The four tires of an automobile are inflated to a gauge...

The four tires of an automobile are inflated to a gauge pressure of $2.0 \times 10^{5} \mathrm{~Pa}$. Each tire has an area of $0.024 \mathrm{~m}^{2}$ in contact with the ground. Determine the weight of the automobile.

Key Concepts

Pressure

Pressure is defined as the force applied perpendicular to the surface of an object divided by the area over which the force is distributed. It provides a measure of the intensity of the force acting on a unit area and is calculated using the formula P = F/A.

Gauge Pressure

Gauge pressure is the measure of pressure relative to the ambient atmospheric pressure. It represents how much the pressure in a system exceeds the atmospheric pressure and is used in many practical applications, such as in tire inflation, to indicate the excess pressure that directly contributes to the force supporting a structure.

Static Equilibrium

Static equilibrium is a state where all the forces acting on a system balance each other out, resulting in no net force and consequently no acceleration. In problems like determining the weight of an automobile, the upward force provided by the tires’ pressure distribution must exactly balance the downward gravitational force, ensuring stability.

Force Distribution

Force distribution refers to the way total force is spread over multiple areas or points of contact. In cases where multiple surfaces (such as the four tires of an automobile) support a load, the total force required to maintain equilibrium is divided among those surfaces, allowing for the calculation of the overall weight if the pressure and contact area of each surface are known.

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