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Normal Force - Car over a Circular Arc

  1. Oct 20, 2010 #1
    1. The problem statement, all variables and given/known data
    An 1850 kg car passes over a bump in a road that follows the arc of a circle of radius 40.60 m as seen in the figure below.

    a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at 14.9 m/s?

    b) What is the maximum speed the car can have as it passes this highest point before losing contact with the road?


    2. Relevant equations
    N-mg=mv^2/r
    mg=mv2/r

    3. The attempt at a solution
    I tried using the equation above and got 28246N, but that was not correct.
    For part b) I got 6.37m/s. Also not correct.
     
  2. jcsd
  3. Oct 20, 2010 #2

    Doc Al

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    Staff: Mentor

    This equation is not quite correct. Hint: What's the direction of the acceleration?
     
  4. Oct 20, 2010 #3
    Do I need a negative sign?
    So like this? mg-N=mv^2/r
     
  5. Oct 21, 2010 #4

    Doc Al

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    Staff: Mentor

    Yes.

    Using your previous convention of positive for up, I'd write it as:
    N - mg = - mv^2/r

    The centripetal acceleration (magnitude v^2/r) points toward the center of the circle, which in this case means it points down. Thus it should have a minus sign.
     
  6. Oct 21, 2010 #5
    Thanks a lot for the help Doc Al!
    If you have time to answer https://www.physicsforums.com/showthread.php?t=440062"too, that'd be great:
     
    Last edited by a moderator: Apr 25, 2017
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