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Test review

  1. Dec 13, 2013 #1
    1. The problem statement, all variables and given/known data
    b7mank.jpg
    A man starts riding on a frictionless roller coaster track at initial velocity v[itex]_{o}[/itex]. At point A the radius of the bend is r.

    a) What is the maximum v[itex]_{o}[/itex] such that when the cart gets at point A it stays on the track?
    b) Using you answer in a) what should h' be such that the cart only just makes it to point B?


    2. Relevant equations

    Ei = Ef
    mv^2/r

    3. The attempt at a solution
    So this question was kind of bugging me, and I want to know if I got it right so for the a) part this is what I did firstly

    mgh + (1/2)mv[itex]_{o}[/itex][itex]^{2}[/itex] = mg(2/3)h+1/2mv[itex]^{2}[/itex]
    v = [itex]\sqrt{2gh/3 + Vo^2}[/itex]

    and then since at point be its a circle and its looking for the max velocity until the normal force = 0 I did
    mv^2/r = mg
    v = [itex]\sqrt{rg}[/itex]
    then
    rg = 2gh/3 + v[itex]_{o}[/itex][itex]^{2}[/itex]
    v[itex]_{o}[/itex] = [itex]\sqrt{g*(r-(2/3)h)}[/itex]


    THEN for b) I just used Energy again.
    so
    v = [itex]\sqrt{rg}[/itex]
    Ei = (1/2)mrg + mg(2/3)h
    Ef = mgh'
    h' = r/2 + 2h/3
     
  2. jcsd
  3. Dec 13, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Looks good to me. :thumbs:
     
  4. Dec 13, 2013 #3
    Oh thank you so much!!!!!!!!!This was one of two questions I was unsure of so I just went with my gut on it.
     
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