The pressure in each of your car tires is 1.80 105 Pa. The mass of your car is 1660 kg. Assuming that each of your tires bears one-quarter of the total load, what is the contact area of each tire with the road?
p=F/A =mg/4A₀
A₀=mg/4F
To find the contact area of each tire with the road, we can use the formula for pressure:
Pressure = Force / Area
In this case, the force is the weight of the car, which is equal to its mass multiplied by the acceleration due to gravity:
Force = Mass * Gravity
Since each tire bears one-quarter of the total load, the force per tire is one-quarter of the weight of the car:
Force per Tire = (1/4) * (Mass * Gravity)
Now, we can rearrange the formula for pressure to solve for the area:
Area = Force / Pressure
Substituting the values, we get:
Area = (Force per Tire) / Pressure
Area = [(1/4) * (Mass * Gravity)] / Pressure
Now let's calculate the contact area of each tire with the road step by step:
1. Calculate the force per tire:
Force per Tire = (1/4) * (Mass * Gravity)
= (1/4) * (1660 kg * 9.8 m/s²)
= 4065 N (approx.)
2. Calculate the contact area:
Area = Force per Tire / Pressure
= 4065 N / (1.80 * 10^5 Pa)
= 0.0225 m² (approx.)
Therefore, the contact area of each tire with the road is approximately 0.0225 square meters.