# Difference between short impact and sustained pressure

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?

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.

• "(conservation of momentum - arm moves to wall, you move away)" you mean I move away from wall or arm? – user82115 Jun 28 '14 at 21:14
• Both actually. But you move away from the arm faster than from the wall... – Floris Jun 28 '14 at 21:15
• I move away from wall before hitting it? How is that possible? – user82115 Jun 28 '14 at 23:00
• 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). – Floris Jun 28 '14 at 23:03
• 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) – user82115 Jun 28 '14 at 23:15