If a bicycle has a crankshaft of 40 teeth, and there are three rear sprockets attached to the rear wheel, 20 teeth, 16 teeth and 12 teeth. The diameter of the rear wheel is 60 cm. Which sprocket should be used to get the most distance in one paddle? What would the distance be?
To determine which sprocket should be used to get the most distance in one pedal, we need to calculate the gear ratio for each combination of crankshaft and rear sprockets. The gear ratio is calculated by dividing the number of teeth on the crankshaft by the number of teeth on the rear sprocket.
1. Calculate the gear ratio for each combination:
- Crankshaft (40) / Rear sprocket (20) = 2
- Crankshaft (40) / Rear sprocket (16) = 2.5
- Crankshaft (40) / Rear sprocket (12) = 3.33 (rounded to two decimal places)
2. The gear ratio represents the number of wheel rotations that result from one crankshaft rotation. So, to calculate the distance covered in one pedal, we need to multiply the gear ratio by the circumference of the wheel.
3. Calculate the circumference of the rear wheel:
- The diameter of the rear wheel (60 cm) can be used to calculate the circumference using the formula: circumference = 2 * π * radius.
- The radius of the wheel is half its diameter, so radius = 60 cm / 2 = 30 cm.
- The circumference is then calculated as: circumference = 2 * 3.14 * 30 cm = 188.4 cm (rounded to one decimal place).
4. Calculate the distance covered in one pedal for each combination:
- Distance = Gear ratio * Circumference.
- For 20 teeth: Distance = 2 * 188.4 cm ≈ 376.8 cm.
- For 16 teeth: Distance = 2.5 * 188.4 cm ≈ 471 cm.
- For 12 teeth: Distance = 3.33 * 188.4 cm ≈ 627.5 cm.
Therefore, using the rear sprocket with 12 teeth will result in the most distance covered in one pedal, approximately 627.5 cm.