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In the first screen you can see that if a person were to push a wall within a typical household the wall would not move while keeping themselves tractioned to the floor. If you push hard and do not traction yourself, you move back.

In screen two if you push a person with no space behind them they will move back, always, or at least have the potential. A 10 year old kid could push a 7'4", 680 lb. person back, but the wall doesn't move despite nothing being behind it. Here are the official questions:

  1. Why or how can the wall push you back?

  2. Why doesn't the wall move if there's nothing behind it to stop it?

  3. Why will a person always move when you push them, and they don't push back?

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Could you clarify your question in part 3? –  Dave Coffman Jun 24 '14 at 21:58
    
When you push a person they move back usually before there's any chance of you moving back. Just imagine pushing a small kid ... do you see yourself moving back? –  Hanley Jun 24 '14 at 22:01
2  
+1 for the drawing. –  Max Ried Jun 24 '14 at 23:02
    
Breaking a wall was indeed the most difficult challenge here: youtube.com/watch?v=hgdh4We8lLQ –  Count Iblis Jun 25 '14 at 1:21

2 Answers 2

A wall is not just standing on the ground, its contact with the ground is made fast by foundations. Pushing against it is pushing against a system wall + ground. Since it is in addition a very rigid solid, it will transmit all of your push to the ground. You can probably be convinced that the resistance of this system to motion is much greater than yours.

Before considering pushing a person, consider pushing some heavy box which is just standing on the ground, and is stable enough (wider than it is tall). Above some minimum force that is needed to overcome friction with the ground, you'll be able to move it -- unless there is something behind, as you state, which will add its own resistance to this pushing motion (but wouldn't resist a pulling motion).

Now consider that the box has the same proportions as a human being: feet (ground contact) quite small compared to height. It will topple down before sliding along the ground.

This is what would happen with the person you're pushing, unless he is either prepared for it (feet apart, high muscle tone, as a wrestler would do e.g.) or unless he moves back to maintain his balance -- this is a postural reflex .

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To push something over, you apply a torque. If the thing you are pushing can provide an equal and opposite counter torque without moving, then it won't move.

In your example, torque can be due to one of two things:

  1. Gravitational: a heavy object with its center of mass displaced relative to its rear support point needs torque to push over because as it rotates, the center of mass is raised:

enter image description here

The force of gravity multiplied by the backset, that is $mg\frac{w}{2}$, is the torque you need to overcome.

  1. Structural: if you glue the "box" in my previous example to the ground, it will resist toppling even more because there is not only the force of gravity, but additionally the force of the glue (cement, bolts, ...) that is holding it to the floor and preventing it from falling over.

Now sometimes when you push objects, they don't fall over - they slide backwards. This happens in cases where the torque needed might be greater than you apply, but the frictional force between the object and the floor is not very high. The force of friction is a function of the normal force (the weight of the object) and the coefficient of friction. This is why it is easier to push somebody backwards on a smooth floor when they are wearing socks than when they have sneakers on.

In short - the wall is heavy and stuck to the floor. This is what makes it hard to push over.

That doesn't mean it's impossible. See this picture for an example of a wall after a tank drove through it in a rather spectacular end to a hostage situation in an elementary school (apologies that the accompanying text is in Dutch...)

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