Question

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 21 minutes.

A) Determine the drag force on the runner during the race. Suppose that the cross section area of the runner is 0.72 m2 and the density of air is 1.2 kg/m3.

B) What is this force as a fraction of the runner's weight?

Answer 1

given

mass m = 60 kg , displacement s = 5 km = 5000 m , time t = 21 min = 21*60 = 1260 m/s

the velocity is v = s/t = 5000 /1260 m/s = 3.968254 m/s

Area of cross section is A = 0.72 m^2 , density is rho = 1.2 kg/m^3 and drag coefficient of air is cd = 0.5

A)

we know the drag force is  

F = 0.5*rho*A*v^2*C_d

F = 0.5*1.2*0.72*3.968254^2*0.5N

F = 3.4014 N

B)What is this force as a fraction of the runner's weight?

runner's weight is W = m*g = 60*9.8 N = 588 N

the fraction of the drag force on weight is = 3.4014/588 = 0.0057846938776

= 0.578 %