Question

A person who weighs 625 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 7.60 x 10 power of 5 Pa, what is the area of contact between each tire and the ground?

Answer 1

The total weight of the person and the bike is \(W=625+98=723 \mathrm{~N}\)

The force \(\mathrm{F}\) on the two tires are equal since it is supportedlyequally. Then the force on each of the tire is \(F+F=W\)

\(2 \mathrm{~F}=723\)

\(\mathrm{F}=361.5 \mathrm{~N}\)

The force \(F=P A\) \(A=\frac{F}{P}=\frac{361.5}{7.60^{*} 10^{5}}=4.76 \times 10^{-4} m^{2}\)

So the area of contact is \(4.76^{*} 10^{-4} \mathrm{~m}^{2}\).