Why is it that when you drop a feather at a certain height it will slowly hit the ground compared to an iron ball?

If you drop objects that weigh different amounts, which will hit the ground first?

What you need:

• balls that weigh different amounts, eg. basketball, tennis ball
• paper

What to do:

1. If you have two balls that are the same, drop them from the same height at the same time. They should hit the ground together (or at slightly different times depending on how well you hold them up to the same height and drop them at the same time).
2. Hold one light ball and one heavy ball. Which do you think will hit the ground first? Try it -they should hit the ground at the same time (or close to the same time).
3. Try holding up a ball and a piece of paper and dropping them at the same time. Which hits the ground first?
4. Scrunch up the piece of paper into a shape similar size to the ball. Try dropping the scrunched paper and the ball. Which hits the ground first this time?
5. Try dropping a flat piece of paper and the scrunched piece of paper. What do you see?

What happens

Gravity is the force that causes things to fall to earth. When you drop a ball (or anything) it falls down. Gravity causes everything to fall at the same speed. This is why balls that weigh different amounts hit the ground at the same time. Gravity is the force acting in a downwards direction, but air resistance acts in an upwards direction. The flat piece of paper takes much longer to hit the ground, not because it is lighter, but because it has a larger surface area so it gets caught up by air resistance. When it is scrunched into a ball shape, it should hit the ground at about the same time as a ball, and hit the ground earlier than a flat piece of paper, even though they both weigh the same.

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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.

QUESTION #6

Sounds extremely convincing. But, I think there is a slight fallacy in the argument. It mentions nothing about the nature of the force involved, so it looks like it should work with any kind of force! However, it is not quite true. If we lived on a world where the 'falling' was due to electrical forces, and objects had masses and permanent charges, things would be different. Things with zero charge would not fall no matter what their mass is. In fact, the falling rate would be proportional to q/m, where q is the charge and m is the mass. When you tie two objects, 1 and 2, with charges q1, q2, and m1, m2, the combined object will fall at a rate (q1+q2)/(m1+m2). Assuming q1/m1 < q2/m2, or object 2 falls faster than object one, the combined object will fall at an intermediate rate (this can be shown easily). But, there is another point. The 'weight' of an object is the force acting on it. That is just proportional to q, the charge. Since what matters for the falling rate is q/m, the weight will have no definite relation to rate of fall. In fact, you could have a zero-mass object with charge q, which will fall infinitely fast, or an infinite-mass object with charge q, which will not fall at all, but they will 'weigh' the same! So, in fact, the original argument should be reduced to the following statement, which is more accurate:

In mathematical terms, this is equivalent to saying that if q1=q2 then m1=m2 or, q/m is the same for all objects, they will all fall at the same rate! All in all, this is pretty hollow an argument.

( G is a constant, called constant of gravitation, M is the mass of the attracting body (here, earth), and m1 is the 'gravitational mass' of the object.)

where m2 is the 'inertial mass' of the object, and a is the acceleration.

Which is proportional to m1/m2, i.e. the gravitational mass divided by the inertial mass. This is our old 'q/m' from the electrical case! Now, if and only if m1/m2 is a constant for all objects, (this constant can be absorbed into G, so the question can be reduced to m1=m2 for all objects) they will all fall at the same rate. If this ratio varies, then we will have no definite relation between rate of fall, and weight.

Answered by: Yasar Safkan, Physics Ph.D. Candidate, M.I.T.