Question

Some runners train with parachutes that trail behind them to provide a large drag force. These parachutes are designed to have a large drag coefficient. One model expands to a square 1.8 m on a side, with a drag coefficient of 1.4.
1. A runner completes a 200m run at 6.0 m/s with this chute trailing behind. How much thermal energy is added to the air by the drag force?

Answer 1

To solve this problem we will apply the concept of drag force which is described as half the product between the density, the drag coefficient, the area and the squared speed. Said expression mathematically is equivalent to,

$F = \frac{1}{2} \rho C_d Av^2$

Here,

$\rho$ = Density

$C_d$ = Drag coefficient

A = Area

v = Velocity

Our values are,

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

$C_d = 1.4$

$v = 6m/s$

$\rho = 1.23kg/m^3 \rightarrow \text{Density of Air}$

Replacing at the previous equation we have that,

$F = \frac{1}{2} (1.23)(1.4)(3.24)(6)^2$

$F = 100.42N$

Energy can be described through the work theorem, which is the product between force and distance traveled. So,

$W = Fd$

$W = (100.42)(200)$

$W= 20084J$

Therefore the thermal energy is 20.084kJ