The four tires of an automobile are inflated to a gauge pressure of 1.8E10^5 Pa. Each tire has an area of 0.025 m2 in contact with the ground. Determine the weight of the automobile.
I was helped with this before, but the answer was wrong. Can someone please help me, I keep doing it, but it's still wrong.
The absolute pressure inside the tire, multiplied by the area in contact with the ground, equals the force of the ground upon the tire. Four times that force equals the weight of the car, if each tire supports the same weight.
The absolute pressure in this case is 2.8*10^5 Pa. It is higher than the gauge pressure by an amount equal to atmospheric pressure, 1.0*10^5 Pa.
I calculate
Wt. = 4 *(0.025 m^2)*(2.8*10^5 N/m^2) =
2.8*10^4 N = 6300 lb
That seems pretty heavy for a car. They may expect you to use gauge pressure instead of absolute pressure in the formula, but I don't agree with that assumption. There is no atmospheric air under the tire at the point of contact.
To determine the weight of the automobile, you need to use the concept of pressure and area.
The formula to calculate pressure is: Pressure = Force / Area
In this case, the pressure is given as 1.8E10^5 Pa, and the area of each tire in contact with the ground is 0.025 m^2.
To find the force exerted by each tire on the ground, we rearrange the formula:
Force = Pressure * Area
Now we can plug in the values:
Force = 1.8E10^5 Pa * 0.025 m^2
Calculating this gives us the force exerted by each tire on the ground. Since there are four tires, we need to multiply this force by 4 to get the total force exerted by all four tires.
Once we have the total force exerted on the ground by the tires, we can equate it to the weight of the automobile using Newton's second law, which states that force is equal to mass multiplied by acceleration due to gravity (F = m * g).
Rearranging the formula to find the weight (W), we have:
Weight (W) = Force (F) / acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2.
To calculate the weight of the automobile, divide the total force by the acceleration due to gravity:
Weight = (Force * 4) / 9.8
Make sure to use scientific notation correctly and check your calculations to ensure accuracy.