Physics Changes

An interesting kind of question is how one quantity varies in terms of another quantity:

(phys '(how does the force of gravitation
         vary with radius))
(varywith gravitation force radius)

inverse-square

(phys '(how does the area of a circle vary
         if radius is doubled))
(varychg circle area ((radius 2.0)))

4.0

These questions can be answered easily as follows:

1. Find an equation that relates these variables.
2. Solve the equation for the desired variable.
3. Evaluate the rhs of the solved equation with all variables set to 1.
4. Change the variable(s) that change to 2.0 (or the appropriate value) and evaluate again.
5. The ratio of the two evaluations gives the answer.