1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Test review

  1. Dec 13, 2013 #1
    1. The problem statement, all variables and given/known data
    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

    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]
    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.
    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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted