Question

Driving down Highway 401 in Ontario, it had rained and stopped raining by the time I came to the
freezing rain on the highway. I knew there was a problem when the cars in front of me started to fly
off the highway at the curve in the road. Assume the curve in the road is banked at an angle of 10.0
and has a radius of 300 m.
(a) At what speed is no friction required to make the turn?
(b) Suppose the coefficient of static friction between my tires and the freezing rain is 0.1, what are
the maximum and minimum speeds at which the curve can be traveled?

Answer 1

a)Fn sinθ = mv^2/r
Fn = mg cosθ
Work backward and solve for v (m's cancel)
b) For min Ff points up.
Fn sinθ - Ff cosθ = mv^2/r
Fn cosθ + Ff sinθ = mg
and to tie it all together
mu Fn = Ff
For max Ff points down.
Fn sinθ + Ff cosθ = mv^2/r
Fn cosθ = Ff sinθ + mg
and
mu Fn = Ff

Hope that helps. A FBD is a must for these problems.