Car bank angle?

Question

Highways are banked at an angle q for a design speed at which friction is not required to steer the car around the curve. If the design speed is 59 mph, and the banking angle is 16 degrees, what is the radius of the curve in meters?

Answer 1

Look at a free body diagram of the car in the curve

since the angular force will be in balance with the frictional forces, we need only consider the forces parallel to the road surface that are radial

gravity

m*g*sin(q)
centripidal
a=w^2*r

linear speed is w/r
so
a=v^2/r

the force is
m*cos(q)*v^2/r

since these balance
cos(q)*v^2/r=g*sin(q)
r=v^2/(tan(q)*g)
plug and crunch
1 mph = 0.447 m/s
r=59^2*.447^2/(tan(16)*9.81) meters

247 m

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