Question

A curve has a radius of 50 meters and is banked 5 degrees. The road is covered with ice and is frictionless. What is the maximum speed, in mph, a car can travel and negotiate the curve? A.) 15.65mph B.) 25.00mph C.)65.00mph D.) 6.55mph E.) None of the above

Answer 1

Answer:

E.) None of the above

Explanation:

Draw a free body diagram.  There are two forces acting on the car.  Normal force perpendicular to the road, and weight downward.

Sum of the forces perpendicular to the road:

∑F = ma

N − mg cos θ = 0

N = mg cos θ

Sum of the forces towards the center of the circle:

∑F = ma

N sin θ = mv²/r

mg cos θ sin θ = mv²/r

g cos θ sin θ = v²/r

v = √(gr cos θ sin θ)

Given r = 50 m and θ = 5°:

v = √(9.8 m/s² × 50 m × cos 5° × sin 5°)

v = 6.52 m/s

v = 14.6 mph