Final answer:
To find the area of contact each tire makes with the road, we can use the equation Area = Force/Pressure. The area of contact for each tire is found to be 612 cm². To find the gauge pressure required to give an area of contact of 107 cm² for each tire, we rearrange the equation Pressure = Force/Area and calculate the pressure to be 188.50 lb/in².
Step-by-step explanation:
A.) To find the area of contact each tire makes with the road, we can use the equation:
Area = Force/Pressure
Since the weight of the car is supported equally by its four tires, the force is the weight of the car, which is 1420 kg x 9.8 m/s² = 13916 N.
Converting the pressure from lb/in² to N/m², we have 33.0 lb/in² x 6894.76 N/m²/lb/in² = 226995.68 N/m².
Area = 13916 N / 226995.68 N/m² = 0.0612 m².
Finally, to convert this to cm², we can multiply by 10000:
Area = 0.0612 m² x 10000 cm²/m² = 612 cm².
B.) To find the gauge pressure required to give an area of contact of 107 cm^2 for each tire, we can rearrange the equation:
Pressure = Force/Area
Using the same force (13916 N) and converting the area from cm² to m² (107 cm² x 0.0001 m²/cm² = 0.0107 m²), we can calculate the pressure:
Pressure = 13916 N / 0.0107 m² = 1301121.5 N/m².
Converting this pressure from N/m² to lb/in², we have 1301121.5 N/m² x 0.000145037 lb/in²/N/m² = 188.50 lb/in².