Pressure in a Bicycle Tyre

The recommended pressure of the air in a bicycle tyre is 45 psi. To translate this into Pa(Newtons per square metre) we use 1 pound =0.454 kg so 1 pound is equivalent to a force of  
\[0.454g=0.454 \times 9.8\]
\[Pressure= 45 \times \frac{Force}{Area}= \frac{0.454 \times 9.8}{(2.54 \times 10^{-2})^2}=3.10 \times 10^5 Pa\]
Suppose, when someone is sitting on the bike, that the tyres have an area of  
\[10 cm^2 =10^{-3} m^2\]
If the person sitting on the bike has a mass of 70 kg, they exert a force of  
\[70 \times 9.8 =686 N\]
  and an added pressure of  
\[\frac{686}{10^{-3}}=6.86 \times 10^5 Pa\]
The total pressure is then  
\[P_{Total}=3.10 \times 10^5 + 6.86 \times 10^5 =9.96 \times 10^5 Pa\]

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