[fnorful]

A friend wants to make a "Rube Goldberg" contraption involving (among other things) steel balls going down a track (under gravity only, of course!). His concern is whether solid or hollow balls will stay along a track best. He states the multiple energies involved (kinetic, angular, potential) would yield different behaviors for equal-diameter spheres of different weights.

He throws a lot of math references around (which I'm not comfortable with debating); yet my understanding of physics principles is that in "perfect" systems, the mass of an object solely under the influence of gravity does not affect how fast the object falls, nor what distance it may travel if "launched" from a ramp of particular angle. E.g. would a heavy roller-coaster stay closer to the tracks of secondary "whoop-de-doos" than a light roller-coaster?

And secondly, how much of a difference would this make in a real-world (friction-ful) practical application?

[cdad]

Here are a few rollercoaster sites you might want to dig into. The first one is pretty interesting.

Roller Coaster Physics Simulation

HowStuffWorks "Roller Coaster G-forces"

Roller Coaster G-Forces

[ebaines]

Your friend is correct - under rolling motion a solid ball will pick up speed quicker than a hollow one (assuming same diameter). The reason has to do with the fact that a hollow ball has a higher moment of rotatinal inertia per unit mass than does a solid one, so gravity is less effective at getting it to roll. Hence the solid ball will get roll the track faster, and in "loop-the-loops" is better able to stay on track.

But if instead he is considering two solid ball bearings of same size but made of different materials and hence different densities then you are correct - in theory both balls will accellerate down the track at the same rate. However, in practice the heavier ball will be better able to overcome the effects of friction and air resistance, and so may perform better.