# Tyres – loss of carbon atoms

## Question:

How many atoms of carbon wear off a tyre per rotation of the tyre?

This will be a very rough estimate but it is a fascinating question.

The wear will depend on how the car is driven, road conditions, braking, make of tyre etc. but roughly car tyres wear down by about 6 mm over 20 000 miles of driving.

My car tyres have a radius of about 0.6 m and a width of 0.15 m and so for 0.006 m (6 mm) of rubber to wear off them they must have lost 0.0017 cubic metres of rubber.

The density of rubber is a little less than water (to test this will a car tyre float in water? If yes then its density is less than water). Lets say 950 kg/cubic metre.

So the mass of rubber worn away = 0.0017x950 = 1.62 kg

Each molecule of rubber (assuming that the tyres are pure rubber) is a chain molecule of many units, each unit is 5 carbons and 8 hydrogens. Therefore 60/68 of the mass is carbon.

Therefore 1.6x60/68 = 1.4118 kg is carbon.

The mass of a carbon atom is 12x1.6x10-27 kg = 1.92x10-26 kg
So the number of carbon atoms rubbed off is 1.4118/1.92x10-26 = 7.35x1025 atoms

The circumference of the tyre is 1.9 m and therefore in travelling 20 000 miles (or 32 000 km = 32 000 000) they will have rotated 32 000 000/1.9 = almost 17 million times!

Therefore in one rotation the tyre will lose 7.35x1025/17 million = 4.3x1018 carbon atoms.

Roughly 4 million million million carbon atoms will be rubbed off every rotation!

This is a very rough estimate that all depends on my guess as to molecular weight and structure of the rubber used in car tyres. Actually it is even worse because tyres are made of 28% carbon black, 27% synthetic polymer, 14% natural rubber, 10% wire, 10% oil, and 11% other materials.

A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB