# Physics of breaking wood

I will be the first to admit it, I am a nerd and proud of it. Anyway as I was watching my anime, Kenichi, a martial arts one I thought about it and wondered how people in the real world break the wood and how much force they hand has to break/withstand the force. So looking into it I found several weird sites, anyway 1 was good. First we assume that to break a piece of wood the mass hitting it is about the weight of the arm and hand so using said sketchy table found online (couldn't find male)

[TABLE="width: 400"]

[TR]

[TD="width: 150"]Body part[/TD]

[TD]% of total body mass (female)[/TD]

[/TR]

[TR]

[TD="width: 150"]Head[/TD]

[TD]6.68[/TD]

[/TR]

[TR]

[TD="width: 150"]Trunk[/TD]

[TD]42.57[/TD]

[/TR]

[TR]

[TD="width: 150"]Upper Arm[/TD]

[TD]2.55[/TD]

[/TR]

[TR]

[TD="width: 150"]Forearm[/TD]

[TD]1.38[/TD]

[/TR]

[TR]

[TD="width: 150"]Hand[/TD]

[TD]0.56[/TD]

[/TR]

[TR]

[TD="width: 150"]Thigh[/TD]

[TD]14.78[/TD]

[/TR]

[TR]

[TD="width: 150"]Calf[/TD]

[TD]4.81[/TD]

[/TR]

[TR]

[TD="width: 150"]Foot[/TD]

[TD]1.29[/TD]

[/TR]

[/TABLE]

Since we only have the weight of hand and forearm hitting that is approximately 2% of your body mass. Also assuming that people punch at an average of 10km/h

we get .5MVo^{2 }= Deformation Energy + .5 (M+ m)V^{2} where M = the 2% mass of body Vo+ velocity of hand at point of impact or about 50km/h m= mass of board, Deformation Energy = the energy that goes into breaking the board and V = Velocity of hand and board after impact

then using law of conservation of momentum says the momentum of the hand before impact is equal to the momentum of the board and the hand after the impact.

MVo + (M + m)V ∴combining the previous equation we get The deformation Energy = .5MVo^{2}- .5(M+m)V^{2}

and the second equation V= MVo/(M+m)

using substitution we get Deformation Energy = .5MVo^{2}-(.5(M+m)M^{2}Vo^{2})/(M+m)^{2}

then simplifying it down to Deformation energy= .5(mMVo^{2})/(M+m)

Then using averages again taken from online we get

The deformation Energy needed to break a 2x4x8 is = (.5(4.64kg)(.14Kg)(10.0)^{2})/(4.64+.14) = 6.794979079 joules of energy

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