A car of mass M = 900 kg traveling at 65.0 km/h enters a banked turn covered wit

Question

A car of mass M = 900 kg traveling at 65.0 km/h enters a banked turn covered with ice. The road is banked at an angle, and there is no friction between the road and the car's tires.  Use g = 9.80 m/s^2 throughout this problem.

A car of mass M = 900 kg traveling at 65.0 km/h enters a banked turn covered with ice. The road is banked at an angle, and there is no friction between the road and the car's tires. Use g = 9.80 m/s^2 throughout this problem. What is the radius r of the turn if the angle is 20.0 degrees (assuming the car continues in uniform circular motion around the turn)?

Explanation / Answer

65km/h =

vertical direction:
The vertical component of normal reaction balances the weight

N*cos(theta) = mg ----(1)

horizontal direction:
The horizontal component of Normal balances the centrifugal force.
N*sin(theta) = m*v^2/r -----(2)

From 1 and 2,
r = v^2/g*tan?

r = 18.0556^2/9.8*tan20

r = 91.4 m

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