The
spherical geometry introduces a complication that was first
analyzed by Hertz2 for a force law of the form F5kx3/2. If
the collision is inelastic, then the relevant force law is generally
an unknown function of the properties of the colliding
objects. The force law is, in fact, often irrelevant since most
problems of this type are cast in the form of conservation
equations describing conditions before and after the collision.
However, a measurement of the force provides useful
information on the behavior of the objects during the collision,
on the duration of the collision and on the elastic properties
of the objects.