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Radial acceleration quesiton

  1. Jun 20, 2008 #1
    Howdy all, I had a quick question:

    An example problem in my physics book (Physics for Scientists and Engineers, 6th edition, Serway and Jewett) is going over tangential and radial acceleration (it is example 4.9, if you've got a copy lying around).

    The question is as follows:
    A car exhibits a constant acceleration of .3 m/s^2 parallel to the roadway. The car passes over a rise in the roadway such that the top of the rise is shaped like a circle of radius 500m. At the moment the car is at the top of the rise, its velocity vector is horizontal and has a magnitude of 6.0 m/s. What is the direction of the total acceleration vector for the car at this instant?

    If someone requests the picture, I can use my scanner to help the discussion along, just lemme know.

    My question comes from their use of the radial acceleration - they plugged the tangential speed (6 m/s) into v^2/r, it is in the negative radial direction, so acceleration(radial)=-.0720m/s^2.

    That is the tangential acceleration coming from moving in a circle at a constant speed. Yeah. But if this car was on Earth, wouldn't we add that to the acceleration due to gravity, which is also in the negative radial direction? That is how I did the problem, then looked at their answer and was confused as to why the hell they wouldn't include acceleration due to gravity here.

    Thanks for the help all!
  2. jcsd
  3. Jun 20, 2008 #2

    Doc Al

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    You mean the radial acceleration.
    No, the radial acceleration is a kinematic quantity that you calculate based on the given information (speed and radius). If the car were in free fall, then its acceleration would be g downward. But it's not. Gravity is not the only force acting on the car--the road pushes up, negating much--but not all--of the force of gravity.

    What if the car were just traveling along a horizontal road with no bump in the road? What would its vertical acceleration be? Would you add g in that case?
  4. Jun 20, 2008 #3


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    Hi TRAyres! :smile:

    I'll just add this to what Doc Al says:

    Acceleration is geometry.

    Force is physics.

    Once you know that a body moves in a certain way, then its acceleration is a matter of geometry, and has nothing to do with forces. :smile:
  5. Jun 20, 2008 #4
    Hot damn, thank you both! Now I'm genuinely glad I asked.
  6. Jun 20, 2008 #5


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    The vertical acceleration comes from gravity and the normal force. Their vector sum will be (v^2/r)
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