INTRODUCTION As an application of the principles of energy and momentum conservation, the ballistic pendulum provides a method for determining the speed of a projectile. In the form of the apparatus used here, the projectile is a small steel ball fired from a spring-loaded "gun" similar to the one used in Experiment 4. After firing, the ball is caught in a completely inelastic collision by a freely-hanging pendulum in such a way that, after the collision, the pendulum-ball system swings upward. As the pendulum (with the ball embedded in it) swings upward, there is a mechanism that catches it just as it reaches its maximum height and would normally begin to swing back down, thereby holding the pendulum at the maximum height of its swing. The equation of momentum conservation for the inelastic collision, coupled with that for energy conservation as the pendulum-ball system swings upward, permits determination of the initial speed of the ball. As a check of the result, the pendulum is removed and the ball is fired horizontally from the edge of the laboratory table, the speed then being calculated from the horizontal distance traveled corresponding to the vertical drop of the ball, as in Experiment 4. PROCEDURE P1. There are two different types of apparatus used for this experiment. The physics is the same for both types. They differ only in the specific type of mechanism that catches and holds the pendulum- ball system after the collision. Begin by comparing your apparatus to Figures 8-1 and 8-2 to determine which apparatus you are using. P2. If you are using the apparatus pictured in Figure 8-1, obtain the mass of the pendulum by reading it from the back of the apparatus. (See Figure 3.) If you are using the apparatus shown Figure 8-2: Alternate Ballistic Pendulum Apparatus in Figure 8-2, detach the pendulum from the apparatus and measure CAUTION! its mass on the laboratory balance. Then reattach the pendulum to the apparatus. Before firing the projectile, make certain no one is in its path. Also measure the mass of the ball. P3. Measure the distance between the red dot on the pendulum and the flat surface of the base of the apparatus.P4. Place the ball on the firing rod and push the ball back against the firing mechanism until the trigger engages and holds the ball against the compressed spring of the mechanism. On the first apparatus, the tension on the spring loaded mechanism can be adjusted continuously by turning the knob on the end opposite the rod that holds the ball. On the second apparatus, there are three positions of compression at which the trigger will engage. If you are using the second apparatus, you will need to take care to use the same spring setting for all measurements in this part of the experiment. (If you are using the first Figure 8-3: Mass of Pendulum apparatus, this is accomplished simply by not turning the knob that adjusts the spring.) P5. Fire the gun by depressing the trigger pad. After the motion of the pendulum-ball system has been arrested at the maximum height, again measure the distance between the red dot on the pendulum and the base of the apparatus. P6. Repeat the measurements of steps P4 and P5 at least four times, being sure to use the same initial compression position of the trigger mechanism each time. P7. Place the apparatus near the edge of the laboratory table, and fire the ball onto the floor. You will need to move the pendulum out of the way. On the first apparatus this can be accomplished simply by loosening the knob, lifting the pendulum and retightening the knob. On the second apparatus, you will need to remove the pendulum. Again be sure to use the same initial compression that was used in steps P4 and P5. Using the technique described in Experiment 4, measure the horizontal and vertical distances traveled by the ball. P8. Repeat steps P4-P7 for two other settings of the trigger compression. (On the first apparatus, you will need to turn the knob through several complete revolutions in order to make a noticeable change in the spring tension. On the second apparatus there are three different positions at which the ball will stop.)QUESTION 1 The variables used in this experiment are m. M. v V and h. Match each of these variables with its definition in this experiment. * m A. mass of steel ball M B. mass of pendulum without steel ball inside C. mass of pedulum with ball inside D. velocity of pendulum, with steel ball inside, immediately after the collision E. velocity of pedulum without steel ball inside, before the collision F. height pendulum rises above its initial position G. velocity of steel ball immediately after colision H. velocity of steel ball before it hits the pendulum 1. initial height of pendulum QUESTION 2 There are two separate processes involved in this experiment: the collision of the steel ball with the pendulum, and the upward swing of the pendulum with the steel ball inside. For which of these process is mechanical energy conserved? a. Mechanical energy is conserved for both the collision and the upward swing of the pendulum. b. Mechanical energy is conserved for the upward swing of the pendulum, but not for the collision. "c. Mechanical energy is conserved for neither the collision nor the upward swing of the pendulum. "d. Mechanical energy is conserved for the collision, but not for the upward swing of the pendulum. QUESTION 3 There are two separate processes involved in this experiment: the collision of the steel ball with the pendulum, and the upward swing of the pendulum with the steel ball inside. For which of these process is momentum conserved? a. Momentum is conserved for neither the collision nor the upward swing of the pendulum. "b. Momentum is conserved for the upward swing of the pendulum, but not for the collision. "c. Momentum is conserved for both the collision and the upward swing of the pendulum. 'd. Momentum is conserved for the collision, but not for the upward swing of the pendulum. QUESTION 4 You will need to calculate the kinetic energy of this system before and after the collision in order to determine the fraction of kinetic energy lost during the collision. Based on your knowledge of kinetic energy and collisions, you should expect that 'a. The kinetic energy after the collision will be substantially less than the kinetic energy before the colision. `b. The kinetic energy after the collision will be much greater than the kinetic energy before the collision. `c. The kinetic energy after the collision will be about the same as the kinetic energy before the collision. 'd. The kinetic energy after the collision may be greater or less than the kinetic energy before the collision, depending on the initial velocity of the steel ball.QUESTION S Suppose you measure the mass of the steel ball to be 52.4 g. the mass of the pendulum (without the steel ball inside) to be 116 g, and the maximum height to which the pendulum swings to be 18.6 cm. Calculate the velocity, in cm/s, of the pendulum, with the ball inside, immediately after the collision. (You may use g = 980 cmis-.) QUESTION 6 Suppose you measure the mass of the steel ball to be 54.5 g, and the mass of the pendulum (without the steel ball inside) to be 117 g. If your value of the velocity of the steel ball before it hits the pendulum is 389 cm/s, and your value for the velocity of the pendulum, with the ball inside, Immediately after the collision is 184 cm/s, what is the kinetic energy of this system, in Joules, immediately before the collision? QUESTION 7 Suppose you measure the mass of the steel ball to be 55.7 g, and the mass of the pendulum (without the steel ball inside) to be 117 g. If your value of the velocity of the steel ball before it hits the pendulum is 401 cm/s, and your value for the velocity of the pendulum, with the ball inside, immediately after the collision is 190 cm/s, what is the kinetic energy of this system, in Joules, immediately after the collision? QUESTION 8 If you found the kinetic energy of this system immediately before the collision to be 0.529 J and the kinetic energy immediately after the collision to be 0.192 J. what fraction of kinetic energy is lost during the collision