The gauge pressure in both tires of a bicycle is 690kPa. If the bicycle and the person riding it have a combined mass of 90kg, what is the areas of contact of each tire with the ground?

Question

sidsiddhartha · Answer

Area = Force/Pressure=F/P 
now calculate F=mg
and pressure is given P = 690,000 Pa

anonymous · Answer

690kpa? 
That is the same as 690 kN/m² 
90 kg is a weight of 90 x 9.8 = 882 newtons 
882 newtons / 690 kN/m² = 1.28e-3 m² 

but that is total, for each tire it is 0.64e-3 m² or 0.00064 m² 
or 6.4 cm²

anonymous · Answer

That's about right.  A typical contact patch on a bicycle tire for an average sized person is about 1 sq. inch or about 6.4 sq. cm.

anonymous · Answer

By definition Pressure is force exerted per unit surface area i.e $$P=\frac{ F }{A  }$$ where symbols retain their usual meanings P=pressure; F=force; A=area. Using Newton II, $$and substituting F with ma where a=9.8ms^-2 , and,  m=90kg,  P      given$$ you will get the intended result numerically