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 30psi , 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 1500kg . It seems reasonable to assume that each tire supports one-fourth of the weight. With the ruler you find that the tires are 15cm wide and the flattened segment of the tire in contact with the road is 13cm long.

what answer would you give your friend?

Explanation / Answer

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

The force in this case is W = 1300*9.8 = 12740N
This weight is evenly distributed over 4 tires, to make 3185N per tire. Convert Newtons to pounds_force. To do this, remember that 1 newton = 0.225 pounds force, therefore, 3185N*.225 = 716.6 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.
13 cm/2.54 = 5.12"
12cm/2.54 = 4.72"
Therefore, the contact area = 5.12*4.72 = 24.1664 inches^2

Pressure = F/A = 716.6lb / 24.1664 inches^2 = 29.65 lb/in^2 = 29.65 psi

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