Originally Posted by
choddo
Why do changes in mass have a cubic function? Force due to gravity is linear with mass, so I must be missing something obvious?
Very good question! Having thought more about it, I’m not sure it’s correct either. Here is the source of that specific info for reference.
https://www.cyclist.co.uk/in-depth/f...ownhill-faster
If we think in terms of max rolling speed, then terminal velocity is actually proportional to the square root of the mass. So not linear (as it is with the force) but certainly not cubic. Similarly, terminal velocity is also inversely proportional to the square root of CdA.
I think what they might have meant was that frontal area only scales in proportion to mass to the power of 1/3. So a large increase in mass only results in a small increase in air resistance.
I checked a few other articles but there were so many fundamental misunderstandings of the physics (some even coming from alleged post-,grad theoretical physicists!) that I gave up in the end. In particular, the classic feather vs cannonball freefall scenario becomes a large red herring once air and rolling resistance is added. That scenario also says nothing about the differences in potential energy (mgh) and momentum (mv) between the feather and cannonball.