change size of spheres
- Dick Lane
Two transparent spheres have the same radius. Inside each sphere, a colored ball changes size in some simple fashion. "Simple Fashion" means some size parameter changes at a constant rate. However, what is "simple" for Green may not be simple for Red.
Animate the size changes (time t varies between 0.00 and 1.00).
- Try to identify what aspect of the Red ball changes at a constant rate;
- identify which aspect of the Green ball changes at a constant rate.
- Suppose radius of the Red ball is a power function of t, i.e., some constant k times a power p of t: . Find a plausible value for p.
- Make a similar conjecture for radius of the Green ball.
- Does either of these balls change in a fashion which is similar to a spherical balloon being inflated at a constant rate by an air compressor (e.g., volume increases at the rate of 200 cubic-inches per minute)?