energy transfer

enough relative to other parts of the board (which are generally held still by the

cinderblocks on which the boards are placed), breakage occurs.

This same phenomenon can be analyzed in terms of energy transfer and resulting

deformation damage. Given and object with mass m1 at rest (the board) and another

object of mass m2 (the karateka’s hand) moving at velocity v upon impact and

ignoring the negligible amount of energy lost as thermal energy (heat), the amount of

energy in the system lost to deformation damage (.E) is given by the following:

2

2 1 2

1 2

(1 )

2 ( )

m m e

E v

m m

· - . = · ·

+

where e is the coefficient of restitution, which measures how elastic the collision is. It

is a function of the hardness or softness of the colliding objects, which along with

velocity determines impulse. If hard objects collide (for a perfectly inelastic collision,

e=0), they will accelerate one another quickly, transferring a large amount of force in

a small amount of time while soft objects colliding (for a perfectly elastic collision,

e=1) transfer smaller amounts of energy to one another for longer periods of time.

Difference in how long momentum takes to transfer and therefore in force at a given

instant is why hitting a pillow with the fleshy part of the hand hurts much less than

hitting a brick with the knuckles.