A 975-kg car has its tires each Problem 17 inflated to "32.0...

A $975-\mathrm{kg}$ car has its tires each Problem 17 inflated to $"32.0$ pounds." (a) What are the absolute and gauge pressures in these tires in $\mathrm{lb} / \mathrm{in.}^{2}$ , $\mathrm{Pa},$ and atm? (b) If the tires were perfectly round, could the tire pressure exert any force on the pavement? (Assume that the tire walls are flexible so that the pressure exerted by the tire on the pavement equals the air pressure inside the tire.) (c) If you examine a car's tires, it is obvious that there is some flattening at the bottom. What is the total contact area for all four tires of the flattened part of the tires at the pavement?

A $975-\mathrm{kg}$ car has its tires each Problem 17 inflated to $"32.0$ pounds."
(a) What are the absolute and gauge pressures in these tires in $\mathrm{lb} / \mathrm{in.}^{2}$ , $\mathrm{Pa},$ and atm? (b) If the tires were perfectly round, could the tire pressure exert any force on the pavement? (Assume that the tire walls are flexible so that the pressure exerted by the tire on the pavement equals the air pressure inside the tire.) (c) If you examine a car's tires, it is obvious that there is some flattening at the bottom. What is the total contact area for all four tires of the flattened part of the tires at the pavement?

Key Concepts

Contact Area and Force Equilibrium

Determining the contact area involves using the relation between the total applied force and the pressure over the area. This concept of force equilibrium allows one to calculate the area in which the pressure is effectively distributed to support an object’s weight. It is a fundamental aspect of statics and mechanics, important for designing systems where load distribution is critical.

Pressure Force Distribution on Surfaces

Pressure exerts force uniformly in all directions when acting on a flexible or isotropic surface. This concept explains that while the internal pressure in a closed, deformable system may balance the external forces, it does not produce a net force on the system boundary unless a pressure gradient is present. This understanding is key when analyzing situations where pressure interacts with contact surfaces.

Absolute and Gauge Pressure

This concept distinguishes between two ways of measuring pressure. Absolute pressure is the total pressure including the ambient atmospheric pressure, while gauge pressure is measured relative to the atmospheric pressure. Understanding the difference is essential because many instruments measure gauge pressure, which must be converted to absolute pressure when compared with standards such as the atmospheric pressure or when used in calculations involving fluid dynamics.

Pressure Unit Conversions

Working with pressures often requires converting between different units such as pounds per square inch (psi), Pascals (Pa), and atmospheres (atm). Mastering unit conversion is vital to ensure consistency in problem solving and to accurately interpret physical phenomena across different measurement systems.

Atmospheric Pressure as a Baseline

Atmospheric pressure serves as a reference level for many pressure measurements. In calculations, especially when converting gauge to absolute pressures, it is important to use the known value of atmospheric pressure. This baseline helps relate laboratory or real-world conditions to standardized units of pressure in physics and engineering.

Transcript

Please give Ace some feedback