Question

Over the course of a multi-stage 4120-km bicycle race, the front wheel of an athlete's bicycle makes 1.69x10⁶ revolutions. How many revolutions would the wheel have made during the race if its radius had been 1.2 cm larger?

Answer 1

Length of the bicycle race = L = 4120 km = 4120 x 10³ m = 4.12 x 10⁶ m

Initial radius of the wheel = R₁

Number of revolutions the initial wheel made to finish the race = n₁ = 1.69 x 10⁶ rev

The bicycle will move a distance equal to the circumference of the wheel that is '2R₁' in 1 revolution.

L = (2R₁)n₁

4.12x10⁶ = 2R₁(1.69x10⁶)

R₁ = 0.388 m

Now if the radius of the wheel had been 1.2 cm (0.012 m) larger.

New radius of the wheel = R₂

R₂ = R₁ + 0.012 m

R₂ = 0.388 + 0.012

R₂ = 0.4 m

Number of revolutions the new wheel makes for the course of the bicycle race = n₂

L = 2R₂n₂

4.12x10⁶ = 2(0.4)n₂

n₂ = 1.64 x 10⁶ rev

Number of revolutions the wheel would make if it's radius had been 1.2 cm larger = 1.64 x 10⁶ rev