Question

A car of mass 1200 kg is traveling at 55.0 km/hour. It enters a banked turn covered in ice. The road is banked at 20.0 degrees and there is no friction between the road and the cars tires. Use g= 9.80 m/s throughout the problem

Find the radius given the 20 degree angle, assuming the car continues in uniform circular motion around the turn.

Answer 1

the horizontal component of the normal force (due to the road's banking)
... is equal to the centripetal acceleration
... n sin(20º) = m v^2 / r

the vertical component of the normal force
... is equal to the weight ... otherwise the car would slide vertically
... n cos(20º) = m g

[m g / cos(20º)] sin(20º) = m v^2 / r

r = v^2 / [g tan(20º)]