Maximum Safe Speed for Cars on Reverse Bank Angle Highway Curve

[jcook735]

A car is on a highway curve of 6160 m radius, and the highway is frictionless. The car on a reverse bank angle, aka the the tilt is angled away from the center of curvature. The angle of tilt is 4 degrees. What is the maximum safe speed for cars driving on the highway?
I know that N= mg/cos(theta), and that the normal force is reduced since the banking angle is reversed, but I don't know how to input this mathematically.

Since Fnet=Centripetal force, I tried

mv²/r = -Nsin(theta) but that gives me a nonreal answer, I have no idea where to go from here

 

[rl.bhat]

When the car is moving on the reverse banked road, the forces acting on it will be i) normal force, ii) weight mg and iii) centripetal force mv^2/r.
Since the road is frictionless, mg*sinθ will try to push it in the downward direction. It can be prevented from sliding down by the component of mv^2/r along the inclined plane.

 

[jcook735]

So if I am understanding you right, there is a component of mg along the inclined plane downwards which is mg*sinθ and there is a component of centripetal force along the inclined plane upwards which is Fc/cosθ? If that is correct, then I thank you

 

[Doc Al]

So if I am understanding you right, there is a component of mg along the inclined plane downwards which is mg*sinθ and there is a component of centripetal force along the inclined plane upwards which is Fc/cosθ? If that is correct, then I thank you

A reverse banking angle and no friction? Good luck with that!

There are only two forces acting on the car:
(1) The normal force, which is outward from the surface
(2) The weight, which is downward

("Centripetal force" is not a separate force.)

Unfortunately, neither of these forces has a component towards the center of the circle. (Friction is required.)

 

[jcook735]

Oh, well my physics professor must hate me then. the problem in full is:

State highway 33 south of Stillwater is scheduled for (extensive) modification between the Cimarron river and US 177 by fall 2012. Dr. Hasty has noticed that one of the curves on this asphalt highway (which is scheduled for replacement) is crowned such that the outside lane is banked away from the turn center rather than into the turn. Consider a car that negotiates this turn, which will be assumed to be symmetrically banked at the road center at angles of 4.00º toward and away from the turn center. For the purposes of these calculations, assume that the turn radius for cars in the inside and outside lanes is identical. What is the radius of this curve for cars on the inside lane to safely negotiate the turn without friction at 65mph (the curve’s posted speed limit)? What is the maximum safe speed for cars in the outside lane without friction? Determine the minimum frictional coefficient for safe travel in the outside lane at the posted speed limit. Is this coefficient reasonable?

 

[jcook735]

I talked to my teacher about it, and he said it was supposed to be a question you can't answer. So thank you Doc Al

 

[Doc Al]

I talked to my teacher about it, and he said it was supposed to be a question you can't answer. So thank you Doc Al

LOL... sneaky, isn't he?