Lab: The Ballistic Pendulum

Introduction: Most textbooks show a diagram of a projectile launched horizontally into a catcher or block. Find the figure and discussion in your book and look at it before lab. The catcher hangs at the end of a rod. The catcher + steel marble swing up after the marble is fired into it. A ratchet system locks the catcher into place at the peak height. Two methods will be used to find the velocity of the marble that we shoot from the apparatus. The first method uses a direct measurement of the velocity. You may fire the marble with the catching arm lifted out of the way and use the same setup with glx setup that you have used previously. This will determine the initial launch velocity of the steel marble. The second method is to use conservation of energy and momentum. There are two events that occur using this setup. Working backwards, the ball plus catcher are stopped at a ratchet position. At the end they have a total energy described by potential only. At the start of rising the ball and catcher were together at the bottom of the pendulum, and had kinetic energy just after the collision. The final potential energy came from that kinetic energy. These two positions (after collision at the bottom, and later stopped at the top) describe the "rising" event after the collision. By measuring the height you can determine the speed just after the collision. Use conservation of energy. The other event is the collision itself. You must use momentum conservation to describe how fast the steel marble was moving before the collision. You know the speed of the ball plus catcher just after the collision (from above). Calculate the speed and momentum of the system just after the collision. The total momentum must be the same before the collision, but is carried by the ball alone. Calculate the speed of the ball (steel marble).

Procedures: 1. Determine the velocity of the steel marble by pasco glx photogate setup (careful to have marble centered). Record the photogate velocity with its uncertainty. 2. Now fire the marble into the pendulum catcher. You must take care to line things up, and hold down your equipment (no recoil of the pendulum apparatus). 3. The pendulum will rise to a notch or ratchet position. Record the notch and repeat several times. 4. Find the average notch position and set the pendulum to that position. 5. Measure the height of the POINTER on the pendulum at the notch position, and also measure the height when hanging down. These are yf and yi. 6. Measure the mass of the marble on a balance if needed.

Analysis: 1. Use conservation of energy and your measurements to first determine the speed of the system immediately after the collision 2. Use conservation of momentum, and results from 1 above to determine the speed of the marble just before the collision. Call this speed your ballistic pendulum determination of the initial velocity. Ideally this would be the same as your measurement from procedure 1 above. 3. Compare (percent difference) the initial velocity of the projectile determined using ballistic pendulum, and the direct measurement. 4. Compute the kinetic energy before the collision and immediately after, compare and discuss. When calculating kinetic energy before, you should use the speed you found from the ballistic pendulum method.

5. You are now able to compare the kinetic energy after the collision to that before the collision. Think about (answer) why you think this specific numerical result happens (it is about 1/7th or so for most of you, but how do I know that).