Question #660d8

1 Answer
Oct 28, 2015

Answer:

#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.


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: