Question

Terminal velocity. A rider on a bike with the combined mass of 100kg attains a terminal speed of 15m/s on a 12% slope. Assuming that the only forces affecting the speed are the weight and the drag, calculate the drag coefficient. The frontal area is 0.9m2 .

Answer 1

Answer:

0.9378

Explanation:

Weight (W) of the rider = 100 kg;

since 1 kg = 9.8067 N

100 kg will be = 980.67 N

W = 980.67 N

At the slope of 12%, the angle θ is calculated as:

$tan \ \theta = \dfrac{12}{100} \\ \\ tan \ \theta = 0.12 \\ \\ \theta = tan^{-1}(0.12) \\\\ \theta = 6.84^0$

The drag force D = Wsinθ

$\dfrac{1}{2}C_v \rho AV^2 = W sin \theta$

where;

$\rho = 1.23 \ kg/m^3$

A = 0.9 m²

V = 15 m/s

∴

Drag coefficient $C_D = \dfrac{2 *W*sin \theta}{\rho *A *V^2}$

$C_D =\dfrac{2 *980.67*sin 6.84}{1.23 *0.9 *15^2}$

$C_D =0.9378$