Ballistic Pendulum

Calculation Reference
Mechanics
Newtonian Mechanics
Dynamics

A ballistic pendulum is a device used to measure the velocity or kinetic energy of a projectile, such as a bullet, by analyzing its impact on a pendulum. It was invented in the 18th century and used as a relatively simple and inexpensive way to measure projectile velocities before the advent of modern electronic measurement techniques.

The ballistic pendulum consists of a heavy mass (the pendulum) suspended from a pivot point by a rod or wire, which is free to swing back and forth. The projectile (e.g., a bullet) is fired into the pendulum, embedding itself into the mass and transferring its momentum to the pendulum. As a result, the pendulum swings upward to a certain height, which can be used to determine the initial velocity of the projectile.

The principle behind this device is the conservation of momentum and the conservation of mechanical energy. When the projectile strikes the pendulum, the system's total momentum is conserved. This means that the momentum of the projectile before the collision is equal to the momentum of the combined projectile-pendulum system after the collision. Using this principle, one can calculate the initial velocity of the projectile.

However, during the swinging motion, mechanical energy is conserved, which means the sum of kinetic energy and potential energy remains constant. As the pendulum swings to its highest point, its kinetic energy is converted into gravitational potential energy. By measuring the height the pendulum reaches, one can calculate the potential energy, which then can be used to determine the initial kinetic energy and velocity of the projectile.

It's worth noting that modern techniques, such as high-speed cameras and laser-based systems, have largely replaced ballistic pendulums in measuring projectile velocities. However, the ballistic pendulum remains an interesting and useful tool for demonstrating the principles of conservation of momentum and energy in physics education.