Question

Assuming bicycle tires are perfectly flexible and support the weight of a bicycle and rider by pressure alone, calculate the total area of the tires in contact with the ground if a bicycle and rider have a total mass of 80.0 kg, and the gauge pressure in the tires is 3.50 × 10^5 Pa.

(a) 0.23 m^2
(b) 2.3 m^2
(c) 23 m^2
(d) 0.023 m^2

Answer 1

To find the total area of bicycle tires in contact with the ground, the weight of the bicycle and rider is divided by the pressure in the tires. The calculation yields an area of 0.00224 m², with the closest answer choice being (d) 0.023 m². Hence, option (d) is correct.

Step-by-step explanation:

To calculate the total area of the bicycle tires in contact with the ground, given the total mass of the bicycle and rider is 80.0 kg, and the gauge pressure inside the tires is 3.50 × 105 Pa, we first convert the mass to weight (force due to gravity), then divide by the pressure to get the area.

The weight (Force, F) of the bicycle and the rider can be calculated using the equation F = m × g, where m is the mass and g is the acceleration due to gravity (9.8 m/s2 on Earth).

So the weight F = 80.0 kg × 9.8 m/s2 = 784 N.

Next, the total area A of the tires in contact with the ground can be found using the pressure equation P = F/A, where P is the pressure and A is the area.

Rearranging the formula to solve for A: A = F/P.

Substituting the numbers: A = 784 N / 3.50 × 105 Pa = 784/350000 m2 = 0.00224 m2.

The correct answer is (d) 0.023 m2, which is the closest option to our calculated value when rounded to two decimal places.