A ballistic pendulum is a device that can be used to determine the speed of a rapidly moving projectile, such as a bullet or an arrow. In this experiment the projectile is a steel ball that is projected by a spring. The ball makes a perfectly inelastic collision with the pendulum bob and after the collision the ball and pendulum swing together up to some maximum height. The faster the ball is moving the higher the pendulum swings. The purpose of this experiment is to use the ballistic pendulum to determine the speed of the projected ball.

Shoot the ball at the pendulum bob and when a perfectly inelastic collision occurs measure the maximum height that the centre of mass of the ball and pendulum rises. Repeat this several times so that you obtain a good average value and so that you have an estimate of the uncertainty. Derive a relationship between the initial speed of the ball before the collision and the maximum height of the system after the collision. You will need to consider first conservation of momentum during the collision and then conservation of mechanical energy after the collision. With the relationship you derive find an estimate of the initial speed and the uncertainty of this value.

Once you have determined an average initial speed for the ball test your result by shooting the ball horizontally off the end of the table. You should be able to predict how far the ball will travel given the initial speed and the height of the table and some knowledge of projectile motion (a commodity which you are now richer for having).

When two balls of equal mass collide elastically in two dimensions momentum and kinetic energy are conserved. If one of the balls is initially at rest then the vector sum of the momenta of the two balls after the collision will be equal to the initial momentum of the incident ball before collision. In addition due to conservation of kinetic energy the angle of separation of the two balls after the collision should be 90^o. The purpose of this experiment is two test these two results.

Set one steel ball into motion using either the spring or the ramp which are provided and allow it to make a clean but glancing collision with a second ball of equal mass that is at rest. You should experiment a bit with the position of the target ball so that a good collision is obtained. Why is it important that the two balls are at the same height when they collide?

After the collision the two balls should move off in different directions and fall to the ground. Record the location of the impact of each of the balls on the ground using carbon paper. Make several trials and find a good average location for each of the balls. The horizontal distance each ball travels between the point of collision and the point of impact with the ground is a direct measure of the speed of the balls after the collision. You will need to determine the location on the ground directly below the point of collision of the two balls to measure these distances. To show that the momentum is conserved in two dimensions you will also need to get a measure of the initial speed of the incident ball before the collision. To do this allow the first ball to move freely without colliding and determine the horizontal distance it travels after leaving the spring or ramp and before impact with the ground. Make a scale drawing of the momenta before and after the collision and test that the predictions above are confirmed to within experimental error.

Place a small piece of plasticine on the target ball at the point of collision of the two balls. This should ensure that the collision is partially inelastic. Repeat the above procedure and determine what changes to your results occur.