BALLISTIC PENDULUM.

Next, we shall consider elastic collision of a body with a ballistic pendulum which consists of the heavy body suspended on four strings of length L as it is shown in animation. After impact the incoming body will be reflected, and the pendulum will oscillate on strings so its longitudinal axis will be parallel to itself, and the center of the pendulum goes on a circle. Thus, the amplitude of oscillation of a ballistic pendulum is proportional to speed of incoming body. Using the ballistic pendulum we can measure the speed of bullet V. However, for such a measurement the pendulum is designed by such a way, that the bullet would be jammed in it. Neglecting the mass of bullet m as compared to the mass M of pendulum, we can take for calculations that all the pulse of a bullet passes to a pendulum, which begins the motion with speed v=(M/m)V. When the pendulum is deviated by the maximal angle j, all its initial kinetic energy is transformed into the potential energy Mgh, where h is the height of the center of the massive pendulum relatively to the initial level. Finally we can derive: