# B Newton's third law confusion

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1. May 5, 2016

### EddiePhys

I am not the best at drawing, I know.
If A exerts a force of 200N on B, then by newton's third law, 200N would be exerted on it. Similarly, if B exerts 100N on A, by newton's third law, 100N would be exerted on it. Then why wouldn't both accelerate in opposite directions with accelerations equal to 300/ma and 300/mb respectively?

2. May 5, 2016

### vanhees71

Why should they? Newton's 2nd Law tells you that
$$m_1 \vec{a}_1=\vec{F}_{1}, \quad m_2 \vec{a}_2=\vec{F}_2.$$
Now, if the forces are interaction forces between the two bodies, i.e., if the system is closed, you have (3rd Law)
$$\vec{F}_1=-\vec{F}_2$$
and thus
$$m_1 \vec{a}_1+m_2 \vec{a}_2=0 \; \Rightarrow \; m_1 \vec{v}_1+m_2 \vec{v}_2=\vec{P}=\text{const},$$
i.e., that the total momentum is a conserved quantity. So Newton's 3rd Law is, from a modern perspective, just the conservation of total momentum of a closed system, which is a necessary consequence of the homogeneity of space in the Newtonian space-time model (via Noether's theorem).

3. May 5, 2016

### sidt36

Remember F = MA
F1 = -F2 is a perfect interpretation of the 3rd law

How ever

The masses aren't equal

m1a1 = m2a2

Hope that helped

4. May 5, 2016

### jbriggs444

You exert either 100N or 200N and you then expect an acceleration as if you applied 100N and 200N together? But let that slide.

Edit: Perhaps you have a violation of Newton's third law in mind so that A pushes on B with 100N at the same time that B pushes on A with 200N. How is that supposed to work?

What about the rest of the picture? One imagines that hand A and hand B are both connected to the same person and that the person is pressing his hands together (with either 100N or 200N of force). That means that his arms are pushing his hands together. The F in Newton's second law is the net force on the object from all the individual forces combined. It is not the single force that happens to appear on a drawing.

When you do a "free body drawing", you are expected to include all relevant forces.

5. May 5, 2016

### EddiePhys

Person A is exerting a 200N force on B and B is exerting 100N on A

6. May 5, 2016

### jbriggs444

Try to do that in real life. You can't.

7. May 5, 2016

### EddiePhys

Why not? Okay, maybe two pistons or some machine instead of human? One exerting 100N and the other exerting 200N acting on each other. Surely that's possible

8. May 5, 2016

### jbriggs444

Nope. Cannot be done. The force the one exerts on the other will always be exactly equal to the force the other exerts on the one.

9. May 5, 2016

### lychette

I think that you are misunderstanding Newton's 3rd Law...read it carefully!
If A is exerting a force of 200N on B then B is exerting a force of 200N on A
The force on A cannot be different to the force on B

10. May 5, 2016

### nasu

Your problem is not even third law so much as the notion of force as a measure of interaction.
In order to have a force you need to have two objects interacting in some way. It's not that one does something on the other but rather a mutual process.
For one interaction there is one pair of forces. If you have another pair of forces, you have some other interaction, either between another pair of objects or a different kind of interaction between the same objects (like gravitational and electric interaction, for example).
It would be less confusing if you stop thinking in terms of "A did this to B" and see it as interaction between A and B, measured by a pair of equal and opposite forces.

11. May 5, 2016

### EddiePhys

So if I take a piston that can push with 200N and one that can with 100N and place their pushing ends together and activate them at the same time, what would happen?

12. May 5, 2016

### jbriggs444

It depends on the pistons. A piston that can push with 200N against a static load may not be able to achieve that against a load that is retreating. A piston that can push with 100 N against a static load may do better or worse against a load that is encroaching. Whatever occurs, the force of the pistons on one another will at all times be exactly equal.

Consider a 1 gram piece of paper placed between the two pistons and suppose, for the sake of argument, that the one piston succeeds in exerting 200N and the other piston succeeds in exerting 100N. Please calculate the resulting acceleration of the piece of paper.

13. May 5, 2016

### EddiePhys

200-100/mass => 100/0.001 wait what is going on. The acceleration can't be this much.

14. May 5, 2016

### jbriggs444

BINGO!. That's exactly right. The acceleration cannot be that much. And the only way to make it not that much is for the two pistons to be exerting [nearly] equal and opposite forces.

15. May 5, 2016

### EddiePhys

This is, for some reason very unintuitive for me. If two people are pushing on each other, wouldn't the stronger one cause the weaker one to accelerate? If the forces are equal and opposite how is this possible?

16. May 5, 2016

### jbriggs444

The two forces do not act on the same object. https://www.lhup.edu/~dsimanek/physics/horsecart.htm

17. May 5, 2016

### nasu

If the forces due to interaction between the two people are the only forces, they will both accelerate, in opposite directions. The one with lower mass will have higher acceleration. If there are other forces present, the accelerations will depend on the net force, for each person.
If the "strong" person pushes the "weak" one against a wall, there will be no acceleration, for example.

18. May 5, 2016

### EddiePhys

What will be the force with which both of them will accelerate in opposite directions? Say the strong person is pushing with 200N and the the weak one with 100N

19. May 5, 2016

### jbriggs444

Newton's third law. They can't.

20. May 5, 2016

### nasu

You still persist in this nonsense?
You were told many times that this is not possible.
The interaction between the two is characterized by a pair of forces equal in magnitude.
Each person is pushed with the same force due to the interaction between them.

What each does (how accelerate or maybe not) depends on all forces acting on each one, forces that have as a source interactions with other objects (ground, walls, chairs, etc)