Question

Some runners train with parachutes that trail behind them to provide a large drag force. These parachutes have a large drag coefficient, by design. One model expands to a rectangle 1.8 m square, with a drag coefficient of 1.4. A runner completes a 200 m run at 5.0 m/s with this chute trailing behind. How much thermal energy is added to the air by the drag force?

Answer 1

To develop this problem it is necessary to apply the concepts related to the Aerodynamic Drag Force.

By definition the Drag Force is defined as

$F_D = \frac{1}{2} \rho A C_D v^2$

Where,

A = Area

$\rho$= Density

$C_d$ = Drag coefficient

v = Velocity

According to our values we have,

$A = 1.8*1.8=3.24m^2$

$C_D = 1.4$

$V = 5m/s$

Replacing we have

$F_D = \frac{1}{2} 1.23*3.24*1.4*5^2$

$F_D = 69.74$

By definition we know that the thermal energy is given by the force applied in a given displacement then

$W = F*d$

$W = 69.74*200$

$W = 13948J$

Therefore the thermal energy is added to the air by the drag force is 13.9kJ