The gauge pressure in both tires of a bicycle is 690 kPa. If the bicycle and the rider have a combined mass of 90.0 kg, what is the area of contact of each tyre with the ground?

##7.35 cm^2##

The equation for is: ##p=F/A##

The force responsible for providing the pressure in the tyres is the weight of the bicycle plus rider. ##w = mg = 90.0 × 9.8 = 882 N##

But the weight is distributed across two tyres equally (we assume this). So the actual force involved is: ##F=w/2 = 882/2=441N##

Now rearrange the pressure equation to solve for the contact area: ##A = F/p=(w//2)/p=441/(600×10^3)=0.000735 m^2##

The area is small so it might be more convenient to use a prefix, i.e. ##cm^2##: ##A=0.000735 × (10^2)^2 = 7.35 cm^2##

That is a reasonable value for the area of bicycle tyres in contact with the ground.

When converting areas into a prefix the conversion factor must be squared that's why I multiplied by ##(10^2)^2## above. The ##10^2## is the conversion factor for centi. Find out more about prefix conversions here: