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 1400 kg. It seems reasonable to assume that each tire supports one-fourth of the weight. With the ruler you find that the tires are 16 cm wide and the flattened segment of the tire in contact with the road is 14 cm long. What answer will you give your friend?
Express your answer using two significant figures.

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

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