Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen on the right. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction parallel to the road (this must supply the centripetal force) and the vertical normal force (which must equal the system’s weight). a)Find an equation for the tangent of the angle between the bike and the vertical (θ). Write this equation in terms of the velocity of the bike (v), the radius of curvature of the turn (r), and the acceleration due to gravity (g). b) Calculate θ for a turn taken at 10.1 m/s with a radius of curvature of 21 m. Give your answer in degrees.
Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen on the right. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction parallel to the road (this must supply the
a)Find an equation for the tangent of the angle between the bike and the vertical (θ). Write this equation in terms of the velocity of the bike (v), the radius of curvature of the turn (r), and the acceleration due to gravity (g).
b) Calculate θ for a turn taken at 10.1 m/s with a radius of curvature of 21 m. Give your answer in degrees.
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