# Homework Help: A basic question about free fall (concerning Galileo and Aristotle)

1. Apr 25, 2014

### Amio

This question is from Resnick, Halliday, Krane; Physics 5th edition. This is not actually a homework problem rather a question and so I hope it's not inappropriate to post it here.

If m is a light stone and M is a heavy one, according to Aristotle M should fall fall faster than m. Galileo attempted to show that Aristotle's belief was logically inconsistent by the following argument: Tie m and M together to form a double stone. Then, in falling, m should retard M, because it tends to fall more slowly, and the combination would fall faster than m but more slowly than M; but according to Aristotle the double body (M + m) is heavier than M and, hence, should fall faster than M.
What's wrong with this reasoning? If nothing then (in order to prove Aristotle wrong) what need is there for experiment?

2. Apr 25, 2014

### micromass

Thoughts?

3. Apr 25, 2014

### Amio

I really cant think my way out of this.

4. Apr 25, 2014

### micromass

5. Apr 25, 2014

### Amio

I can't find what is wrong with Galileo's reasoning. And I wonder why an experiment was necessary to prove Aristotle wrong?

Last edited: Apr 25, 2014
6. Apr 25, 2014

### AlephZero

Well, Aristotle didn't need an experiment to prove he was right

But seriously, the whole basis of modern science is experiment. Galileo was one of the first to start down that road.

There's a story about a group of Greek philosophers arguing for days about how many teeth a horse ought to have. When somebody suggested they should answer the question by getting a horse and looking in its mouth, he was thrown out of the discussion as a crackpot. That's not how science works!

7. Apr 25, 2014

Do you think there is any other way?

8. Apr 25, 2014

### Rellek

Hey there!

Mathematically, this is pretty quick to prove, but conceptually, it is pretty interesting.

Think of the properties of the lighter object.. obviously, by holding it, it seems that gravity is not pulling as hard on the lighter object. This is pretty obvious because the heavier object obviously takes more effort to hold up.

But, if you were to factor gravity out, how would these objects behave then?

Imagine you had the two objects on a table. If you wanted to push the lighter object, you would notice that getting the lighter object to move would take less "effort" than trying to get the heavier object to start moving. In other words, the smaller object will move at the same rate as the heavier object would, but the heavier object would need a larger force in order to get it to move.

With that logic, then it would seem that the lighter object would fall faster, because gravity should be able to get it moving faster, but you obviously know that the heavier object is being pulled down harder than the smaller object.

This is how I assume Newton came up with his third law, which takes into account both of these properties of the objects.

9. Apr 25, 2014

### Amio

Firstly, do you agree that the (above stated) logical inconsistency of Aristotle shown by Galileo is sound? (Which is my original question.)
Secondly, I understand the importance of experiment in science. But if we can easily show that a theory is logically inconsistent then can't we stop and say that that's wrong with out going into further experiment?

10. Apr 26, 2014

### Jano L.

This is an interesting question: did Galileo prove Aristotle wrong by argument or by experiment?

There are more points involved which makes this bit hard to untangle. I do not know who said exactly what. But here are some interesting statements:

(casual observation)

1. when two bodies of unequal weight are dropped, the heavier body falls towards the ground faster than the lighter one.

The claim 1. is quite right in common situations of course; usually heavier things fall faster (there is air drag which is usually much more effective for light objects). This also makes convincing demonstration of the free fall law difficult to produce.

But let us think of the case the air has negligible effect, like observing ISS from the ground or doing physics demonstration on the Moon like David Scott did :

http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html

In these situations, it is clear that 1. is wrong; it was observed that all loose things move with the same acceleration, independently of their mass. Hence it seems clear that this is an experimental question and was resolved experimentally.

Now let us think of this:

(stronger claim)

2. acceleration of a body when it falls freely in vacuum is the greater the heavier the body and is independent of its shape and other things (it is a function of the weight only).

I believe Galileo's argument was against this kind of claim. Let body C be composed of heavier piece H and lighter piece L. When 2. is applied to C and H, we conclude that C should fall faster than the piece H would do alone, because C is heavier. But if common sense about forces and motion is added to 2. (connected objects pull each other when other agents are separating them apart), and 2. is applied only to composing parts H and L, we conclude that the composed body C falls slower than the heavier piece H would do alone, because the part L slows it down.

Did Galileo disprove 2. purely logically? That seems suspicious and would be very strange if true, since physics is empirical science and we expect that the law of gravity has some empirical ground. But I think experiments win in this case. The part of the argument about the common sense, how forces work, is based on experience. So I think Galileo proved 2. wrong, not necessarily experimentally, but just pointing out that we already know enough from daily experience to rule 2. out.

[Actually, only the first part of 2. is wrong. The part "acceleration in vacuum is a function of weight only" is true and this function is a constant:-) ]