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Find the Radius of Curvature

  1. Jan 20, 2014 #1
    1. The problem statement, all variables and given/known data
    The speed of a car increases uniformly with time from 50km/hr at A to 100km/hr at B during 10 seconds.

    The radius of curvature of the bump at A is 40m.

    if the magnitude of the total acceleration of the car’s mass center is the same at B as at A, compute the radius of curvature of the dip in the road at B. The mass center of the car is 0.6m from the road.


    2. Relevant equations
    an=VB2



    3. The attempt at a solution
    Before I solve this problem, I want to get some conceptual questions out of the way.
    It says the magnitude of acceleration is constant, does this mean that the normal and tangential components of acceleration are constant from A to B?
    If so can I just compute an=VA2/ρ at A and use that for an at B?
     
    Last edited: Jan 20, 2014
  2. jcsd
  3. Jan 20, 2014 #2
    Total acceleration is not indicated to be constant. All that is said about total acceleration is that its magnitude is the same at A and B.
     
  4. Jan 20, 2014 #3
    but velocity increases uniformly, wouldn't that imply that the tangential acceleration is constant?
    and if tangential acceleration is constant, and the magnitude of acceleration at A and B are the same, then that must mean the normal acceleration at A and B are equal?
     
  5. Jan 20, 2014 #4
    Velocity is a vector, it cannot increase. The speed does increase uniformly, and that makes the rest of your reasoning correct.
     
  6. Jan 20, 2014 #5
    Ah I see, so when computing normal acceleration at A, ρ is given to be 40meters from the curve, however since the center of mass of the car is .6meters from the surface, I would use VA2/40.6 correct?
     
  7. Jan 20, 2014 #6
    Yes, that looks correct to me.
     
  8. Jan 20, 2014 #7
    Thank you for the help!
     
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