## Estimation and Order of Magnitude

As the rubber wears off the tread of your tires, it mostly becomes airborne pollution called "particulate matter." Estimate what mass of rubber is worn off all the tires in the United States each year. (Assume the depth of the tread on new tires is 1 cm and the density of rubber is 1200 kg/m^{3})

There are approximately 300 million people in the US. They are (on average) divided into families of four, with two cars for each family, with the typical car having four tires.

This means that there are 600 million (6 x 10^{8}) tires in use.

How much tread rubber does each tire have? Lets assume that a typical tire has a tread that is a rectangle 1 cm thick and 10 cm across, wrapped around a wheel with a diameter of 1m (that is, about three meters long).

There volume of this tread is: 1 cm * 10 cm * 300 cm = 3000 cm^{3} = 3 x 10^{-3} m^{3} per tire.

Thus, the 600 million tires, between when they’re new and when they’re bald, produce:

600 million * 3 x 10^{-3} m^{3} = 1.8 x 10^{6} m^{3} of rubber.

Which has a mass of 1.8 x 10^{6} m^{3} * 1200 kg/m^{3} = ~2 x 10^{9} kg.

Now, this rubber is not all used up in one year – a typical tire lasts a lot longer than that – perhaps four years:

Mass of rubber per year: 2 x 10^{9} kg/4 years = 5 x 10^{8} kg/year.

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