Question

3. Two spherical objects at the same altitude move with identical velocities and experience the same drag force at a time t. If Object 1 has twice (2x) the diameter of Object 2, which object has the larger drag coefficient? Explain your answer using the drag equation.

Answer 1

Answer:

Object 2 has the larger drag coefficient

Explanation:

The drag force, D, is given by the equation:

$D = 0.5 c \rho A v^2$

Object 1 has twice the diameter of object 2.

If $d_2 = d$

$d_1 = 2d$

Area of object 2, $A_2 = \frac{\pi d^2 }{4}$

Area of object 1:

$A_1 = \frac{\pi (2d)^2 }{4}\\A_1 = \pi d^2$

Since all other parameters are still the same except the drag coefficient:

For object 1:

$D = 0.5 c_1 \rho A_1 v^2\\D = 0.5 c_1 \rho (\pi d^2) v^2$

For object 2:

$D = 0.5 c_2 \rho A_2 v^2\\D = 0.5 c_2 \rho (\pi d^2/4) v^2$

Since the drag force for the two objects are the same:

$0.5 c_1 \rho (\pi d^2) v^2 = 0.5 c_2 \rho (\pi d^2/4) v^2\\4c_1 = c_2$

Obviously from the equation above, c₂ is larger than c₁, this means that object 2 has the larger drag coefficient