# Should you use GAUGE or ABSOLUTE pressure to solve for force exerted by tire?

A problem in our text asks to solve for the mass of a car and provides you with the area of contact of the tires with the road and the GAUGE pressure in the tires. The intent is for you to use the product of Pressure and the total Area to solve for a force (weight) from which you can determine the mass of the car.

I solved for the Absolute Pressure (including atmospheric pressure) before plugging it in to solve for force. However, the solution in the text shows them only using the gauge pressure to solve for the force & mass.

Why would we use the gauge pressure instead of the absolute (true) pressure in this problem?

If the tires only have atmospheric pressure in them, they will be flat, and they will not be supporting any of the weight of the car. Only the pressure above atmospheric pressure supports the weight of the car, and that pressure is, by definition, gauge pressure.

• I get the logic. But can this argument be re-stated more mathematically? Sep 9, 2020 at 0:18
• @MANTICOLE, I was waiting on that kind of reply, but I didn't expect it from the original poster. Physics is NOT math. Physics is based on experimental observations, and mathematical models of varying degrees of precision are used to describe those observations, depending on how much precision is deemed to be necessary. By observation alone, you and your students already know that atmospheric tire pressure does not support any of a vehicle's weight. Obscuring this logic with math tends to teach students that math is more important than observation, which is an invalid conclusion. Sep 9, 2020 at 1:51
• @MANTICOLE, just to satisfy my own curiosity, what level of students are you teaching? And note - I am recently retired, but I taught high school physics for 13 years. Sep 9, 2020 at 2:02
• On the flip side of that argument, I find that relying on mathematics forces you to make sure you're applying the concepts properly. It is sometimes easy to trick yourself into believing that you have the right answer conceptually but when you go to prove it with the math, it falls apart. In my experience at the high school level, math is a big part of the physics process and serves as an excellent scaffold that students can use to build their conceptual knowledge upon. Sep 10, 2020 at 11:06
• @MANTICOLE, you'll think it "strange", but I always had the opposite viewpoint. I typically told students to memorize the concepts, and the concepts drive the math. Sep 10, 2020 at 15:52

Atmospheric pressure is acting on the car from all directions, so one atmosphere of pressure in the tyres only counteracts the one atmosphere of pressure pressing down on the same area. Only the pressure in the tyres over and above atmospheric pressure supports the car’s weight.

• My confusion comes with the idea of the atmosphere pushing down on the car/tires. Unless there is a difference in pressure there should be no net force as a result of the atmosphere. If I set a book on a table, it doesn't become heavier just because there's no longer air pushing up on it. And if there's no net force from the atmosphere then there's nothing there for the tire pressure to counteract. Sep 9, 2020 at 0:16
• @MANTICOLE The book on the table does not become heavier because at a microscopic level air is still present between the book and the table and so is still pressing up on the book. If the air pressure between the book and the table is lowered then the excess air pressure from above will hold the book more firmly to the table - this is how a suction cup works. Sep 9, 2020 at 8:42
• Suction cup example is a good one. Sep 10, 2020 at 11:08