The ballistic pendulum is a device used to determine the speed of objects moving too fast for conventional instruments. The basic idea is that a projectile is fired into a pendulum, which then swings upward to some height, which is measured. Working backwards, we can determine the speed of the projectile if the mass of the projectile and pendulum are known. The steps are as follows:
- Assume friction and air resistance are negligible during the swing so we can use conservation of mechanical energy to determine the speed of the pendulum + projectile immediately after the collision.
- Use conservation of momentum to determine the speed of the projectile immediately before the collision.
Order of Magnitude Estimate
Compress the spring on the ballistic pendulum and launch the projectile into the pendulum. Provide an order of magnitude estimate for the speed of the ball by comparing the observed speed to that of other objects that move much faster and much slower. Cite all sources.
Find and record the mass of both the projectile and the pendulum:
Find the center of gravity of the pendulum when the projectile is already embedded. If it is not already marked, then estimate its location by finding where the pendulum will balance on your finger and then mark it with a piece of tape.
Measure and record the initial height of the center of gravity of the pendulum:
Fire the projectile and measure the final height of the center of gravity of the pendulum. Record below:
Calculate the change in gravitational potential energy of the pendulum during the swing.
Use energy conservation, assuming friction and air resistance are negligible, to find the change in kinetic energy during the swing.
If the final kinetic energy is zero when the pendulum stops at its maximum height, what was the initial kinetic energy when the swing started?
Calculate the initial velocity of the pendulum when the swing started.
Use conservation of momentum to find the initial velocity of the ball before the collision. The final velocity of the collision is equal to the velocity at the start of the swing, which you found above.
Was your estimate for the speed of the ball correct within an order of magnitude? Explain.