The meaning of force and Newton's third law

[physio]

I push on a wall and the wall pushes me back (according to Newton's third law), but what i don't understand is that no acceleration is produced hence is it not that i have not applied any force?

If i jump then i return to the ground (obviously) then doesn't the Earth accelerate towards me?
How much is that acceleration? How come nobody can tell if it has accelerated?

I know these questions are dumb, but just trying to clear a few niggling doubts..!

 

[Simon Bridge]

I push on a wall and the wall pushes me back (according to Newton's third law), but what i don't understand is that no acceleration is produced hence is it not that i have not applied any force?

1. it is an unbalanced force that is equal to the rate of change of momentum - forces can be balanced, in which case they produce a constant velocity ... in this case: zero.
2. you have misidentified the reaction force to you pushing on the wall. The reaction force cannot cancel out the acting force - otherwise acceleration would be impossible.

If i jump then i return to the ground (obviously) then doesn't the Earth accelerate towards me?

Yes it does.

How much is that acceleration?

equa and opposite reaction remember - when you push against the Earth, you push it a little away from you (see conservation of momentum) then you and the Earth gravitate towards your common center of mass (law of gravity).

How come nobody can tell if it has accelerated?

The Earth is very much more massive than you ... so it's motion is very small.

 

[Doc Al]

I push on a wall and the wall pushes me back (according to Newton's third law), but what i don't understand is that no acceleration is produced hence is it not that i have not applied any force?

What determines the acceleration of an object is the net force on it. Your push is not the only force acting on the wall. The ground holds it in place.

If i jump then i return to the ground (obviously) then doesn't the Earth accelerate towards me?
How much is that acceleration? How come nobody can tell if it has accelerated?

Sure the Earth accelerates toward you (as seen from an inertial frame). Figure out that acceleration using Newton's 2nd law. How does the mass of the Earth compare to your mass?

 

[physio]

2. you have misidentified the reaction force to you pushing on the wall. The reaction force cannot cancel out the acting force - otherwise acceleration would be impossible.

But Newton's 3'rd Law says that action=-reaction, then shouldn't it necessarily cancel out the force.

I have always understood force as a change in momentum, where momentum is the "amount of motion", then shouldn't the 3rd law read "a change in momentum of one particle is equal and opposite to a change in momentum of the other particle." Also, the momentum exists only for a body in motion. Thus Newton's 3rd Law should be only defined for bodies in motion and not for those which are in a state of rest.

Hence the conclusion follows: no force is being applied when I am pushing against the wall.

I just haven't understood Newton's 3rd Law and please please correct me if I am wrong.

Thank You,
@Simon Bridge & Doc Al

P.S.:- Can you give some examples where forces are applied and the object moves with constant velocity...

 

[Dale]

But Newton's 3'rd Law says that action=-reaction, then shouldn't it necessarily cancel out the force.

No. Action and reaction always act on different objects. So they never cancel.

 

[D H]

I have always understood force as a change in momentum.

That's Newton's second law. Newton's second law talks about the relation between the net (or total) force acting on some body and the change in that body's momentum. It says nothing about change in momentum due to individual forces. Newton's third law talks about individual forces acting on two different bodies. It too says nothing about change in momentum due to individual forces.

What you are missing is that forces are subject to the superposition principle. The net force acting on an object is the vector sum of all of the individual forces acting on that object. Superposition of forces is essentially corollaries I and II to Newton's law of motion. The superposition principle is the glue that connects Newton's third law to his first two laws of motion.

Let's go back to your example of pushing on a wall. Suppose you are standing on a frictionless surface. Now when you push on the wall you will accelerate away from the wall. So what makes this frictionless situation different? When you are pushing on a wall while standing on a non-slippery surface, that surface exerts a horizontal force on you due to static friction. The force exerted by the wall on you cancels the horizontal component of the force that the floor exerts on you. The horizontal component of the net force on you is zero. The vertical vertical component of the net force is also zero because the upward force exerted by the ground on you cancels the downward force exerted by gravity on you.

Note well: Just because the force from the wall happens to be equal but opposite to the static friction force from the floor does not mean these are third law force pairs. Third law force pairs always involve two forces, one acting on one object and the other acting on some other object. The third law reaction to the force exerted by the wall on you is the force you exert on the wall. The third law reaction to the horizontal friction force exerted by the floor on you is an equal but opposite horizontal friction force exerted by you on the floor.

 

[Simon Bridge]

But Newton's 3'rd Law says that action=-reaction, then shouldn't it necessarily cancel out the force.

But then acceleration would be impossible and how would anything come to be in motion? Clearly this idea is not consistent with reality and must be discarded.

Aside: Try the following http://tap.iop.org/mechanics/Newton/212/file_46379.pdf:
If the force on the carriage is equal and opposite to the force on the horse how can the horse
pull the carriage? Is the answer:
(a) The horse cannot pull the carriage because the carriage pulls as hard on the horse as
the horse pulls on the carriage.
(b) The carriage moves because the horse pulls slightly harder on the carriage
(c) The horse pulls the carriage before it has time to react.
(d) The horse can pull the carriage only if the horse is heavier than the carriage.
(e) Another explanation. What might it be?

I'll give you an example - a box sits on a table. It has weight due to the force of gravity. There is an equal and opposite force of the box on the Earth - it acts at the center of the Earth and points towards the box.

There is also a force from the table, pointing upwards, balancing the force of the Earth on the box. There is an equal and opposite force of the table on the Earth also - at the feet. These are not reaction forces to actions but separate (from electromagnetic repulsion of electrons in the objects). This is where you get the idea of opposite reactions cancelling out - since, as the box presses the table, so the table presses the box back. The trick is identifying the pairing for action and reaction.[1]

Remove the table and the box accelerates towards the Earth and the Earth accelerates towards the box. The force and the reaction force are the same but now they are no balanced by other forces.

If I put a parachute on the box, I can arrange for the box to fall at a constant speed. Here the drag force of the chute is equal and opposite the gravity from the Earth. There is no such additional drag on the Earth so the Earth still accelerates towards the box the same as before (more correctly - towards their common center of mass).

If you have ever driven an automobile at a constant speed, maintaining a constant direction, then you are in a situation where there are clearly forces on the object and yet it is not accelerating and it is not stationary... how did you think this happens?

Newtons laws work in concert ... they are often misquoted:
1. a body continues at constant velocity until it is acted upon by an unbalanced force
2. the net force on an object is equal to the rate of change of it's momentum
3. the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

The third law is easy to misunderstand - even Newton needed a lengthy passage to get the idea across.

I have always understood ...

What you have always understood is, in this case, incorrect. It happens a lot - you'll get used to it.

----------------------------
[1] I think misspoke myself earlier. You push the wall, the wall pushes back equally but if the wall were on low friction ground it would slide under your force ... so the ground must push back on the wall. You are also pushing the ground with your feet. The ground is being pushed in opposite directions by your feet and the wall so nothing moves.

Note: if there is zero force on the wall from your pushing, how come you get tired? How come the pushing gets easier if the wall can slide?