The gauge pressure in each of 4 car tires is 240kpa. If each tire has a footprint of 220cm^2 , what is the mass of the car?
Pgauge*(Footprint Area)*4 = M g
Solve for M.
The 4 is the assumed number of tires. This assumes the CM is midway between front and rear tires.
I get about 1980 kg. Make sure your area is in m^2.
Thanks, very much.
To solve this problem, we need to use the concept of pressure and the area of each tire footprint. The formula to calculate pressure is:
Pressure = Force / Area
We know the gauge pressure for each tire is 240 kPa, so we need to convert it to pascals (Pa) to match the SI unit we'll use in the formula. 1 kPa = 1000 Pa, so:
240 kPa = 240 * 1000 Pa = 240,000 Pa
Now, we have the pressure in pascals. Since we want to calculate the force, we rearrange the formula and solve for force:
Force = Pressure * Area
The area of each tire footprint is given as 220 cm^2. To convert it to square meters (m^2), we divide by 10,000:
220 cm^2 = 220 / 10,000 m^2 = 0.022 m^2
Now, we can calculate the force exerted by each tire:
Force = 240,000 Pa * 0.022 m^2 = 5,280 N
Since there are four tires on the car, we multiply the force by 4:
Total Force = 4 * 5,280 N = 21,120 N
Now, we have the total force exerted by the car. To find the mass, we can use Newton's second law of motion:
Force = Mass * Acceleration
In this case, the car is not accelerating vertically, so the acceleration is the acceleration due to gravity, which is approximately 9.8 m/s^2.
21,120 N = Mass * 9.8 m/s^2
Now, solve for the mass:
Mass = 21,120 N / 9.8 m/s^2 ≈ 2,153 kg
Therefore, the mass of the car is approximately 2,153 kilograms.