Askiitians Tutor Team
Last Activity: 10 Days ago
To tackle your question about the car's tire pressure and the contact area, let's break it down into two parts: first, we'll calculate the absolute and gauge pressure in the tires, and then we'll determine the contact area of the tires on the pavement.
Understanding Tire Pressure
When we talk about tire pressure, we often refer to two types: gauge pressure and absolute pressure. Gauge pressure is the pressure relative to atmospheric pressure, while absolute pressure includes atmospheric pressure in its measurement.
Part (a): Calculating Tire Pressure
The tire pressure is given as 32.0 pounds per square inch (psi). To convert this into different units, we can use the following conversions:
- 1 psi = 6894.76 Pa (Pascals)
- 1 atm = 101325 Pa
Now, let's calculate the gauge and absolute pressures:
Gauge Pressure
The gauge pressure is simply the pressure indicated by the tire gauge, which is 32.0 psi. In terms of other units:
- In Pascals: 32.0 psi × 6894.76 Pa/psi = 220,632.32 Pa
- In atmospheres: 32.0 psi ÷ 14.696 psi/atm = 2.18 atm
Absolute Pressure
To find the absolute pressure, we need to add the atmospheric pressure (approximately 14.7 psi) to the gauge pressure:
- Absolute Pressure in psi: 32.0 psi + 14.7 psi = 46.7 psi
- In Pascals: 46.7 psi × 6894.76 Pa/psi = 321,632.32 Pa
- In atmospheres: 46.7 psi ÷ 14.696 psi/atm = 3.18 atm
Summary of Tire Pressure Calculations
To summarize:
- Gauge Pressure: 32.0 psi, 220,632.32 Pa, 2.18 atm
- Absolute Pressure: 46.7 psi, 321,632.32 Pa, 3.18 atm
Analyzing Tire Contact Area
Next, let's discuss the contact area of the tires. When a car is parked, the weight of the car causes the tires to flatten slightly at the bottom, creating a contact patch with the ground. To find the total contact area for all four tires, we need to consider the weight distribution and the pressure in the tires.
Calculating Contact Area
The weight of the car is given as 975 kg. The force exerted by the car due to gravity can be calculated using:
- Force (F) = mass (m) × gravity (g) = 975 kg × 9.81 m/s² = 9,577.75 N
Next, we can use the pressure formula to find the contact area (A). The pressure in the tires can be expressed as:
- Pressure (P) = Force (F) / Area (A)
Rearranging this gives us:
- Area (A) = Force (F) / Pressure (P)
Using the gauge pressure in Pascals (220,632.32 Pa), we can find the contact area for all four tires:
- Area for all four tires: A = 9,577.75 N / 220,632.32 Pa ≈ 0.0434 m²
- Since this is the total area for all four tires, we can divide by 4 to find the area for one tire: 0.0434 m² / 4 ≈ 0.01085 m²
Final Thoughts on Contact Area
Thus, the total contact area for all four tires is approximately 0.0434 m², and the contact area for each tire is about 0.01085 m². This flattening is crucial for providing traction and stability while driving.
In summary, we calculated both the absolute and gauge pressures of the tires and analyzed the contact area created by the weight of the car. Understanding these concepts is essential for maintaining proper tire health and ensuring safe driving conditions.
