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When we punch a wall our hand hurts...

Do we feel the pain due to the normal force exerted by the wall or due to the reaction force?


marked as duplicate by Aaron Stevens, Thomas Fritsch, Jon Custer, stafusa, Bill N Oct 7 at 16:11

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  • $\begingroup$ The people who answered this question really should have searched for duplicates first. There are many questions on this site essentially asking this exact question. $\endgroup$ – Aaron Stevens Oct 4 at 11:35

The normal force is a reaction force, so the two options are equivalent I guess :D

The term reaction force is usually used when you have two bodies and the first body exerts a force to the second, then by Newton's 3rd law, in the first body appears the corresponding reaction force. The key idea is to think about forces separately for each body, which only interact when they are in the same body.

In your example the bodies would be the person and the wall. In the wall there would only be the punch's force and the person would only feel the normal force (which is the reaction force to the punch's force). See figure:

enter image description here

Imagine this situation in outer space. Because there is no air friction, you would be thrown back and the wall would move very slowly forward.

  • $\begingroup$ So suppose I punch a wall but It doesnt break, and after the punch my hand stays at rest on the wall. Then it means there must be a force which is cancelling out the force of my punch, the Normal Force (if there wasnt any force to cancel out my force then my hand would go straight through the wall). This cant be caused by the reaction force - the reaction force always acts on different objects. So how can reaction force and normal force be the same? So what would be the normal force in this scenario? $\endgroup$ – user243275 Oct 4 at 9:35
  • $\begingroup$ But isnt normal force supposed to act on the same objects? $\endgroup$ – user243275 Oct 4 at 9:51
  • $\begingroup$ Yes, see the figure. The $F$ in the guy is the normal force. The $F$ in the wall is the force from your punch. $\endgroup$ – Puco4 Oct 4 at 9:52
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    $\begingroup$ yeah, they don't cancel out. They are just forces acting in different bodies. I don't know how else can I explain it :S $\endgroup$ – Puco4 Oct 4 at 10:02
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    $\begingroup$ Actually the forces your describe would still be the same in a non-inertial reference frame (they would just be described differently). If you are taking about pseudoforces, then yes that's true, but that's not what I read talking about. $\endgroup$ – Aaron Stevens Oct 5 at 11:44

The normal force is the reaction force.

  • You punch the wall with a punching force. You don't feel that punching force yourself, only the wall does.
  • The wall responds by exerting a reaction force back on your hand, equal to the punching force but opposite (Newtons' 3rd law).
  • We then give this reaction force a name: we call it a normal force!

To be fully accurate, it is not the reaction force entirely, which we call a normal force, it is the perpendicular component of the reaction force which we call a normal force. The parallel/tangential component, if any, is called a friction force - it is not present in this punching example.

Do we feel the pain due to the normal force exerted by the wall or is it the reaction force?

The answer is: they are the same thing.

  • $\begingroup$ Is the normal force also the reaction force only in this case? Or is the reaction force always the same as the normal force? $\endgroup$ – user243275 Oct 4 at 11:05
  • $\begingroup$ There are many types of reaction forces. It is just a category. As an example: When Earth pulls in you with a gravitational force, then the reaction force is your gravitational force pulling oppositely but equally in the Earth. In the case of punching a wall, we name the reaction force: "normal force". The term "normal force" is not used for anything else, no - the normal force always only exists as a reaction to something else. If nothing is pushing on the wall, then there is no normal force exerted by the wall, because there is nothing to react to. $\endgroup$ – Steeven Oct 4 at 11:29
  • $\begingroup$ the normal force always only exists as a reaction to something else By N3L technically all forces only exist as reactions to something else (the other force in the pair) :) $\endgroup$ – Aaron Stevens Oct 4 at 11:31

When you hit the wall your fist imposes a force on it and the wall imposes a corresponding force on your fist. The instantaneous force will be high enough to do damage to your hand, which is why it hurts.

There are a number of misunderstandings in the comments following the question, so I will clear them up here.

The 'reaction force' is always equal and opposite to the applied force, so if you hit the wall with a glancing blow, say at 20 degrees to the wall, the reaction force will be at 20 degrees too, pointing back along the direction of the incoming blow.

The phrase 'normal force' just means the component of a force acting at a right angle to something. If you hit the wall with a glancing blow the normal force of reaction (ie the component of the reaction force at right angles to the wall) will not be as great as it would be if you hit the wall head on.

When you say that the reaction force and the applied force 'cancel each other out' you have to be careful to understand the idea properly. If you get caught in a crusher, the forces applied by the jaws in the crusher will eventually 'cancel each other out' but only after you have been flattened between them. Each jaw is continuing to push the other with a massive force, but the effects are perfectly balanced so the two jaws are held motionless by the two opposing forces. The key thing is that the forces continue to operate- it is the combined effect that is cancelled out rather than the forces themselves.

If you looked at what happens in slow motion you will see that when the foremost part of your fist first meets the wall it is stopped, but the rest of your fist piles in behind it, effectively distorting it. At the same time, the wall gives ever so slightly under the impact then rebounds. At every instant the overall force applied by your first to the wall equals the overall force being applied by the wall to your fist.