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Question about Centripetal Force

  1. May 22, 2016 #1
    1. The problem statement, all variables and given/known data
    Question 2.b. from this paper - http://www.sqa.org.uk/files_ccc/PhysicsEQPAH.pdf

    2. Relevant equations
    let theta = x
    Tcosx = mg
    Tsinx = 2.5 (2.5 is the centripetal force)

    3. The attempt at a solution
    I rearranged the above equations and got 52 degrees as my answer. The mark scheme(at the bottom of the same document says it's 36 degrees.
     
  2. jcsd
  3. May 22, 2016 #2
    Maybe you can write down your way to find the angle?
    You use the information you gave to get ##\tan \theta?##
     
  4. May 22, 2016 #3
    I did that and I got 52 degrees as my answer. The mark scheme says 36 but I'm not too sure if they used the correct value for mass.
     
  5. May 22, 2016 #4

    PeroK

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    You will need to show your working for people to help you properly. You haven't said at all how you use the angular velocity, for example.
     
  6. May 22, 2016 #5
    F = mrw^2
    F = 0.2(0.35)(6)^2
    Central force = 2.5 N
    Let Tension = T and the angle theta = x
    From the diagram, Tcosx = mg
    Tsinx = central force
    hence Tsinx = 2.5
    Dividing the first eq by the second:
    Tsinx/Tcosx = 2.5/mg
    Simplifying gives tanx = 2.5/mg
    Weight, mg, = 0.2 x 9.8 (0.2kg is the mass of the plane)
    hence tanx = 1.28
    x = 52 degrees.
     
  7. May 22, 2016 #6

    PeroK

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    You're correct. You can see in the solution that they put ##0.35## for the mass. The funny thing is that the answer is independent of the mass of the plane! There was never any need to use the mass. I guess even the people who set these questions don't like algebra!
     
  8. May 22, 2016 #7
    Ahh thank you for the clarification! Yeah the Scottish qualifications board are subpar compared their English counterparts.
     
  9. May 22, 2016 #8

    PeroK

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    I can't believe that!
     
  10. May 22, 2016 #9
    I also got 52 degrees as my answer.
     
  11. May 24, 2016 #10

    haruspex

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    It's worse than that. For part b they used the centripetal force calculated in part a. In part a, the correct mass was used, but in part b they got confused between the mass number, 0.2, and the radius number, 0.35. So in their calculation the masses did not cancel, which is why they got the wrong answer for the angle.
    It's also a bit naughty that you have to pretend the plane develops no lift.
     
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