One of the toughest things to do in science is to figure out — of all the things that exist in the world — is which ones are relevant to your problem. Take the Leaning Tower of Pisa, for instance.
Specifically, I wrote about Galileo’s famous problem, where you take two cannonballs, one that’s 10 lbs and one that’s 1 lb, and drop them simultaneously off of the Leaning Tower of Pisa, about 55 meters up.
Perhaps you’ll make the simplest model, and say that the only thing that matters is gravity. Perhaps you’ll neglect air resistance, friction, the Coriolis forces, wind, horizontal motions, updrafts, and only consider gravity. If you did, what you’d find is that, as long as you drop them from rest at the same time, they will fall at exactly the same rate, and hit the ground at the same exact time.
But in real life, this is not what happens. In real life, we’re dropping these balls from a great height (55 meters), and they’re falling through air, not a vacuum. If we want to get an accurate model, we need to take into account air resistance in addition to gravity. Air resistance depends on a few things:
- The speed of the ball through the air,
- The density of the air,
- The drag coefficient of the ball,
- The surface area of the ball, and
- The mass of the ball.
For dropping a 1 lb ball and a 10 lb ball of the same material off of this tower, the major differences are the mass and surface area of the ball. How do you know mass matters? Take a wiffleball and a baseball of approximately the same size, and throw them at the same speed.
The baseball will go higher and farther, because the heavier mass makes it harder for the air to stop it. More surface area also makes it easier to stop, which is why a balled-up piece of paper falls much more quickly than a loose sheet of paper.
The 10 lb ball would take 3.375 seconds, while the 1 lb ball would take 3.39 seconds. Seems like a tiny difference, right? Practically indiscernible, you say, perhaps looking at the graph above? Well, I’ve got news for you: your eyes don’t see time, they see distance. What would the height differences between these two balls be as they fell?
A-ha! The 10 lb ball starts to pull away from the 1 lb ball the farther they fall, so that by time they hit the ground, they’re separated by over half a meter (almost 2 feet), a difference that’s easy to see!
So no, Galileo never performed this experiment, and if you did, this is pretty much exactly what you would see. And if you like, you can do the math for yourself, and find the same thing. And that’s what a good physical model does: it models all of the relevant behavior. If Galileo had done the experiment, what do you suppose he would have concluded about gravity and falling objects? Would physics ever have even developed?