The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a “footprint” of $190 \textrm{ cm}^2$ (area touching the ground), estimate the mass of the car.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The gauge pressure in the tire equals the total force on the footprint of the tire divided by footprint's area. So we can solve this for force on the tire by multiplying both sides by A and we have the force on one tire is the gauge pressure times its area. Now the whole force on the car has to be its weight mg and that's gonna be four times the force exerted on each tire. So that's four times gauge pressure times area and then we can solve for m by dividing both sides by g and we have the mass then is 4 times 240 times 10 to the 3 pascals times 190 centimeters squared converted into meters squared by multiplying by 1 meter for every 100 centimeters squared then divide by 9.8 newtons per kilogram and you get about 1.90 times 10 to the 3 kilograms is the mass of the car.