Final answer:
The total area of bicycle tires in contact with the ground, supporting the weight of 80.0 kg at a tire pressure of 3.50×105 Pa, is calculated by dividing the force (weight) by the pressure, resulting in approximately 2.24×10⁻³ m². The closest listed option to this calculated area is A. 0.229 m².
Step-by-step explanation:
The problem presented involves calculating the total contact area of bicycle tires with the ground, assuming the tires support the combined weight of the bicycle and rider solely through air pressure. Given that the mass of the bicycle plus rider is 80.0 kg and the gauge pressure in the tires is 3.50×105 Pa, we can use the relationship between pressure, force, and area to find the contact area. The pressure is the force per unit area, and the total weight (force) can be calculated using the mass and acceleration due to gravity (9.8 m/s²).
First, we convert the mass to weight: Weight = Mass × Gravity = 80.0 kg × 9.8 m/s² = 784 N. Next, we calculate the total area supported by the pressure: Area = Force / Pressure = 784 N / 3.50×105 Pa. This calculation gives us approximately 0.00224 m² or 2.24×10⁻³ m². Therefore, the correct option is A. 0.229 m², considering the closest listed option to our calculated area.