Physics - Estimate the mass of a car?

Question

The guage pressure in each of the four tires of an automobile is 240,000 Pa. If each tire has a "footprint" of 220 cm^2, estimate the mass of the car.

Answer 1

The sum total of forces on the four tires equals the weight of the car. Why? Because the car is not falling or rising. Thus, f = ma = 0 = 4T - W; where T is the force on each tire and W = mg the weight of the car of mass m.

4T = 4pa = mg = W; where p = your tire pressure and a = area of contact with the road. Thus m = 4pa/g; you can do the math. Remember to use consistent units throughout. Best do the whole thing (including the pressure) in kg-m-sec units. In which case, your mass would be in kg, area in m^2, and pressure in Newtons/m^2.

The physics lesson. When a body (m) is not changing velocity, the net forces on it are zero. Since the car is not accelerating up or down, the forces from the four tires have to equal the weight of the car. Also, the pressures within each tire are equal to the pressures over the area of contact for each tire due to Pascal's Law where pressures are evenly distributed throughout the enclosed tire.

Answer 2

p=f/a
force over area
so
220cm^2=220 *10^-4m^2/cm^2
=0.022m^2
240000*.022=5480N
mass=f/a
so about 5480/10=548 kg *4 since that's the mass supported by each tire essentially
so mass is about 550*4 = 2200 kg