The pressure in each of your car tires is 2.30X10^5 Pa. The mass of your car is 1640 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?
To find the contact area of each tire with the road, we can use the relationship between pressure, force, and area. Here's how you can calculate it:
Step 1: Calculate the total force exerted by the car on the road.
The total force exerted by the car on the road is equal to the weight of the car. The weight can be calculated using the formula: Weight = mass x acceleration due to gravity.
Given:
Mass of the car (m) = 1640 kg
Acceleration due to gravity (g) = 9.8 m/s²
Weight of the car (W) = m x g
W = 1640 kg x 9.8 m/s²
Step 2: Calculate the force exerted by each tire.
Since each tire bears one-quarter of the total load, we divide the total weight by 4.
Force exerted by each tire (F) = W / 4
Step 3: Calculate the contact area of each tire.
The contact area of each tire (A) can be obtained by dividing the force exerted by each tire by the pressure.
A = F / P
Given:
Pressure (P) = 2.30 x 10^5 Pa
Substitute the values:
A = (W / 4) / P
Now, substitute the value of W into the equation and calculate A.