Physics: Contact Patch?

Question

What will the size of the contact patch be for an 90kg rider on a 10kg bike if his tires are pumped to 500kPa?

My process went as this:

(90kg + 10kg) (10m/s^2) = 1000N

500kPa = 500 x 10^3 N/m^2

(1000N / 500 x 10^3 N/m^2) = 2 x 10^-3 m^2

The correct answer is 1 x 10^-3 m^2

I apologize in advance for whatever stupidity I am presenting, physics is not my field.

Answer 1

You got too close to the problem.

Your reasoning and math were perfect, but you forgot there are 2 wheels supporting the weight; your answer is correct for a unicycle!