Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a 60 kg runner completes a 5.0 km race in 23 minutes. (a) Determine the drag force on the runner during the race. Suppose that the cross section area of the runner is 0.72 m^2 and the density of air is 1.2 kg/m^3. (b) What is this force as a fraction of the runner's weight?

a) Drag force = 5.67 N

b) Fraction of (drag force/weight) = 0.00964 = 0.964% (just less than 1%)

Step-by-step explanation:

Drag force is given by the expression

Drag force = CρAv²/2

C = Drag coefficient of air for an average human moving through air = 1.0

ρ = density of air = 1.2 kg/m³

A = Cross sectional Area of runner facing the air = 0.72 m²

v = velocity of the runner = (5km/23min) = (5000/23*60) = 3.623 m/s

Drag force = 1 (1.2) (0.72) (3.623²) / 2

Drag force = 5.67 N

b) Runner's weight = mg = 60*9.8 = 588 N

Fraction of (drag force/weight) = (5.67/588) = 0.00964 = 0.964% (just less than 1%)