The pressure in each of your car tires is 2.30 105 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 equation:
Pressure = Force / Area
We know that the pressure is 2.30 x 10^5 Pa and each tire bears one-quarter of the total load.
The total load on the car can be calculated by multiplying the mass of the car by the acceleration due to gravity (g). Assuming the acceleration due to gravity is approximately 9.8 m/s^2:
Total Load = Mass of the car x g
= 1640 kg x 9.8 m/s^2
= 16072 N (Newtons)
Since each tire bears one-quarter of the total load, the load on each tire can be calculated by dividing the total load by 4:
Load on each tire = Total Load / Number of tires
= 16072 N / 4
= 4018 N
Now we can rearrange the pressure equation to solve for the area:
Area = Force / Pressure
= Load on each tire / Pressure
= 4018 N / 2.30 x 10^5 Pa
≈ 0.0175 m^2 (rounded to four decimal places)
Therefore, the contact area of each tire with the road is approximately 0.0175 square meters.
To find the contact area of each tire with the road, we need to use the concept of pressure and force. Here's how you can calculate it step by step:
Step 1: Calculate the total force exerted by the car on the ground:
The force exerted by the car on the ground is equal to the weight of the car, which can be calculated using the mass and gravity. The formula is:
Force = mass * gravity
Given:
Mass of the car (m) = 1640 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Substituting the given values, we can find the force:
Force = 1640 kg * 9.8 m/s^2
Step 2: Divide the total force by 4 to find the force exerted by each tire:
Since the problem states that each tire bears one-quarter of the total load, we need to divide the total force (calculated in step 1) by 4 to find the force exerted by each tire:
Force exerted by each tire = Total force / 4
Step 3: Calculate the contact area of each tire with the road using pressure:
The pressure (P) is defined as the force (F) divided by the contact area (A). Rearranging the pressure formula, we get:
Contact area (A) = Force (F) / Pressure (P)
Given:
Pressure in each tire (P) = 2.30 * 10^5 Pa
Substituting the known values, we can find the contact area:
Contact area of each tire = Force exerted by each tire / Pressure in each tire
Step 4: Substitute the values into the equation and calculate the contact area:
Substitute the force exerted by each tire (calculated in step 2) and the pressure in each tire (given) into the contact area equation. Calculate the final contact area value.
You can plug the calculated values into the equations and solve to find the contact area of each tire.