What will happen to the object below it drop at the same time from the same height in a perfect vacuum?

See the video Apollo astronauts do this test on lunar surface. Here's the famous footage of the Apollo 15 astronaut that dropped a hammer & feather on the moon to prove Galileo's theory that in the absence of atmosphere, objects will fall at the same rate regardless of mass.

Youn tube video.

Do heavier objects fall faster? Newton observed the infamous apple falling from a tree, and drew important conclusions about the behavior of everyday objects under the force of gravity. In the case of a feather and a coin, one would believe that a feather will always fall more slowly to the ground, and the coin faster. However, as we will explore below, heavier objects do not always fall to the ground more quickly than lighter objects do! When dropped from the same height, objects fall to the earth at the same time when there is no major amount of air mass acting on them. Let’s discover why this is!

First, some background info: Mass, the quantity of matter an object contains, is (typically) constant in an object and does not change. In comparison, weight is the measurement of gravitational force being acted upon a particular object. Think about it this way: The mass of your body is the same on earth as it would be on the Moon, while your weight on earth would be much heavier here because the earth’s gravity is much stronger than the moon’s. This experiment aims to remove the variable of air mass acting on objects so we can measure the effect of gravitational acceleration produced by the earth’s gravity.

1 vacuum pump with tube and end caps (available at scientific supply stores)
1 feather
1 coin
stopwatch

Assemble vacuum pump but do not turn it on.
Leaving the pump lying horizontal, place a feather and a coin in top end of the pump.
Turn the pump vertically and record your observations.
Return the feather and the coin to the top of the vacuum pump.
Seal both ends of the vacuum pump. Turn the pump on to remove the air.
Now, turn the pump vertically and record your observations.

The vacuum created an airless chamber for both items to fall freely. You should have noticed that the second time you dropped the feather and the coin, they both fell together at the same speed.

Gravitational acceleration was constant both times you dropped the items. The only difference from one trial to the next was the presence of air mass acting upon the feather: because the feather is an object of low density (it has a low ratio of mass to volume), the feather encounters more drag as it falls through the air. By removing most of the air, the feather should fall the same speed as the denser penny.

This experiment shows us that weight does not determine the rate at which something falls—only air resistance does. Try other things in the tube: a paper clip and a cotton ball, a crayon and a small leaf. Disregarding air resistance, can you believe a piano and pea would hit the ground at the same time if dropped from the same height? You bet!

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Here is a better example. In this case I have a crumpled up piece of paper and some type of foam board. The paper has a mass of 5 grams and the board is 240 grams. Just as a hint, that's a big difference in mass. But which one hit the ground first? Yup, the piece of paper. Awesome, right? And then when I turn the foam board so that the thin side faces down, BOOM. They both hit the ground at the same time.

So, what hits the ground first? Everything. Above you can see it all. Both heavier and lighter things can fall faster. Clearly, you can't just say "heavier is faster".

Acceleration of Falling Objects

Let's look at the case of a falling bowling ball and basket ball. This is a force diagram showing the two objects.

The bowling ball has a greater mass so it also has a greater gravitational force. You can calculate this gravitational force as the product of the mass (m) and the gravitational field (g). There is something else that depends on the mass, the acceleration. If there is only one force on an object then the following would be true (in one dimension):

Since both the acceleration AND the only force depend on mass, I can write:

Heavier things have a greater gravitational force AND heavier things have a lower acceleration. It turns out that these two effects exactly cancel to make falling objects have the same acceleration regardless of mass.

Air Resistance

Clearly, I didn't fully address all the issues above. If all objects have the same falling acceleration, then why did the crumpled up paper hit the ground before the foam board? The problem is that I left off a force - the air resistance force.

Here's another experiment. Put your hand out the window of a moving car. What do you feel? You can feel the air pushing against your hand. If the car drives faster, the air resistance force gets larger. If you make your hand into a fist instead of an open hand, the force decreases.

This air resistance force is really just the sum of the tiny impacts with your hand and the air. It depends on the air speed as well as the size of the object.

Then what happens as you drop both a foam board and a crumpled piece of paper? At first, they have the same acceleration since they both have a zero velocity which makes zero air resistance force. However, after some short time the forces might look like this:

The foam board has a larger gravitational force but it also has a very large air resistance force. The net (total) force on the foam board will give it a smaller acceleration than paper.

But what about the basketball and the bowling ball? Shouldn't they have different accelerations? Technically, yes. Let me redraw the force diagrams for these two objects and include air resistance.

For these objects, the gravitational force is huge in comparison to the air resistance force. Essentially, it doesn't do much to change the falling acceleration of these objects. But when does it matter? This is a tough question. First, anything at a very low speed will have a mostly negligible air resistance and at high speed will have significant air resistance. Here are some cases where you would NOT ignore air resistance:

A falling piece of paper or a feather.
A falling human at high speeds (a sky diver).
A professionally thrown baseball (100 mph).
A ping pong ball.
Tiny rocks or gravy.

I know that doesn't fully answer the question about air resistance, but it gives you an idea of where to start. But it turns out that there are many situations where a heavier object does indeed hit the ground before a lighter object (because of air resistance). I guess this is why Aristotle and many others think this is always true.

Oh, Veritasium has a some great videos about falling objects. Here are my favorite three videos with questions to consider.