SNHS Physics Blog 8: Ballistic Pendulums

Yunhui Shim

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It was 1742, when Benjamin Robins, an English mathematician and engineer invented the ballistic pendulum, which in his days allowed great advances in ballistics. Ballistic pendulums are simple devices that are used to measure the momentum of a projectile. The momentum derived can then be used to determine the velocity of the projectile, and its kinetic energy. All of these can be accomplished without the need to collect any time data.

The ballistic pendulum bases itself on the conservation of momentum. The pendulum consists of the wooden block of mass m, and the suspension of strings. A projectile of mass m is fired on the wooden block, and the resulting collisions of the projectile is able to embed itself in the block, and thus cause it to rise through a certain height. Most of the projectile’s energy is converted into heat and work, and thus leads to kinetic energy being unable to be conserved. Total horizontal momentum however is conserved, because there are no external horizontal forces that act on the system, and applying the conservation of momentum, we are able to derive the final speed of the system. The equation is v_f=mv/(m+M). The kinetic energy of the system after the collision become KE=0.5(m+M)v_f^2m. All of the kinetic energy is able to be converted into the potential energy of v={(M+m)/m}*sqrt(2gh).

Thus, the pendulum represents a classic example of a dissipative collision in which the conservation of momentum is used for analysis, but the conservation of energy during the collision is unable to be invoked due to the fact that energy goes into inaccessible forms of internal energy. After collision, the conservation of energy can be used in the swing of the combined masses upward, because the gravitational potential energy is conservative.