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Circular motion A-Level

  1. Jan 29, 2017 #1
    1. The problem statement, all variables and given/known data
    An aircraft flies with its wings tilted, in order to fly in a horizontal circle of radius r. The aircraft has mass 4.00 x 104 Kg and has a constant speed of 250ms-1 . with the aircraft flying in this way, two forces are acting on the plane, P [lift] and W [weight which is given as 3.92*105 N] . P is acting at 35 degrees to the vertical. calculate P

    2. Relevant equations
    centripetal force=mass * velocity2 / radius
    centripetal force= mass * angular speed2 * radius
    angular speed = theta / time
    angular speed = velocity/ radius
    angular speed = 2pi * frequency
    centripetal acceleration = velocity2 / radius
    centripetal acceleration = angular speed2 * radius
    Force = mass * acceleration
    3. The attempt at a solution
    I cant do it. I swear we need more information. can someone enlighten me.
     
    Last edited: Jan 29, 2017
  2. jcsd
  3. Jan 29, 2017 #2

    PeroK

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    What information do you think you need?

    By the way, I think the weight should be ##3.92*10^5N##. Personally I would do this question algebraically and just plug the numbers in at the end. That's also a good way to work out what quantities you do need.
     
  4. Jan 29, 2017 #3
    yes I think that the weight is correct. I couldn't read the sheet correctly.
    the info that I think we need : time or radius
    I am not sure whether we need to plug it into an equation or just use trig??
     
  5. Jan 29, 2017 #4

    PeroK

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    You need to think about the forces involved. There's a key equation that will open up the whole problem. And, by equation I mean two quantities that must be equal.

    Hint: why doesn't the plan fall out of the sky?
     
  6. Jan 29, 2017 #5
    Correct me if I am wrong,
    but can I say that the vertical component of P is PCos(35), and it doesn't fall out of the sky because Weight is equal to PCos(35)
    Therefore, PCos(35) = 3.92 * 105
    So, If we rearrange that equation, P = 3.92*105 / Cos(35) == 321107.6 [1dp]
    ??
     
  7. Jan 29, 2017 #6

    PeroK

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    Yes, that's it exactly. Although, I prefer:

    ##P = \frac{mg}{\cos \theta}##

    or:

    ##P = \frac{W}{\cos \theta}##
     
  8. Jan 29, 2017 #7
    Thanks,
    Could you please explain to me how you came to those equations?
     
  9. Jan 29, 2017 #8

    PeroK

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    I just copied what you had done! I just used letters for the quantities involved instead of plugging in the numbers. There are a lot of advantages to this. Not least, once you plug in the numbers, you lose sight of what is related to what and if you make a mistake, well one number looks very like another, and it is hard to spot an error.

    That said, I thought the question was to calculate ##r##. I see now that all you need is ##P##, which is a lot simpler.

    Is part 2 of the question to calculate ##r##?
     
  10. Jan 29, 2017 #9
    Yes it is.

    but I am pretty sure how to do it

    F=mv2 / r ,, rearrange for r
     
  11. Jan 29, 2017 #10

    PeroK

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    If you post your answer, I can show you the algebraic approach, which might be interesting and/or enlightening!
     
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