Im not sure how to relate the energy into force.
     

    Attached Files:

  2. jcsd
  3. Jul 22, 2012 #2

    CWatters

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    Think about the path of the car over the top of the hill. It's a curve of radius R so what force do objects moving on a curved path experience?
     
  4. Jul 22, 2012 #3
    ok thanks.
    so now I have
    [itex] \frac{mv^2}{r}=mg [/itex]
    [itex] v=\sqrt{rg} [/itex]
    then
    [itex] mg(h-r)=m\frac{rg}{2} [/itex]
    and this gets me the correct answer.
    thanks for the help .
     
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