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 calculate the absolute pressure inside the tire, we need to divide the force by the surface area of the tire. The formula for pressure is:
Pressure = Force / Surface Area
1. To find the absolute pressure inside the tire, divide the force by the surface area of the tire:
Absolute Pressure = Force / Surface Area
Absolute Pressure = 1.58 × 10^7 N / 26.3 m^2
Absolute Pressure = 6.015 × 10^5 N/m^2
The absolute pressure inside the tire is approximately 6.015 × 10^5 Newtons per square meter (N/m^2).
2. To find the gauge pressure on the tire's surface, we need to subtract the atmospheric pressure from the absolute pressure. Gauge pressure is the pressure measurement relative to atmospheric pressure.
Gauge Pressure = Absolute Pressure - Atmospheric Pressure
Assuming the atmospheric pressure is at sea level, which is approximately 101,325 Pascal (Pa) or 101,325 N/m^2, we can calculate the gauge pressure:
Gauge Pressure = Absolute Pressure - Atmospheric Pressure
Gauge Pressure = 6.015 × 10^5 N/m^2 - 1.01325 × 10^5 N/m^2
Gauge Pressure = 4.00175 × 10^5 N/m^2
The gauge pressure on the tire's surface is approximately 4.00175 × 10^5 Newtons per square meter (N/m^2).