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Centripetal Acceleration

  1. Sep 20, 2008 #1
    1. The problem statement, all variables and given/known data

    An amusement park ride carries riders in a horizontal circle with radius 5m.

    1) If the centripetal acc. is limited to .4 g for safety, what is the max tangential speed?
    2) If the tangential speed is doubled, what is the new acceleration?

    2. Relevant equations

    A= v^2/r

    3. The attempt at a solution

    1) (.4g(5m))^(1/2)
    max speed = 1.41 m/s

    2) A = 2root2 m/s / 5m = 1.6 m/s^2

    Does this look right?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 20, 2008 #2


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  4. Sep 20, 2008 #3
    I wasn't sure because the next problem refers to a bike traveling around a circular curve and asks for acceleration. I was going to do the same thing, but there's a note next to the question that says "Remember this is a vector!". Why is that a vector and not this?
  5. Sep 20, 2008 #4


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    I don't believe this is correct; I think you forgot to multiply by the factor of g.

    The acceleration started out as (0.4 g) which is about 4m/s^2, and increasing the speed will not make the acceleration decrease.
  6. Sep 20, 2008 #5
    I see. Using 9.8 m/s^2 for g, I get 19.6^(1/2) m/s for part 1 and 15.68 m/s^2 for part 2.
    Still don't understand the next question. How can I calculate acceleration on a curve as a vector?
  7. Sep 20, 2008 #6


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    He's right. I missed the g. Sorry.

    As to the acceleration that's given by v2/r but it's radially directed. If the tangential speed is also accelerating then the value of the tangential acceleration is a vector that is added to the radially directed centripetal acceleration.The resultant vector is then directed at an angle to the radius.

    Btw: the first one is a vector too. It's radial. The question though was only concerned with its magnitude.
    Last edited: Sep 20, 2008
  8. Sep 20, 2008 #7
    Um, not sure I get all that.
    This problem deals with constant speed, so I assume the tangential speed is not increasing.

    It says " A bike travels around a circular curve of radius 80m at a constant speed of 10 m/s.
    1) Calculate the bike's acceleration.
    2) The bike slows uniformly to rewst in 6 seconds. Calculate the tangential acceleration component.
    3) The instant the bike is traveling 8 m/s, determine total acceleration.
  9. Sep 20, 2008 #8


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    In the first part, you calculate the the V2/r as before.

    In the second part the tangential is slowing so there is also a (-) tangential acceleration. This is a vector too.

    The third part is asking you when the V is 8, and it's slowing at the negative tangential rate, what is the sum of those 2 vectors. Since the tangential is negative it will be trailing the radial vector at an angle.
    Last edited: Sep 21, 2008
  10. Sep 20, 2008 #9
    OK, I think I get it. I'm gonna go take a break before I try this. Thanks a lot for helping!
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