Problem 6 - College Physics

Question

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.

Step-by-Step Solution

Answer

The weight of the car is \(19200 N\).

Step 1: Knowing the formula and understanding the problem

In a physics context, the pressure of a fluid is defined as the force per unit area exerted on an object. Mathematically, this is written as: Pressure = Force / Area. In this problem, we are given the pressure (P) exerted by each tire and the area (A) of contact each tire has with the ground. We are asked to find the weight of the automobile, which is essentially the force (F) applied by the car due to gravity.

Step 2: Calculate the total force

The force for one tire can be calculated by rearranging our formula to Force = Pressure * Area. Using the given values, the force (F) for one tire = \(2.0 * 10^{5} Pa\) * \(0.024 m^{2}\) = \(4800 N\) since Pascals = Newtons per square meter. As there are 4 tires, the total force = 4 * \(4800 N\) = \(19200 N\).

Step 3: Convertion of force into weight

Since weight is just a force due to gravity, the weight of the car is equal to the total force that the tires exert on the ground; which we have calculated to be \(19200 N\).