A sedan has a mass of 1.20×10^3 kg and is supported by four identical tyres. The gauge pressure inside each tyre is 220 kPa when the car is unloaded. Atmospheric pressure is 101 kPa.
Assume the tyres behave like flexible membranes so that the upward normal force from the road on each tyre equals the force exerted by the enclosed air on the contact patch. Take g = 9.8 m/s².
(a) Calculate the total weight of the car.
(b) Determine the absolute pressure of the air inside an unloaded tyre.
(c) Using your answers, compute the contact area between a single tyre and the road when the car is unloaded.
(d) The owner loads the trunk with luggage, increasing the total mass of the car to 1.50×10^3 kg while the gauge pressure remains at 220 kPa. Calculate the new contact area per tyre and the percentage increase compared with the unloaded condition.
(e) Discuss briefly how an increase in gauge pressure (instead of an increase in contact area) could support the additional load, and identify one practical limitation on how much the gauge pressure can be safely increased.