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

0.9378

Step-by-step 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 = (12)/(100) \\ \\ tan \ \theta = 0.12 \\ \\ \theta = tan^(-1)(0.12) \\\\ \theta = 6.84^0`

The drag force D = Wsinθ

`(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 = (2 *W*sin \theta)/(\rho *A *V^2)`

`C_D =(2 *980.67*sin 6.84)/(1.23 *0.9 *15^2)`

`C_D =0.9378`