# How to understand Newton's 3rd Law

1. Jun 26, 2014

### ultrauser

I have problem undestanding newton's III law. When i press the wall the wall react with the same force on me but as I have less mass I have greater acceleration so I am moving away from wall.

When I hit the wall according to newton's III law the wall should react with the same force on me (and give me acceleration) but I am not moving(away from wall). Can someone explain it to me?

Also in the first example shouldn't I give a wall a little acceleration(even if a tiny bit) as well so why is the wall not moving at all?

2. Jun 26, 2014

### Staff: Mentor

However you exert a force on the wall--whether pressing or hitting--it will always exert an equal and opposite force on you.

But to determine whether something accelerates or not you must look at all the forces acting on it. (That's Newton's 2nd law.) Other forces act on you besides the force exerted by the wall. Friction from the floor, for one. Similarly, the wall is attached to the floor, which exerts a force on the wall to hold it in place.

3. Jun 26, 2014

### Staff: Mentor

Acceleration is a change of speed, whether an increase or a decrease. If you are approaching the wall at some speed, when you hit the wall and your speed is reduced to zero - that's acceleration, caused by the force of the wall on you pushing you backwards.

It's confusing sometimes when people use the word "deceleration", but as far as Newton's $F=ma$ is concerned $a$ can be positive or negative.

it does. But the wall is connected to the earth, so you are accelerating the entire planet... And its mass is so enormous that the resulting acceleration is far too small to detect with even the most sensitive instruments (Don't take my word for it! Google for "mass of earth" and calculate it for yourself!).

4. Jun 26, 2014

### ultrauser

But why I move(from the wall) when I press the wall and I don't move(from the wall) when I hit it(even very hard)?

Edit:Just read Nugatory answer so while hitting the wall I get acceleration that stops me from moving instead of move me away from wall (in case of pressing it) is that right?

Also Is the wall giving the same resistance or lower in case I crush it?

Last edited: Jun 26, 2014
5. Jun 26, 2014

### Staff: Mentor

When you press the wall, you are exerting the force for a long time. But when you hit the wall, the force is only exerted briefly.

If you were to stand on a perfectly frictionless surface when you hit the wall, you'd be able to see a bit of movement.

6. Jun 26, 2014

### Staff: Mentor

I thought by "hit" the wall you mean stand there and hit it with your fist. (D'oh!) But if you mean body slam into it, as Nugatory thought, then he's correct. The key is that a net force on you will produce an acceleration, and that might just slow your motion down, not necessarily move you away.

7. Jun 26, 2014

### ultrauser

Thanks for answers but I still have a little problem with that law.

There 3 more examples I would like answered to understand it.

When we have 2 cars with the same mass. First car is standing and second driving.
When second car hit the first one it moves it in the direction the second one was driving.
But according to newton's 3rd law the 2 forces and accelerations of 2 colliding objects should be the same(they have same mass) with contrary directions so why they are both moving in 1 direction? (Shouldn't second car stop moving? - third example shows what I mean )

When I throw a rock I cause a force on it and a rock causes equal force on me. So if I would stay at frictionless surface would I move backward when throwing rock?

Let's say there are no gravitational forces.
We have 2 planetoids: 1 standing still and second moving at certain speed. Both have mass M=10.
The second planetoid hit the first one.In that momemnt the second planetoid had acceleration a=2.
So it will cause force F=20 (a*M) on first planetoid and the first planetoid will react with the same force.
Does it mean the first planetoid will get acceleration 2 and the second one will stop moving(2-2=0)?

8. Jun 26, 2014

### LURCH

The second car did receive an acceleration, as mentioned by Nugatory earlier. Let's say the second car is traveling at 60 (kph, mph, fps, doesn't matter). Then, that is the car's constant speed. So, from that car's frame of reference, that is called "sitting still". If you were sitting in that car (and I'm not for one instant suggesting that you should!), you would be experiencing no acceleration forces. However, when your vehicle collides with the other, and very suddenly slows to 30, you'll feel enormous acceleration forces! In fact, if you were sitting in the first vehicle, and it suddenly gets launched up to 30 whatevers, you would feel exactly the same acceleration; a wrenching, retina-detaching lurch to the rear.
Doesn't even have to be frictionless. Try it while standing on ice. If you throw hard forward, you will slide backward.
A little unclear what you mean by "the second planet had acceleration a=2" but no; the first planet will get an acceleration in the direction the second was moving, and the second will get an equal acceleration in the opposite direction, which will slow it down, but not stop it.

9. Jun 26, 2014

### ultrauser

To the third example if action=reaction why it slows down and not stop (doesn't the reaction force when colliding is equal to the force the second planetoid have(the force that moves it) ) ?

10. Jun 26, 2014

### Staff: Mentor

All you can say from Newton's 3rd law is that the two planetoids will exert equal and opposite forces on each other (assuming for the moment they just don't break up into a zillion pieces). Thus they will have equal and opposite changes in momentum. Only under certain conditions will the first one come to rest.

11. Jun 26, 2014

### ultrauser

It is probably my bad way of thinking but I understand that law as:
1.planetoid has force(so it moves)
2.planetoid hit other planetoid
3.reaction=force the planetoid has (but in opposite direction)
4.Now planetoid doesn't have force (0)

12. Jun 27, 2014

### Staff: Mentor

No forces are involved when the planetoid is just moving along at constant velocity. Consider Newton's 1st law.

When they hit, they exert forces on each other.

I don't know what you mean by "force the planetoid has". I think you are thinking that the moving planetoid "has force" because it is moving. That is not correct. Forces only happen when they hit.

But when they hit, they exert equal and opposite forces on each other.

The planetoids only experience forces when they are in contact. Before and after they hit, there are no forces acting. (Forces are not required to maintain velocity; forces are required to change velocity.)

13. Jun 27, 2014

### A.T.

Maybe you confuse momentum with force, which is the change of momentum over time.

14. Jun 27, 2014

### ultrauser

Let's say both have mass M=10 and one planetoid(right one) has velocity v= 10(the velocity in the moment of impact) and acceleration a=2.

So shouldn't the force (action or reaction) be equal to 20 (F= mass * acceleration).

What acceleration and velocity will both planetoid have after the impact (let's say they won't crush and mass not change) ??
(will they both get acceleration a=2 (a=F/M) so the right asteroid which had acceleration a=2 now will have a=2-2=0 and stop accelerating - in that case the left asteroid(the one which was standing) would accelerate in left direction and the right asteroid would not accelerate

15. Jun 27, 2014

### olivermsun

The two planetoids collide and exert "forces" on each other during a brief (but nonzero) amount of time. So say P1 is moving in the positive 'x' direction and hits P2, which is originally at rest. During that brief time of contact, P1 is pushing on P2 and causing it to accelerate in the 'x' direction. At the same time, Newton's third law tells us that P2 is pushing back on P1 with the opposite force, therefore it is decelerating at the same rate. When the planetoids are done being in contact, P1 has lost exactly as much velocity as P2 has gained, because they were both accelerated in opposite directions by the same amount over the same time.

16. Jun 27, 2014

The same force does not mean the same acceleration. $F=ma$. Mass also affects acceleration. Your assumption is only true for two objects of same mass.

17. Jun 27, 2014

### olivermsun

Sorry, I probably got confused through the (several) examples above and thought the planetoids were assumed to have the same mass.

So I'll state it here: mass P1 = mass P2.

18. Jun 27, 2014

It will be a lot easier if you include the units and use a coordinate system.
Acceleration and force is a vector quantity. They have magnitude and direction.

Rephrase the question including the direction(With + for right and - for left) and units.
Keep the non-moving object at the centre of the coordinate system. And make the moving object move in the x-axis. I am sure all these will make you understand things more.

19. Jun 27, 2014

### Staff: Mentor

Before the collision, one planetoid is stationary and the other is moving. There is no force and no acceleration of either.

During the collision they exert forces on each other. If that force produces an acceleration of 2 units (while it acts), then the force must equal 20 units.

After the impact there's no more force or acceleration. To determine the velocity of each after the impact, you'll need more information. All you can say is that the increase in velocity of one will equal the decrease in velocity of the other. (Momentum is conserved.)

Again, once the collision is over they no longer touch and thus exert no force on each other. So the acceleration of both is zero. But they will have different speeds than before the collision.

20. Jun 27, 2014

### ultrauser

if velocity decrease and mass won't change how can momentum(p=mv) be conserved?

what do I need to know besides mass and velocity of objects to determine force during impact? (I will try to rewrite it and understand properly)