The largest tires in the world, which are used for certain huge dump trucks, have diameters of about 3.50 m. Suppose one of these tires has a volume of 5.25 m3 and a surface area of 26.3 m2 . If a force of 1.58 × 107 N acts on the inner area of the tire, what is the absolute pressure inside the tire? What is the gauge pressure on the tire’s surface?
To find the absolute pressure inside the tire, we can use the formula:
P = F/A
where P is the pressure, F is the force, and A is the area.
Given:
Force inside the tire (F) = 1.58 × 10^7 N
Surface area of the tire (A) = 26.3 m^2
Absolute pressure inside the tire can be calculated as follows:
P = F/A
P = (1.58 × 10^7 N) / (26.3 m^2)
Calculating this:
P ≈ 6.01 × 10^5 Pa
Therefore, the absolute pressure inside the tire is approximately 6.01 × 10^5 Pascal (Pa).
To find the gauge pressure on the tire's surface, we need to subtract atmospheric pressure from the absolute pressure.
Atmospheric pressure is approximately 101,325 Pa.
Gauge pressure is the difference between absolute pressure and atmospheric pressure:
Gauge pressure = Absolute pressure - Atmospheric pressure
Gauge pressure = 6.01 × 10^5 Pa - 101,325 Pa
Calculating this:
Gauge pressure ≈ 5.90 × 10^5 Pa
Therefore, the gauge pressure on the tire's surface is approximately 5.90 × 10^5 Pascal (Pa).