# What is the reaction force of the normal force when I push a wall?

If I apply a force $$F$$ on the wall, the wall also applies an equal and opposite force, $$F_R$$, to me. However, as the wall is not moving, there must be a normal force, $$F_N$$, equal in magnitude to $$F$$, acting on the wall in the opposite direction.

As all forces act in pairs, the normal force must also have a reaction force. What is that reaction force?

This answer by @Steeven and this video might help you in answering the question.

## 2 Answers

the wall is connected to the floor which is connected to the earth. if you assume the wall is 'perfectly' attached to the floor which in turn is 'perfectly' attached to the earth, you will actually accelerate the earth by an extremely tiny amount

however, it makes much more sense to say that the wall simply does not move when you push it, and the force that ensures the wall does not move is provided by the objects the wall is attached to (e.g. molecular attraction)

• So, there is no normal force acting here? Jul 6, 2021 at 5:34
• @AbuSafwan not necessarily. the wall is touching several objects (eg ceiling, you, floor) and these will exert a normal force on the wall Jul 6, 2021 at 5:38
• Are you trying to say that the reaction force of the normal force is accelerating the wall (and the earth in extension, as the wall is connected to the earth)? If that's what you are saying, you are wrong. Action-reaction forces never act on the same object. Jul 6, 2021 at 5:55
• "if that's what you are saying, you are wrong". As a general advice, you will learn faster by not being overconfident in your grasp of physics ;) (I'm genuinely saying that as a recommendation I would have given to my past and maybe current self, not to trigger you) Jul 6, 2021 at 7:30

Maybe the wall is moving when you jump up and roundhouse kick it, just far too little for you to notice?

If the wall is rigidly attached to the earth (ideal case), then your kick on the wall does make the wall-and-earth move ever so slightly.

If you want to isolate the wall in your analysis, then your kick tries to make the wall move, but the Earth resists at the attachement point. So, the wall applies a force on the earth and the earth reacts with a force back on the wall which keeps the wall practically stationary. I'm not sure I would classify these involved forces as normal forces; they might be friction forces and bonding force in general mainly (but this depends on how idealised we have made the scenario).

• Magnificent as always. Thanks for answering! Jul 6, 2021 at 6:42