OSH/Example/1
From UBCMATH WIKI
Example problem statement
The drag force on a sphere is given by the product of the sphere's velocity and its drag coefficient. The drag coefficient is proportional to the sphere's cross-sectional area. The gravitational force on a sphere is proportional to its volume. The velocity at which these two forces are equal is called the terminal velocity. How does the terminal velocity of a sphere depend on its radius?
Solution 1
- $F_1= - \mu V$
- $\mu=\pi r^2 k_1$
- $F_1=\pi r^2 k_1 V$
- $F_2= 4/3 \pi r^3 k_2 d g$
- $\pi r^2 k_1 v= 4/3 \pi r^3 k_2 d g$
- $V=4 r k_2 d g / (3k_1) $