Finding Speed on Slippery Curves: R, Theta, Mu

[vivekfan]

Homework Statement

A car rounds a slippery curve. The radius of curvature of the road is R, the banking angle is theta and coefficient of friction is mu. What should be the cars speed in order that there is no frictional force between the car and the road?

Homework Equations

F=mv^2/r

The Attempt at a Solution

In general, I have no idea how the components or forces work for banking curves, so an explanation and help would be greatly appreciated.

 

[Oscar Wilde]

im not sure about what to do with the bank, but since the force of friction (along with the banking) is providing the centripetal force, set mu*m*g= mv^2/r I'm sorry I can't quite remember what to do with the bank angle.

 

[LowlyPion]

Centripetal acceleration is a horizontal force. Resolve it into the components on the incline.

Gravity is vertical. Resolve its force components.

If you are gong to ignore friction then the component of gravity down the incline must be balanced by centripetal force up the incline.

 

[vivekfan]

is centripetal acceleration always a horizontal force?

 

[Oscar Wilde]

looking back from what I recall you should use:


tan(theta)= v^2/rg

I can't really explain it, I am going to review the concept now

 

[LowlyPion]

is centripetal acceleration always a horizontal force?

Yes, for this type problem you should take it as horizontal.

On a roller coaster though it will be radial but in the vertical plane.