# Help Explaining Newton's Third Law

1. Nov 28, 2009

### ediggity

1. The problem statement, all variables and given/known data
This isn't a homework question, but I thought this would be the appropriate place for the thread.

I am having trouble explaining Newton's Laws to my friend. His confusion lies in the fact that the second Law F=ma does not equate to the sum of Forces in The third Law.

Ex. A bus, and a mosquito

The mosquito and the bus collide, the Force of the bus on the mosquito is equal to the force of the mosquito on the bus. I tried to tell him they are equal.

He seems to think that if (and these are totally made up numbers)
Mb=100mg
ab=4m/s^2

mm=.2mg
am= .5m/s^2

then Mb(ab) =/= - mm(am), so the third Law is incorrect.

2. Relevant equations

F=ma

F=-F

3. The attempt at a solution

I tried to explain the conservation of momentum for inelastic and elastic crashes, but he doesn't want to hear it.

Does anyone have any ideas of how I can explain the third law using his not equal example? Thanks for the help in advance.

2. Nov 28, 2009

### cepheid

Staff Emeritus
You can't just make up arbitrary numbers, then use those to try to illustrate general principles, and expect it to work. The fallacy arises from the fact that the numbers are not representative of what would occur in a real example *as a result of Newton's Third Law.*

If a bus (mass M) and a mosquito (mass m) collide, then Newton's Third Law says that

$$F_{bm} = - F_{mb}$$ ​

Where Fmb is the force of the mosquito on the bus, and vice versa for Fbm. From Newton's second law, the force on the object is equal to its mass times its acceleration. The result is:

$$ma_m = - Ma_b$$ ​

Therefore, it *must* be true that:

$$\frac{m}{M} = - \frac{a_b}{a_m}$$ ​

For your made up example, the accelerations and the masses are not related in this way, so of course it doesn't work.

3. Nov 28, 2009

### ediggity

He wants to replace Fbm=-Fmb

with ma

I told him the exact same thing. You can't just make up numbers and plug them into the third Law, and say they don't work.

Would it be correct to say that the third Law in the made up mosquito case is independent of the Second law, because it is taking into account the sum of the Forces?

4. Nov 28, 2009

### diazona

Well, umm... they are two different statements. One could imagine a universe in which the 3rd law is true but the 2nd is not, or vice-versa. So I guess you could say they're independent.

The 3rd law deals with forces on different objects, while the 2nd law deals with forces on one object.

5. Nov 28, 2009

### ediggity

I also forgot to post his other argument for the Third Law.

I gave him the example for the book on the table, because I figured it would be easiest to understand. However, before I could even explain it he didn't believe it was correct, because the book was not in motion, and they are called Newton's Laws of Motion.

6. Nov 28, 2009

### diazona

okay, I think I feel your pain

You could tell him there's a whole other set of Newton's Laws of Non-Motion, that just happen to be the same...

7. Nov 28, 2009

### ediggity

I think my next example is going to be explaining the Force from punching myself in the face.

8. Nov 28, 2009

### cepheid

Staff Emeritus
His argument is based on semantics and demonstrates his lack of understanding of what physics is trying to do, which is to determine, what, if any, general laws apply to systems in nature.

If he's really so hung up on the wording, maybe you should ask him the following: is there any reason why Newton's Laws of *Motion* shouldn't tell you when it occurs and when it doesn't? Furthermore, it's only from his point of view that the book is "at rest". From the point of view of an observer in an airplane flying overhead, or an observer on Mars, the book is in motion. There is *no* preferred reference frame that can be used to define an absolute notion of "rest."

As for the book example:

The book example is totally consistent with Newton's Second Law. The net force on the book is zero, therefore it is *not* accelerating.

The book example is totally consistent with Newton's Third Law. The force of the book downward on the table is equal to the force of the table upward on the book.

9. Nov 28, 2009

Touche