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 17 minutes.

Part B

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

Answer 1

Drag Force is resistive force experienced by runners against the airflow. The equation for this drag force is given as :

            Drag Force = 1/2 .p .v2 .A .D

where p is the density of the fluid (in runner’s case: air); 1 kg/m3

v is the velocity of the runner; 5km in 17 mins = 4.90 m/s

A is the cross-sectional area perpendicular to the runner’s velocity( assuming human body as rectangular block of height 175cm and width 34 cm) => 0.6 m2 ; and

D is the dimensionless quantity called the drag coefficient. (generally D=1-1.15 for rectangular shape (assuming human body as rectangular )

PUT IN VALUES

DF = 1/2 x 1 x 4.92 x 0.6 x 1.15 =8.2 N

Runner weight is W = mg = 60*9.8 = 588 N

force as a fraction of the runner's weight is 8.2 N/ 588 N= 0.0139 ======== > 1.39 % of runner weight

ANSWER : 1.39 % of runner weight