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Car on a banked curve

  1. Nov 24, 2012 #1
    1. The problem statement, all variables and given/known data

    A certain curve on a freeway has a radius of 200m and is banked at an angle of 25°. A 200-kg car moves around the curve at constant speed.

    1. If the speed of the car is 35m/s, what friction force is needed to keep the car moving in a circle?
    2. If the speed of the car is 35m/s, what normal force acts on the car?
    3. If the speed of the car is 35m/s, what is the minimum value of the coefficient of friction?

    2. Relevant equations
    a[itex]_{cent}[/itex]=[itex]\frac{v^{2}}{R}[/itex]
    F[itex]_{cent}[/itex]=m*a[itex]_{cent}[/itex]


    3. The attempt at a solution
    I have been attempting to solve this problem for about a week now but have but hopelessly stuck.

    1. I tried to set up the equation so that the x-component of Weight plus the friction force (since the friction force points inwards) was equal to the Centripetal Force, like so:

    F[itex]_{x}[/itex] = Wsin(25) + f = m*a[itex]_{cent}[/itex]
    (Where f = friction force)

    But I couldn't seem to get the right answer.

    2.I figured that since the car has no vertical acceleration the sum of the net forces in the Y direction should equal to zero. In this case the only forces with Y components are the weight and normal force. Therefore:
    F[itex]_{y}[/itex] = N - Wcos(25) = 0

    However, this also produced an incorrect result.


    3. I know that I can simply divide the force of friction by the Normal force to get the coefficient, so I guess I don't really need help on this one.

    Answers were provided to me for these questions, but I still can't seem to get the same figures:
    1. 2820N
    2. 22900N
    3. 0.123
    3. 0.123

    Thanks in advanced for any help.
     
  2. jcsd
  3. Nov 24, 2012 #2
    If the diagram of the forces is shown one finds it easier to give help.
     
  4. Nov 24, 2012 #3
    No diagram of the forces was given. Only a picture showing a car on a banked curve.
     
  5. Nov 24, 2012 #4
    Usually one starts the solution of this problem with a diagram of the forces.

    So what I meant was the diagram that YOU have to try to do showing these forces.
     
  6. Nov 24, 2012 #5
    I think that the answers for (1) and (2) are 282N and 2290N respectively.
     
  7. Nov 24, 2012 #6
    So I ended up solving the remainder of the questions using the equations I found here.

    Also, the free body diagram on that website was essentially what I had drawn out initially. I think the trigonometry involved was what was throwing me off.

    The only problem I am now having issues solving is finding the minimum possible speed of the car if the coefficient of friction is .20.
    EDIT: Never mind, just figured that one out too. Thanks for the help guys.
     
  8. Nov 24, 2012 #7
    Let us call the coefficient of friction μ. Then the frictional force will be given by
    frictional force = μN where N is the normal reaction of the road on the car.

    I do not think that you will have any problem in finding the speed.
     
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