Hi I tried asking this question yesterday but still had some confusion.Since the area must be in cm^2.
IP The weight of your 1440 kg car is supported equally by its four tires, each inflated to a gauge pressure of 30.0 lb/in^2 .
What is the area of contact each tire makes with the road?
What gauge pressure is required to give an area of contact of 122 for each tire?
Let me critique your work.
OK i have one attempt left, first i change the gauge pressue to newton/m^2? And since P= F/A solve for A after making f = 1440*g? Theni have to divide it by 4 for every tire? but im having trouble with conversions, and my final answer being in cm^2. SOOO confused
To find the area of contact that each tire makes with the road, we can use the concept of pressure.
1. First, convert the weight of the car from pounds to newtons. We can use the conversion factor of 1 pound = 4.45 newtons.
Weight of the car = mass × acceleration due to gravity
Weight of the car = 1440 kg × 9.8 m/s^2 (acceleration due to gravity)
Weight of the car = 14112 newtons
2. Since the weight is supported equally by all four tires, each tire carries one-fourth of the total weight.
Weight supported by each tire = 1/4 × 14112 newtons = 3528 newtons
3. Next, convert the gauge pressure from pounds per square inch (psi) to pascals. We can use the conversion factor of 1 psi = 6895 pascals.
Gauge pressure = 30.0 lb/in^2 × 6895 pascals/psi
Gauge pressure = 206,850 pascals
4. Now, we can use the formula for pressure:
Pressure = Force/Area
Since the force is the weight supported by each tire and the pressure is the gauge pressure, we can rearrange the equation to solve for the area:
Area = Force/Pressure
Area = 3528 newtons / 206,850 pascals
Finally, we can calculate the area each tire makes contact with the road.
Area = 0.017 cm^2 (approximately)
To find the gauge pressure required to give an area of contact of 122 cm^2 for each tire, we can rearrange the equation for area:
Pressure = Force/Area
Since the force is the weight supported by each tire and the area is given, we can solve for the pressure:
Pressure = Force/Area
Pressure = 3528 newtons / 122 cm^2 (convert cm^2 to m^2 because pressure is in pascals)
Pressure = 28.92 pascals (approximately)
Therefore, the gauge pressure required to give an area of contact of 122 cm^2 for each tire is approximately 28.92 pascals.