A friend asks you how much pressure is in your car tires. You know that the tire

Question

A friend asks you how much pressure is in your car tires. You know that the tire manufacturer recommends 30 psi, but it's been a while since you've checked. You can't find a tire gauge in the car, but you do find the owner's manual and a ruler. Fortunately, you've just finished taking physics, so you tell your friend, "I don't know, but I can figure it out." From the owner's manual you find that the car's mass is 1000kg . It seems reasonable to assume that each tire supports one-fourth of the weight. With the ruler you find that the tires are 17cm wide and the flattened segment of the tire in contact with the road is 13cm long.

Explanation / Answer

The key thing to remember is that pressure = force/area

The force in this case is W = 1000*9.8 = 9800N
This weight is evenly distributed over 4 tires, to make 2450N per tire. Convert Newtons to pounds_force. To do this, remember that 1 newton = 0.225 pounds force, therefore, 2450N*.225 = 551.25 lb.
Because the tire base supports the force of the car, we can say that the pressure in the tires is therefore this force, divided by the contact area of the tires with the road

To convert cm to inches, you must remember that 2.54cm = 1inch.
17 cm/2.54 = 6.69"
13cm/2.54 = 5.12"
Therefore, the contact area = 6.69*5.12 = 34.2528 inches^2

Pressure = F/A = 551.25lb / 34.2528 inches^2 = 16.09lb/in^2 = 16.09 psi

Your friend is slightly under the recommended pressure. He should put a touch of air in his tires.

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