Question

Question #660d8

Answer 1

`7.35 cm^2`

Explanation:

The equation for pressure 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.

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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: