Stuff falls all the time. Maybe you’ve dropped a ball. Perhaps that cup of coffee slipped out of your hands. The mostly likely situation is that a cat decided to knock an object off a table—because that's what cats do.
And for as long as things have been falling, people have had questions about what is going on (and about the cat's motivation). Does a falling object move at a constant speed, or does it speed up? If you drop a heavy object and a light one at the same time, which will fall faster?
The great thing about these two questions is that you can ask pretty much anyone and they will have an answer—even if they are actually wrong. The even greater thing is that it's fairly simple to determine the answers experimentally. All you have to do is drop some stuff.
Some of the earliest explanations for what happens when you drop things go all the way back to Aristotle (around 350 BC), who was interested in explaining how the world works. Aristotle's answers were quite simple: If you let go of something, it will fall toward the ground. It will fall at a constant speed. If you drop two objects at the same time, the heavier one will move downward with a greater speed than the lighter one. That's it. And really, this seems like it could be true. I mean, if I drop a rock and a feather, it seems clear that the rock will hit the ground first.
But there is a problem. There's not an experiment to check if this is correct. Aristotle was a philosopher, not a scientist, and like most of the other Greek philosophers of his time, he was into thought experiments, not science experiments. (The Greeks knew that there couldn't be a perfect experiment, because some error would always be introduced into the data. They thought that seeking imperfect real-world evidence would just push them off the path of determining the ultimate truths of the universe through logic and reasoning.)
Aristotle's reasoning for this kind of motion actually makes sense. We can all agree that if you push something, it will move. The greater the pushing force, the more it will move—that means it would go faster. That makes sense, right? And if you hold a rock and a feather, the gravitational force on the rock is clearly greater. You can just feel that force when you lift the two objects up to compare them. There's no mystery there. So if the rock has a greater downward-pulling force, then it will have a greater downward falling velocity. If you drop a rock and a feather, the rock will hit the ground first. See? Physics isn't that hard.
Well, even though this explanation makes sense, it is indeed wrong. Really, the only thing that is correct is that normally a rock will hit the ground before a feather.
To understand why, let's start with the most basic idea—the relationship between force and motion. Most people call this Newton's second law, but if you go with “force-motion model,” that would be cool too. For movement in one dimension (like with a falling object), we can write this as:
This says that the total force on an object (Fnet) is equal to the product of the object's mass (m) and the acceleration (a).
But what is the acceleration? In short, this is a value that describes how the velocity changes. So, an acceleration of 0 meters per second per second means that the velocity won't change. An acceleration of 10 m/s2 means that in 1 second, the object's velocity will increase by 10 meters per second. The important thing is that forces change the velocity of an object. If something has a greater force, it doesn't move faster. It changes more. Change is the key.
There's a small problem, though. When you drop a rock from shoulder height above the ground, it will only take about half a second to fall. That's not very much time—certainly not enough for a person to determine that it's speeding up. It just looks like it falls very fast. In fact, the human eye is pretty good at detecting if something moves, but not so great at judging changes in speed. (Check out this awesome video from Veritasium on how humans track objects.) So it's hard to fault anyone (like Aristotle) for saying things fall at a constant speed. It really does look that way to the naked eye.
OK, but what about dropping a rock and feather—doesn't the rock hit first? Usually, the answer is yes. But let's replace the rock with a hammer and then just take a change of scenery and move the experiment to the moon. This is exactly what happened during the Apollo 15 lunar mission in 1971. Commander David Scott took a hammer and an eagle feather and dropped them onto the lunar regolith. Here's what happened:
The feather and the hammer hit the ground at the same time.
Why did it happen? First, it is indeed true that even on the moon there is a greater gravitational force on the hammer than the feather. We can calculate this gravitational force as the product of mass (m in kilograms) and the gravitational field (g in newtons per kilogram). On the surface of the moon, the gravitational field has a value of 1.6 N/kg. If you put this expression in for the net force on a falling object, it looks like this:
Since both the gravitational force and the acceleration depend on the same mass, it's on both sides of the equation and cancels. That leaves an acceleration of -g. The hammer and the feather fall down with identical motions and hit the ground at the same time. Honestly, I'm just a little sad that the astronauts didn't use one of the higher-quality film cameras instead of a TV camera—but that's just me.
So, what's different about dropping something on the moon versus on Earth? Yes, there is a different gravitational weight on the moon—but that's not the issue. It's the lack of air that makes the difference. Remember that Newton's second law is a relationship between the net force and the acceleration. If you drop a feather on the surface of the Earth, there are two forces acting on it. First, there is the downward-pulling gravitational force that is equal to the product of mass and the gravitational field. Second, there is an upward-pushing force due to the interaction with the air, which we often call air drag. This air drag force depends on several things, but the important ones are the object's speed and the size of the object.
Let's look at a simple example. Suppose the feather has a mass of 0.01 kilograms. This would give it a downward gravitational force of 0.098 newtons. Now imagine the feather is moving downward with a velocity of 1 meter per second, and this produces an upward air drag force of 0.04 newtons. This means that the net force would be 0.04 N - 0.098 N = -0.058 N. That would give a downward acceleration of 5.8 m/s2 compared to an object without air resistance, which would have an acceleration of 9.8 m/s2.
Yes, a falling rock also has an upward-pushing air drag force. If it was the same size as the feather and moving at the same speed, it would have the same upward drag force of 0.04 N. However, if it has a mass of 1 kilogram, then its downward gravitational force would be 9.8 newtons. The net force would be 9.4 N, to produce an acceleration of 9.4 m/s2. Because of the rock's larger mass, it would have a much greater acceleration and it would hit the ground first—at least on Earth.
Do heavier objects always hit the ground before lighter ones? Nope. Here are some simple experiments you can do at home to show that Aristotle was wrong. (Bonus: You don't even need to go to the moon to do them.)
The first experiment uses two sheets of paper—just plain paper that you can get from your printer. If the pieces are identical, then they have the same mass and the same downward gravitational force. Now take just one of those sheets and crumple it up into a ball. This decreases the size of the object, but not its mass. When you drop the normal paper and the crumpled paper, which one will hit the ground first?
Oh, you don't have any paper with you? Fine, here is what that looks like:
You can see that the crumpled paper hits first—even though the two pieces have the exact same mass. Right there, Aristotle is busted.
But wait, here’s another experiment. This one requires more complicated objects. See if you can get something with a large surface area but a low mass. For example, I have a piece of cardboard and a tiny piece of chalk. The cardboard is indeed more massive (100 grams vs. 1 gram for the chalk). But if I drop them, which will hit the ground first? Let's find out.
Check that out. Thanks to air resistance, the more massive cardboard hits after the chalk.
Again, Aristotle was wrong. (And if you repeated both of those comparison drops on the moon, where there isn't air resistance, the objects would hit the surface at the same time.)
Did we really have to go all the way to the moon to show how things fall? Of course not. But it's still one of the coolest physics demos I've ever seen. I can't wait for a repeat the next time there's an astronaut on the moon. Hopefully, this time they will use a better video camera.
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