Flat tire

The truck is kept off the ground by the air pressure in the tires pushing on the ground. Initially, the pressure is 301.325 kPa. This changes when the car is placed on the ground as the volume changes. We can calculate the initial volume of a tire as

$V_i=\pi W (r_o^2-r_i^2)$

where W is the width of the tire, and $r_o$ and $r_i$ are the outer and inner radius of the tires respectively. This yields an initial volume of $0.1508~m^3$ . The final volume of each tire can be calculated with a little geometry. Let the distance the tire squishes be h (in this case 5 cm). Then the angle $\theta$ between the vertical and the edge of the squished part is given by $\theta=cos^{-1}(1-h/r_o)=0.451~rad$ . The cross-sectional area of the segment of the circle removed by squishing is $A_{seg}=\theta r_0^2-(r_0-h)^2 tan \theta$ , and so the total volume lost due to squishing is $V_s=WA_{seg}=0.00294~m^3$ . The final volume of the tire is therefore $V_f=0.1479~m^3$ .

Since the tires squish very quickly, the compression is adiabatic. They are filled with diatomic molecules, and so we can calculate the final pressure by $pV^\gamma=const.$ where $\gamma=7/5$ . This yields a final pressure of 309.736 kPa. The area each squished tire has with the ground is $2 r_0 W sin \theta=0.0872~m^2$ . The force each tire exerts on the ground is therefore $F=pA=27002~N$ . The total force then of the truck+tires is 108,008 N, which yields a mass for the truck+tires of 11021 kg.