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Airplane diving with a circle radius

  1. Jun 27, 2013 #1
    1. A 55 kg airplane pilot pulls out of a dive by following, at constant speed, the arc of a circle whose radius is 320 m. At the bottom of the circle, where her speed is 230 km/h, what is the magnitude of her acceleration?



    2. Relevant equations

    v^2= vi^2 +2a(x-xi)

    3. The attempt at a solution

    i suppose that the plane has a height of the radius and the initial velocity would be 0. Am I wrong? if I am, please tell me!
     
  2. jcsd
  3. Jun 27, 2013 #2
    i think only acceleration will be of gravity.
     
  4. Jun 27, 2013 #3

    CWatters

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    The equation you cite isn't relevant. Hint: centripetal acceleration.
     
  5. Jun 27, 2013 #4

    CWatters

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    No. It's moving in a circle.
     
  6. Jun 27, 2013 #5
    I first saw at the eqn he has given and so declared as the acceleration is of gravity.
    I think you are right it is centripetal acceleration.
     
  7. Jun 27, 2013 #6
    oh! that's true! i totally forgot about centripetal forces!
     
  8. Jun 27, 2013 #7
    You are visualizing the question wrongly I believe. The aeroplane is in the air, and is heading down towards the Earth. The pilot then pulls out of the dive - he will not go vertically up straight away, rather, he will move along a curved arc upwards. You have the radius of this arc, you have the velocity, and you have the mass. This is a straightforward formula application question.
     
  9. Jun 27, 2013 #8
    if centripetal force is Fc= m(v^2/r)
    then
    the centripetal acceleration formula can be derived from the circular acceleration right? a=v^2 /r ,right?
     
  10. Jun 27, 2013 #9
    Yes. All you need to do is divide the force by the object's mass to get it's acceleration.
     
  11. Jun 27, 2013 #10
    really? so i just do:

    Fc=m (v^2/r)
    Fc/m=a ? i already got confused!

    they are giving me:
    m=55kg
    r=320m
    v=230km/h

    and a=v^2/r, wouldn't it be easier to just substitute the values in this formula?
     
  12. Jun 27, 2013 #11
    You don't need the mass to calculate the acceleration. You may use the formula in the last line. All the same thing really.
     
  13. Jun 27, 2013 #12

    CWatters

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    The answer is not just the centripetal acceleration :-)
     
  14. Jun 27, 2013 #13
    they want me to find the magnitude of her acceleration, which tells me that they only want a numerical value without a direction, so if they are not asking only for centripetal acceleration then what is it!?
     
  15. Jun 27, 2013 #14

    CWatters

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    In level flight a pilot experiences 1g.
     
  16. Jun 27, 2013 #15
    Why do you say that?
     
  17. Jun 27, 2013 #16

    CWatters

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    I take it back. She feels like she is accelerating at v^2/r + g but is actually only accelerating at v^2/r.
     
  18. Jun 27, 2013 #17
    so how this affects the acceleration? would it be a=(centripetal accel.)(gravity) ??
     
  19. Jun 27, 2013 #18

    haruspex

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    No, you already have the answer in the last line of your post #10.
    Acceleration is completely determinable by knowing the position as a function of time. With that information, the forces that led to that pattern of movement become irrelevant.
     
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