Solving for Frictional Force in Banked Curve Problem

[TheRaiderNati]

Homework Statement

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?

Homework Equations

a_{cent}=\frac{v^{2}}{R}
F_{cent}=m*a_{cent}

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_{x} = Wsin(25) + f = m*a_{cent}
(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_{y} = 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.

 

[grzz]

If the diagram of the forces is shown one finds it easier to give help.

 

[TheRaiderNati]

No diagram of the forces was given. Only a picture showing a car on a banked curve.

 

[grzz]

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.

 

[grzz]

I think that the answers for (1) and (2) are 282N and 2290N respectively.

 

[TheRaiderNati]

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.

 

[grzz]

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.