# Confusion over Newton's 3rd law

1. Jan 1, 2012

### johnathon

If there is always an equal an opposite reaction, wouldn't everything always be in equilibrium and there'd be no net forces? If a car's exhaust is pushing back with xN, the car gets pushed forwards with xN. So the net force is 0 so how can there be acceleration?

2. Jan 1, 2012

### D H

Staff Emeritus
Newton's third law says that if object X exerts a force F on object Y, then object Y must necessarily exert a force -F on object X. Two objects, two forces (which are equal but opposite).

The force that object X exerts on object Y has nothing to do (directly) with the motion of object X. All that matters with respect to the motion of object X is the force exerted by object Y on object X, and by object Z, and every other object that exerts a force on object X.

3. Jan 1, 2012

### Staff: Mentor

No. Realize that the 'action' and 'reaction' forces act on different objects.
Look at the exhaust and the car (rocket?) as separate systems. There's a force (from the exhaust) on the rocket, so the rocket accelerates; there's a force (from the rocket) on the exhaust, so it accelerates. (Ignoring other forces, of course. And I assume you are thinking of a rocket and its exhaust, not a car.)

Sure, if you treat the 'rocket + exhaust' as a single system there's no net force, then the center of mass of the system does not accelerate. But each subsystem certainly does.

4. Jan 1, 2012

### johnathon

Ok. But what about if I push a box forward and it moves across the floor (with no air resistance or friction)? How would you approach that with Newton's 3rd law?

5. Jan 1, 2012

### Staff: Mentor

The box would push you backward (Newton's 3rd law) and you would move across the floor in the opposite direction (Newton's 2nd law with no air resistance or friction).

6. Jan 1, 2012

### Staff: Mentor

You push the box (to the right, say) and the box pushes back on you with an equal force (to the left). That's what Newton's 3rd law says.

Of course there must be other forces acting on you, otherwise you wouldn't get very far. Presumably the floor is able to exert a force on you so you can accelerate to the right and maintain the force on the box.

If there really were no friction at all, you'd push the box (and the box would push back on you) and you'd both accelerate in opposite directions. (Until you broke contact, after which you'll continue to move at constant speed in opposite directions.)

7. Jan 1, 2012

### johnathon

So because my mass is much greater than the mass of the box I'll accelerate much less?

8. Jan 1, 2012

### johnathon

But wouldn't me pushing back on the floor and the floor pushing on me balance out so nothing would change?

9. Jan 1, 2012

### Staff: Mentor

No. Sure, if you only push back on the ground with a force exactly equal (and opposite) to the force you exert on the box, then the net force on you would be zero and you wouldn't accelerate. But that's got nothing to do with Newton's 3rd law. There's no reason why you couldn't push back on the ground with a force greater than you exert on the box.

Newton's 3rd law says, regardless of anything else:

Whatever force you exert on the ground will be equal and opposite to the force exerted by the ground on you.

Whatever force you exert on the box will be equal and opposite to the force exerted by the box on you.

10. Jan 1, 2012

### johnathon

So just with the example of walking forward, I push back on the ground with my foot and the ground pushes equally back on me? Because the earth is so massive it's movement away is insignificant and my movement forward is a lot more noticeable? Is that correct? But then surely it's still a state of equilibrium. So how can the idea of a net force ever exist?

11. Jan 1, 2012

### Staff: Mentor

That's true.
The ground is exerting an unbalanced force on you, so you accelerate forward. That's not equilibrium.
Net force on what?

12. Jan 1, 2012

### johnathon

But doesn't my force backwards on the ground balance it out?

13. Jan 1, 2012

### Staff: Mentor

How can a force on the ground balance out a force on you?

For forces to 'balance out' they must act on the same object.

14. Jan 1, 2012

### johnathon

Ah, thanks. I finally get it. So does that mean if I'm falling on earth (disregarding air resistance) the earth is pulling me down so I'm pulling back on the earth? If I jump up the earth moves back in response?

15. Jan 1, 2012

### Staff: Mentor

Yes, you and the earth exert equal and opposite gravitational forces on each other.

Sure. When you shove off against the earth, you exert equal and opposite forces on each other. Of course, the earth is massive compared to you and barely moves.

16. Jan 1, 2012

### johnathon

And if I'm standing on the floor and not moving, would there be two action reaction pairs? The earth pulling on me and me pulling the earth. The floor pushing up on me to stop me falling and me pushing down on the floor? So the floor pushing me up isn't the reaction to gravity?

17. Jan 1, 2012

### Staff: Mentor

Exactly!
Right! That's one of the most common errors, to think that the floor pushing up is a Newton's 3rd law 'reaction' to gravity. You've got it right.

18. Jan 1, 2012

### johnathon

Out of me pushing on the floor and the floor pushing up on me, which is the reaction? An I pushing down on the floor because the earth is pulling me down? So the upwards force of the floor is responding to that? So the floor pushing up is a response to me being pulled by gravity, but it isn't the reaction force in terms of action reaction pairs?

19. Jan 1, 2012

### Staff: Mentor

The terms 'action' and 'reaction' are somewhat old fashioned and misleading. It makes it sound like one force is the 'action' and the other is the 'reaction', but those distinctions are arbitrary. It's better just to refer to those forces as Newton's 3rd law pairs.
Sounds good to me. If there were no gravity, then there would be no need for the floor to push you up. But they are not Newton's 3rd law pairs.

A good example to illustrate why the force exerted by the floor on you need not necessarily equal your weight is to think of you standing on a scale while in an elevator. As long as the elevator is not accelerating, then the scale pushes up on you with a force equal to your weight. But if the elevator accelerates upward, then the force exerted by the scale must be greater than your weight. So obviously those forces are not 3rd law pairs.

20. Jan 1, 2012

### johnathon

So if the elevator is Pushing up on me more than gravity pulls down, would I feel heavier because I have to push down with more to match the force from the elevator?

21. Jan 1, 2012

### Staff: Mentor

Yes. You don't 'feel' gravity directly, what you feel is the force supporting you. So if you're being accelerated upwards, you'll feel heavier. And if you fell out of a window, you'd feel weightless (until you hit the ground).

22. Jan 1, 2012

### johnathon

Would an object not actually in contact with the elevator but still in it feel this force? So if I were to throw a ball upwards in an elevator accelerating upwards, would the ball still accelerate with the elevator?

23. Jan 1, 2012

### Staff: Mentor

Nope.
Nope. As soon as it left your hand, the only force acting on it would be gravity.

24. Jan 1, 2012

### johnathon

I know I'm getting very off topic on the elevator idea but I promise these are my last two questions :-)
If an elevator was in freefall what would happen?
And if an elevator is accelerating downwards faster than gravity would I stay "stuck" to the ceiling?

25. Jan 1, 2012

### Staff: Mentor

You would feel 'weightless' and just float in the elevator. There would be no force between you and the elevator, since you'd both be in freefall.
Yes. Once you were in contact with the ceiling, you'd stay there. You could stand upside down, if you wanted.