Question

Suppose that when you ride on your 7.00-kg bike the weight of you and the bike is supported equally by the two tires. If the gauge pressure in the tires is 76.5 lb/in2 and the area of contact between each tire and the road is 7.13 cm2, what is your weight? N

Answer 1

{Weight of Bike} = (7 kg)*(9.81 m/sec^2) = (68.67 N)
{Rider's Weight} = W
{Total Tire Contact Area} = 2*(7.13 cm^2) = 2*(7.13e(-4) m^2)
{Tire Pressure Holding Bike + Rider} = (73.5 lb/in^2) = (5.0677e(+5) N/m^2)

Because system is at equilibrium, we have:
{Force Applied By Tire Pressure} = {Weight Bike + Rider}
{Tire Pressure Holding Bike + Rider}*{Total Tire Contact Area} = {Weight Bike + Rider}
(5.0677e(+5) N/m^2)*{2*(7.13e(-4) m^2)} = W + (68.67 N)
(722.65 N) = W + (68.67 N)
W = (654 N) ::: (or mass of 66.6 kg = 147 lbs)