# Question 660d8

Oct 28, 2015

$7.35 c {m}^{2}$

#### Explanation:

The equation for pressure is:
$p = \frac{F}{A}$

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:
$F = \frac{w}{2} = \frac{882}{2} = 441 N$

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. $c {m}^{2}$:
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 ${\left({10}^{2}\right)}^{2}$ above. The ${10}^{2}$ is the conversion factor for centi.
Find out more about prefix conversions here: