Question

A person who weighs 645 N is riding a 98 N mountain bike. Suppose the entire weight of the rider and bike is supported equally by the two tires. If the gauge pressure in each tire is 6.35 ✕ 105 Pa, what is the area of contact between each tire and the ground

Answer 1

The equation for pressure is:
p=FA

The force responsible for providing the pressure in the tyres is the weight of the bicycle plus rider.
w=645N+98N= 743N

But the weight is distributed across two tyres equally (we assume this). So the actual force involved is:
F=w/2=743/2=371.5N

Now rearrange the pressure equation to solve for the contact area:
A=F/p=(w/2)/p=371.5/6.35×10⁵=0.000585m²

The area is small so it might be more convenient to use a prefix, i.e. cm²:
A=0.000585×(10²)²=5.85 cm²