# Breaking Materials

When the board is struck, it begins to vibrate sinusoidally with a certain frequency and amplitude. The frequency of vibration is represented by f=1/2Π√k/m where k is the spring constant for the board (in this case 274 lbs/in ) and m is the apparent mass of the part of the board that is moving (0.5 lb mass or 0.22 kg). This gives a frequency of vibration of about 54 Hz a note that is at the lowest level of our hearing to hear, the sound you hear is that of the board breaking apart. The amplitude of the vibration is related to frequency times the velocity of the striking. This is represented by A=v √m/k where v is the velocity imparted to the board at contact. The breaking speed v in our example would be 4 m/s or 14.8 km/hr. Although this seems low, for an inelastic collision, the speed of your fist must be twice this speed or 29.6 km/hr. To attain this speed, the arm (0.6 m in length) must snap forward in less than 0.3 s.

An elastic collision is almost twice as efficient, which means that hitting the board with a fore fist punch takes less power than with hammer fist. However, because a board hits back with the same force with which it is hit, you must be careful when hitting objects harder than your fist. For these objects, hitting with a softer part of the hand, such as with a hammer fist or knife hand strike, will be less painful.

As you double or triple the number of boards, you must similarly double or triple the striking speed. To break three boards, it takes a breaking speed of about 90 km/hr.