Newton's Third Law and pushing against a wall

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My teacher just explained to us Newton's Third Law, and one example she used was her pushing against a wall. She stated that the net force would equal zero because the wall was pushing back, but that doesn't make sense to me... What I was thinking was that the force of her pushing was weaker than the tension in the wall, therefore she couldn't push through/break/whatever. But if it was tension rather than some force pushing back, that would mean the net force wouldn't equal zero, right? Because the tension isn't going to equal exactly the force of her pushing. It would have to be as great as the maximum force needed to break it, which is more than how much she is pushing. I'm confused I guess.
tannerjack, I am new to the forum. I think the point she was trying to make is that "For every action there is an equal and opposite reaction". Meaning forget (for your example) the sum of forces, just know that the wall is resisting the force you are applying, it is in fact giving you an equal and opposing force reaction.
Confusing example.

Better to think of two blocks in space, very close together. You push them apart. Whatever mechanism pushes between them, it affects both equally.

As for the wall not doing anything, it is really a very stiff spring. I've seen machines measure the strength of concrete or rocks, and a micro gauge in line with the sample shows it squishes. This squeezing provides the restoring force.
There is difference between stress and strength.
Strength is a property of a material or of a mechanical element.
Stress is a state property at a specific point within a body, which is a function of
load, geometry and so on.
So the material has some maximal strength, but how much is stress is induced depends on the external forces and is equal but opposite if the forces (per unit area) if they are smaller then the maximal strength of the material.
So was her example wrong, or just poorly chosen? Because the way she made it seem was that some unknown force we haven't learned yet is being exerted by the wall.
Your teacher is sucks, tell her she is dumb.

Newton's third law is the force pair between interacting objects. Best way to remember it is this:

When you punch/slap somebody in the face, they take a hit, but your hand also takes a hit (from his face). That's how I used to think of it back in highschool.
So was her example wrong, or just poorly chosen? Because the way she made it seem was that some unknown force we haven't learned yet is being exerted by the wall.
Well her example is OK, and there really is a force that is exerted by the wall on you. If you had rollerskates on, this force would push you away.
What newton's third law says, is that if an object exerts any kind of force on a second object, than the second object will exert an equal force in the opposite direction on the first object:
you push against the wall, the wall pushes against you, The earth's gravity attracts the moon, so the moon's gravity must attract the earth. If one magnet repels a second magnet, the second one must repel the first.

Where I think you teacher goes, wrong, is when she gives the third law as explanation for the fact that the net force is 0. (she doesn't mention if it's the net force on you or on the wall) The net force on the wall is zero, because the force you exert on it, is equal to the force the rest of the house exerts on it, and the force on you is zero, because the force the wall exerts on you, is equal to the friction force the floor exerts on your shoes. These equalities have nothing to do with newtons third law.

If the wall wasn't attached to the house, it might fall over, and the net force on it wouldn't be equal to 0. If you are wearing rollerskates, the net force on you wouldn't be 0, but at all times, the force you exert on the wall, equals the force the wall exerts on you.

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