The pressure in each of your car tires is 2.10 105 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 = 1660•9.8/4•2.1•10⁵=
=1.94•10⁻² m²
To find the contact area of each tire with the road, we can use the formula:
Pressure = Force/Area
We know the pressure and the force on each tire (one-quarter of the total weight of the car), so we can rearrange the formula to solve for the area:
Area = Force/Pressure
Step 1: Calculate the force on each tire.
The total weight of the car is the mass multiplied by the acceleration due to gravity (9.8 m/s^2).
Force = mass * acceleration due to gravity
Force = 1660 kg * 9.8 m/s^2 = 16268 N
Step 2: Calculate the contact area of each tire.
Area = Force/Pressure
Area = 16268 N / 2.10 * 10^5 Pa
Now, let's calculate the answer:
Area = 16268 N / 2.10 * 10^5 Pa
Area = 77.4667 * 10^-4 m^2
Therefore, the contact area of each tire with the road is approximately 77.4667 * 10^-4 square meters.
To find the contact area of each tire with the road, we can use the formula:
Contact Area = Force / Pressure
First, let's calculate the total force exerted by the car on all four tires. Since each tire bears one-quarter of the total load:
Force = (1/4) * Mass * Acceleration due to gravity
Given that the mass of the car is 1660 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force:
Force = (1/4) * 1660 kg * 9.8 m/s^2
Next, let's calculate the contact area of each tire by dividing the force by the pressure:
Contact Area = Force / Pressure
Given that the pressure is 2.10 x 10^5 Pa, we substitute the values into the formula:
Contact Area = Force / (2.10 x 10^5 Pa)
Now, let's calculate the contact area.