A cube has a drag coefficient of 0.8.What would be the terminal velocity of a sugar cube 1 cm on a side in air (ρ = 1.2 kg/m³)? Take the density of sugar to be 1.6 x 10³ kg/m³. A)1.4 m/s B)5 m/s C)18 m/s D)60 m/s E)320 m/s

Question

Quizplus · Accepted Answer

The formula for terminal velocity is:

Vt = (2mg/ρACd)^(1/2)

Where:
m = mass of object
g = acceleration due to gravity (9.8 m/s^2)
ρ = density of fluid (in this case, air)
A = cross sectional area of object
Cd = drag coefficient

Substituting the given values:

m = density x volume
   = (1.6 x 10^-12 kg/m^3) x (0.01 m)^3
   = 1.6 x 10^-15 kg

A = (0.01 m)^2
   = 1 x 10^-4 m^2

Vt = (2 x 1.6 x 10^-15 kg x 9.8 m/s^2 / (1.2 kg/m^3 x 1 x 10^-4 m^2 x 0.8))^(1/2)

Vt ≈ 18 m/s

Therefore, the correct answer is choice C (18 m/s).

A Cube Has a Drag Coefficient of 0