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Normal force in Ferris wheel

  1. Dec 6, 2011 #1
    1. The problem statement, all variables and given/known data
    The original problem is
    Figure P6.61 shows a Ferris wheel( I have attached the image) that rotates four times
    each minute. It carries each car around a circle of diameter
    18.0 m. (a) What is the centripetal acceleration of a
    rider? What force does the seat exert on a 40.0-kg rider
    (b) at the lowest point of the ride and (c) at the highest
    point of the ride? (d) What force (magnitude and direction)
    does the seat exert on a rider when the rider is
    halfway between top and bottom?

    I have already done a), b) and c) with no problem. I also have a solution manual to check and I know that I am correct.

    For d) This is my reasoning
    [tex]\begin{array}{l}
    \sum {{F_r} = m{a_r} = (\ddot r} - r{\left( {\dot \theta } \right)^2}) = \frac{{ - m{v^2}}}{r} = - mg\sin (\theta ) + n\\
    n = mg\sin (\theta ) - \frac{{m{v^2}}}{r}\\
    \theta = 0,n = \frac{{ - m{v^2}}}{r}
    \end{array}[/tex]

    however, this is not what the solution manual says. This is what the solution manual says:

    [tex]n = m\sqrt {{g^2} + {a_r}^2} [/tex]

    I am not dealing with the numbers yet. I want to know why I am wrong and the solution manual is correct. Thankyou.
     

    Attached Files:

  2. jcsd
  3. Dec 6, 2011 #2
    because the direction of the gravity and the acceleration are not in the same direction.
     
  4. Dec 6, 2011 #3

    Delphi51

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    Homework Helper

    I don't understand the sin(θ) in your answer.
    It is easy to see the book answer. The seat has to push up with force mg to cancel weight. And it also has to push in with ma to provide the centripetal force. Combine those with the Pythagorean theorem to get its answer.
     
  5. Dec 6, 2011 #4
    it is obviously true that the gravity and the acceleration are not acting in the same direction. However, my solution does not imply that they are acting in the same direction. I have put a figure for clarification.

    The forces acting in the radial direction are
    mgsinθ and n which are both point into the center
     

    Attached Files:

  6. Dec 6, 2011 #5

    Delphi51

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    Homework Helper

    For part (d), isn't θ = 0?
     
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