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If I press the wall (with my hand) I feel a little pressure at my hand and I move away from it.

If I hit the wall (lets say using the same amount of energy for total work) I feel pain in my hand.

Why is it? Is it because time of impact is shorter?

Would I move away from the wall in second case if standing on perfectly frictionless ground?

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When you are pressing against the wall, what you are feeling is the reaction of the wall to the force you are exerting with your muscles; since this force is spread over the area of your hand, the pressure is not very large: no pain.

In contrast, when you hit the wall (say with a closed fist), the force that is exerted is the force needed to stop the momentum of your fist and arm - in other words, considering the momentum equation

$$p \Delta v = F \Delta t$$

then you have significant initial momentum ($pv$) in the fist+arm which has to be stopped in a very short time (there is not much elasticity in your arm, so the entire arm has to stop "in an instant" or break). This means that $\Delta t$ is very short, and that $F$ must be correspondingly large. On top of that if you make a fist the area is small, so the pressure ($F/A$) is large. Hence, pain.

In principle, if you were standing on frictionless ground, then you would start to move backwards as you swung a punch at the wall (conservation of momentum - arm moves to wall, you move away). After you hit the wall, the arm stops moving towards the wall (may even move away a little0 but the rest of your body is still moving backwards. So yes, you would move away from the wall.

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  • $\begingroup$ "(conservation of momentum - arm moves to wall, you move away)" you mean I move away from wall or arm? $\endgroup$ – user82115 Jun 28 '14 at 21:14
  • $\begingroup$ Both actually. But you move away from the arm faster than from the wall... $\endgroup$ – Floris Jun 28 '14 at 21:15
  • $\begingroup$ I move away from wall before hitting it? How is that possible? $\endgroup$ – user82115 Jun 28 '14 at 23:00
  • $\begingroup$ As your arm extends, your body moves away, your fist moves towards the wall. Your center of gravity (fist + torso) stays put until you hit the wall (at that point there is a net force on the body+arm system, but not before). $\endgroup$ – Floris Jun 28 '14 at 23:03
  • $\begingroup$ So my body(torso) moves from the fist perspective but not in actual universe? (Sorry if I messed it up again but it sounds a little tricky) (does it have someting to do with what einstein said- when you move relative to something it moves relative to you) $\endgroup$ – user82115 Jun 28 '14 at 23:15

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