# Punch in the face!

## Main Question or Discussion Point

When you punch someone in the face and leave your hand there, it'll be less effective than doing a strike where contact time is kept minimal: hit and back.
The reason is the conservation of linear momentum and impulse.
In the first case:
(As the force-average is the change in the momentum of system(hand+face) divided by
Δt)
F=(Pfinal - Pinitial)/Δt=(0-Pinitial)/Δt=-Pinitial/Δt

[P hereby refers to the initial and final momentum of hand and therefore minus sign becomes + when subtraction is carried out as the direction of the speed changes]

In the second case:
F=(Pfinal - Pinitial)/Δt
so anything added to the Pfinal will increase the Force applied to face by also keeping the time minimal.

Am I correct?

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dextercioby
Homework Helper
No, the momentum transfer is done within a short interval $\delta t$ (the shorter, the better), but $p_{final}$ is always zero in the frame attached to the object being hit.

So the more devastating the blow, the less $\delta t$ have to be, and of course the greater the incoming object's speed.

Try thinking of it qualitatively this way:

The hand-to-face collision is highly inelastic - in other words, your hand does not really "bounce off" very much when you punch someone.

Therefore, in order to pull your arm back, you are using that muscle energy to do work on your arm to pull it backward, rather than doing work on the guy's face.

to sum up, if you want devastating effect, make sure contact area is small. taking it to extreme, just use the knife.

The devastating effect does not depend on how fast you pull back your punch. In martial art, you pull back your punch fast because then you can give the opponent another punch.