Designing a Curved Exit Ramp: Angle Calculation for Speed & Radius

[ballahboy]

An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. He does so by banking the road in such a way that the necessary force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the circular path. Show that for a given speed v and a radius of r , the curve must be banked at the angle (theta) such that tan(theta)=v^2/r*g

 

[vsage]

What have you tried? think about what tan(theta) is in terms of sine and cosine and what sine and cosine would represent in this case.

 

[ballahboy]

this is what i was thinking...

Fn sin(theta) = mv^2/r
(mg/cos(theta))sin(theta) = mg tan(theta) = mv^2/r
tan theta = v^2/(rg)

does that look right?