Bicycle Racing
Have you ever noticed that banking a curie makes it easier to get around at high speed? This problem will show you why.
A) Draw a diagram of a bike wheel perpendicular to a banked track, whose normal is at an angle of, say, θ from the vertical. Relate the horizontal component of acceleration to the normal force and the gravitational force; now and an expression for the bank angle θ at which they Just. balance.
B) A bicycle race is conducted on a circular track, of 400 ft. diameter. The speed is constant at 25 ft./sec. Find the optimum bank angle.
C) Now the track is an ellipse, major axis 400 ft., minor axis 100 ft. Find the maximum and minimum bank angles. Where do they occur? (Assume a constant speed of 25 ft./sec.)