# Ballistic Pendulum Lab

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 = h1 - h2. 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 ball-pendulum 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:

Do not fire the gun towards anyone or towards a glass-faced cabinet. You may choose to wear safety glasses. Do not cock the gun before you are ready to fire it; if it hits your fingers (even without a ball), it could do serious damage.

What to do:

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.]