I've been studying Classical Mechanics lately. It's rather useful. Especially when we're working with the simple center of mass equations that totally stumped me in my Quantum Mechanics I midterm.
Anyway, as the story goes, Galileo dropped a wooden ball and a cannon ball from the leaning tower of Pisa and astonishingly both of the balls landed at the same time, hence showing the acceleration due to gravity near the earth is independent of mass! The popular belief had been (as expressed by Aristotle) that heavier objects fall faster!
But really what happens is that on Earth heavier objects fall faster than lighter objects even if they have the exact same shape (we're not comparing a feather and a hammer, but the same wooden and metal balls). The force of air resistance depends only on the speed of the object and its shape. The force of gravity depends on the mass and the value of g (it’s actually mass times g). The lighter object has a smaller force acting on it due to gravity (but that was OK in the absence of resistance as the lighter mass needed a proportionally smaller force for the same acceleration). Once the masses start falling the force due to air resistance they face is the same (they have the same shape and same speed). A point comes when the force of air resistance is equal to the force of gravity on the small mass and so it now feels no net force and stops accelerating (reaches its terminal velocity i.e the fastest speed it can fall). The larger mass has a greater force of gravity and so keeps accelerating. Of course this effect kicks in much before the objects reach terminal velocity and so the heavier mass in fact is in the lead much earlier on.
Galileo rolled different masses down different inclined planes in a very controlled systematic and scientific way. It wasn't just dropping them down a tall building. Had he dropped them down from the leaning tower of Pisa they would not, as explained, reach the ground at the same time.
But of course Galileo was a smart man and he knew this:
When Galileo was an old man, one of his students did perform the demonstration to an audience of Aristotlean scholars and found in fact a slight difference in the time the two balls struck the ground. This came as no surprise to Galileo who had already explained the effects of viscosity (wind friction) years before. However the Aristotlean scholars, completely ignorant of the (then new) scientific method, walked away from this demonstration convinced that their old master had been thereby proven correct. Talk about "accommodation"!
- Joe Milana, Department of Physics, University of Maryland