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Circulation motion problem?

  1. Oct 29, 2012 #1
    1. The problem statement, all variables and given/known data
    A giant wheel, 40m in diameter, is fitted with a cage and platform on which a man can stand.
    The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by
    the man on the platform is equal to his weight. The speed of the man is:
    X is located at the top of the vertical wheel.
    A. 14m/s
    B. 20m/s
    C. 28m/s
    D. 80m/s
    E. 120m/s

    2. Relevant equations
    Fn + Fg = ma


    3. The attempt at a solution
    Well it states the normal force is mg. So I got 2mg = m(v^2/r)
    which I got that v = 28 m/s.
    But the answer key says it's b.
     
  2. jcsd
  3. Oct 29, 2012 #2
    any ideas
     
  4. Oct 29, 2012 #3
    your method is correct I believe you just made a computational error.
     
  5. Oct 29, 2012 #4
    I see no image.
     
  6. Oct 29, 2012 #5
    it's 2mg = mv^2/r
    so v = sqrt (2gr) which is sqrt(784) = 28.

    I don't know how to put an image up.
    Basically it's just a vertical circle and point X is at the top of it.
     
    Last edited: Oct 29, 2012
  7. Oct 29, 2012 #6
    any ideas
     
  8. Oct 29, 2012 #7
    It appears to me that you are using the diameter in your calculation rather than the radius.

    2mg = m*v^2/r
    v = sqrt(2gr)
    v = sqrt(2*(9.8m/s^2)*20m)
    v = sqrt(392) = 19.798 which rounds up to 20 m/s

    If you do the same math with r = 40 you get 28 m/s. However, the question states that the diameter is 40, so the radius must be 20.
     
  9. Oct 29, 2012 #8

    rl.bhat

    User Avatar
    Homework Helper

    Take g = 10 m/s^2. Then 2gr = ? ( 2r = diameter)
     
  10. Oct 30, 2012 #9
    the reason you keep getting sqrt(784) is because you are using 40m for radius when you should be using 20m
     
  11. Oct 30, 2012 #10
    ohhhh lol thanks.
     
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