Suppose a large dump truck tire has a surface area of 26.3 m^2. If a force of 1.58×10^7 Newtons acts on the inner 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:
Pressure = Force / Area
Step 1: Calculate the absolute pressure inside the tire:
Absolute Pressure = Force / Area
Absolute Pressure = 1.58 × 10^7 N / 26.3 m^2
Absolute Pressure ≈ 6.01 × 10^5 Pascal (Pa)
Therefore, the absolute pressure inside the tire is approximately 6.01 × 10^5 Pa.
Next, to calculate the gauge pressure on the tire's surface, we need to consider atmospheric pressure. Gauge pressure is the difference between absolute pressure and atmospheric pressure.
Step 2: Determine the atmospheric pressure:
Atmospheric pressure varies, but on average, it is approximately 1.01 × 10^5 Pa (or 1 atmosphere).
Step 3: Calculate the gauge pressure:
Gauge Pressure = Absolute Pressure - Atmospheric Pressure
Gauge Pressure = 6.01 × 10^5 Pa - 1.01 × 10^5 Pa
Gauge Pressure ≈ 5.0 × 10^5 Pa
Therefore, the gauge pressure on the tire's surface is approximately 5.0 × 10^5 Pa.