Answer to Question #106567 in Mechanics | Relativity for Adam Yaacoub

Question

The tires of a 15700 N automobile are inflated to a pressure of 172000 Pa (25 psi). Assuming that each tire supports 1⁄4 of the weight of the car, calculate the area of contact between a tire and the road.

Answer 1

We have our pressure in each of the four tires that withstands car's weight:

$$4p(\text{1 wheel})=\frac{F}{4A(\text{1 wheel})},\\ \space\\ A(\text{1 wheel})=\frac{F}{16p(\text{1 wheel})}\\ \space\\=\frac{15700}{16\cdot172000}=5.7\cdot10^{-3}\text{ m}^2,$$

or 57 square centimeters. This is a rectangle 21.5 cm wide - average wheel width and 2.7 cm long - the flat part that you see on the round surface of the wheel:

Source of the image: https://www.autotrader.ca/newsfeatures/20180507/under-inflated-tires-are-dangerous-and-cost-you-money/