Banked Curves angle theta on highway

  • Thread starter pstfleur
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  • #1
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1. Two curves on a highway have the same radii. However, one is unbanked and the other is banked at an angle theta. A car can safely travel along the unbanked curve at a maximum speed Vo under conditions when the coefficient of static friction between the ties and the road is ms=0.81. The banked curve is frictionless, and the car can negotiate it at the same maximum speed Vo. Find the angle theta of the banked curve.



2. Tan theta= v^2/rg, v=2pie(r)/T



3. Ok Im lost again.. The problem looks like french to me. I know that I need to find the velocity first in order to get my angle, but it doesn't give me any values other than the coefficient of static friction..PLease help me go in the right direction
 

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  • #2
LowlyPion
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1. Two curves on a highway have the same radii. However, one is unbanked and the other is banked at an angle theta. A car can safely travel along the unbanked curve at a maximum speed Vo under conditions when the coefficient of static friction between the ties and the road is ms=0.81. The banked curve is frictionless, and the car can negotiate it at the same maximum speed Vo. Find the angle theta of the banked curve.

2. Tan theta= v^2/rg, v=2pie(r)/T

3. Ok Im lost again.. The problem looks like french to me. I know that I need to find the velocity first in order to get my angle, but it doesn't give me any values other than the coefficient of static friction..PLease help me go in the right direction
The first part tells you what the Radius is.

Then you use the radius to determine the angle of the second curve.
 
  • #3
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The first part tells you what the Radius is.

Then you use the radius to determine the angle of the second curve.

Where? a radius of what? 1?
 
  • #4
LowlyPion
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Where? a radius of what? 1?
No. Draw a force diagram. There are two forces acting on the car on level ground. There is the Frictional force and there is the Centripetal force. You know what the coefficient of friction is, so what is radius in terms of Vo?
 
  • #5
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No. Draw a force diagram. There are two forces acting on the car on level ground. There is the Frictional force and there is the Centripetal force. You know what the coefficient of friction is, so what is radius in terms of Vo?

But its says the banked curve is frictionless?? i still don't see the correlation for Vo
 
  • #6
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bump.. I still need help on this problem:confused:
 
  • #7
LowlyPion
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But its says the banked curve is frictionless?? i still don't see the correlation for Vo
Did you develop an equation for the Radius in terms of Vo on the flat surface?

Because if you had you would then be able to use that in the expression that accounts for the frictionless incline.

You've already related that equation even.
 
  • #8
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Did you develop an equation for the Radius in terms of Vo on the flat surface?

Because if you had you would then be able to use that in the expression that accounts for the frictionless incline.

You've already related that equation even.

:confused: I think I'll just give up on this problem. Im getting lost
 
  • #9
LowlyPion
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:confused: I think I'll just give up on this problem. Im getting lost
OK. But the answer isn't that far away.

The unbanked curve tells you the relationship between the radius and the velocity in question.

The banked curve tells you the angle when you substitute for the Velocity.
 

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