In a two-side hold, in which the board holders ability to hold the board stationary may affect the break, can be modeled in several different ways. The amount that they allow the board to move backward could be expressed as a fixed distance, or a fixed or percentage amount of energy or force absorbed. A percentage of the force absorbed is the best option, because the holders are applying a force. This will let the distance that the board moves be a function of the strike. With F as a fraction of the force absorbed by the holders, the board now absorbs the net force Fnet=(1-F) (mav )/0.25 s, which gives an acceleration to the board of Fnet/mb. Since the board has this acceleration for the same 0.25 seconds and W=Fnet*1/2ab*t2, the energy imparted to the board during a strike is:
E=1/2mav2 – ((1-F) (mav ))2 /2 mb
In general, for F values greater than 0.9 the difference is small. For 0.90, the difference becomes significant and only a very powerful strike can fracture the board. Below this range the model breaks down as the board undergoes an acceleration that causes it to move away from the strike faster than the strike itself, so the board cannot be broken regardless of the strike. It is interesting to note that this model can also handle F values slightly greater than one, such as when the holders push the board into the strike, such as when an adult pushes the board against a child’s strike to make it easier for them to break.
Pottle, Bill. ABEN 456, 10/9/00
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