Purpose:
To study the laws of Conservation of Linear Momentum and of Mechanical Energy
in an inelastic collision.
Introduction:
The ballistic pendulum (Fig. 1) consists of a removable arm (A) pivoted at point O. A spring gun (G) fires a ball (of mass m) into the cage (C) at the lower end of the arm. The ball is trapped in the cage; thus, the collision is totally inelastic. The ball and cage together then rise a vertical distance h = h_{1}  h_{2}. When the ball hits the cage and is trapped, linear momentum is conserved since there are no external horizontal forces acting.  Figure 1: The Ballistic Pendulum 
Write the conservation of momentum equation:
Write the equation that conservation of mechanical energy requires for the ballpendulum combination at its lowest point (initial position) compared to its highest point (final). [Note: we will neglect air resistance and friction in the pendulum bearing.]
Now combine these two equations to find an equation for the speed of the ball just as it leaves the spring gun, its “muzzle speed”.
Equipment we’ll use: Ballistic pendulum; metric rule; catch boxes;
and carbon paper.
Safety Considerations:
Caution: Treat the pendulum with care since it is easily bent. When you cock the gun, pull the pendulum completely out of the way; do NOT push it sideways!
1. Remove the pendulum arm from its support and measure the mass of the
pendulum arm and of the ball.
2. Insert the ball into the cup and find the center of mass of the combination. Measure the length of the pendulum (from where to where did you measure?).
3. Replace the pendulum in the support, and make the gun ready to fire. Put
the ball in the mouth of the gun, swing the pendulum up out of the way, and
use the ramrod to push the ball against the spring as you cock the gun. Note:
if the ball rolls toward the mouth of the barrel, it may be necessary to tilt
the base slightly.
Be certain that the pendulum is at rest, and swing the angle indicator down
to zero. Record the angle (with sign) for the pendulum in this vertical position.
To fire the gun, lift up on the release at the top of the gun. Fire the gun
twice before making any measurements to make certain that the mechanism is working.
4. Fire the gun and record the angle to which the indicator is pushed
and its uncertainty. Repeat these measurements five times.
5. Find the average angle and its uncertainty; calculate the angle the
pendulum swings through. Use this angle to find the average height that the
pendulum rose and its uncertainty. Discuss how to dothis calculation if you
are uncertain.
6. Use your equation from p.1 to find the muzzle speed of the gun and its uncertainty.
7. You will check your answer by predicting the distance the ball will travel when fired horizontally and allowed to hit the floor. Find the distance and its uncertainty.

Figure 2: Ballistic Pendulum Ball as Projectile 
8. Now check your prediction. Remove the pendulum from the support and
lay it aside. Place the gun near the edge of a table. Measure the predicted
horizontal distance xmax and tape a box at this location. Lay a piece of carbon
paper face up in the box and tape a piece of blank paper over it. On the paper
mark the predicted distance and the uncertainty lines indicated in the diagram.
Fire the gun at the box 9 times. Make certain the gun and paper are in the
same places for each shot.
What fraction of the shots fall within 1 deviation of your prediction? What
fraction should? What fraction of the shots fall within 2 deviations of your
prediction? What fraction should? [Refer to handout from previous class for
info.]
This page maintained by Anne G. Young. Last modified 12Feb2003 .