Question

Suppose that when you ride on your 7.75 kg bike the weight of you and the bike is supported equally by the two tires. The gauge pressure in the tires is 75.2 lb/in2 and the area of contact between each tire and the road is 7.13 cm2.

Part A What is your weight?

Answer 1

From problem statement:

{Weight of Bike} = (7.75 kg)*(9.81 m/sec^2) = (76.03 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} = (75.2 lb/in^2) = (5.1848e(+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}

::: ? (5.1848e(+5) N/m^2)*{2*(7.13e(-4) m^2)} = W + (76.03 N)

::: ? (739.35 N) = W + (76.03 N) ::: ? W = (663.32 N) ::: (or mass of 67.6 kg )