E202: CONSERVATION OF MOMENTUM: THE BALLISTIC PENDULUMFRISNEDI, Nadine T. OBJECTIVE MATERIALS AND METHODS The experiment aims to accomplish its two main objectives. The first one is to use the principles of conservation of energy and momentum in determining the velocity of the steel ball. Through the experiment, the students will be able to gain more knowledge and appreciation about the concepts of conservation of momentum and how it is helpful in determining the velocity of moving objects and even the distances it covers. The experiment can also help the students understand on how the angular displacement of an object is important in getting its initial velocity. The experiment will also show how Kinetic Energy and the Gravitational Potential Energy is closely related with the conservation of momentum and during a collision. (Figure 1. The materials and equipment used in the experiment. ) The second objective is to be able to validate the initial velocity of the steel ball through projectile motion. The students will not just learn how to compute for the velocity of the steel ball using the ballistic pendulum but also though the use of projectile launcher. The experiment will help the students be able to understand the applications of the given laboratory formulas in solving problems involving Physics and will surely be helpful in studying other concepts about it. Another thing about this experiment is that it is very easy to conduct and it is not time consuming, thus students will enjoy doing it. The significance of this experiment is that it a way of showing how an inelastic collision happens, what are the things happened afterwards and lastly it shows how fast an object in two dimensions is moving. Before the experiment was actually performed, in which the ballistic pendulum with the steel ball were tested first to prevent accidents since a few of them are releasing the ball accidentally even before the release. The projectile launcher with ballistic pendulum was set up away from the class and pointing towards a bag to prevent it from hitting anything else or a person. The level or range assigned for the group was medium. At the beginning of the experiment, angle marker on the ballistic pendulum was set up to 0Β°. Since group had trouble making it stay at that angle, the group decided to check first if the working table is leveled and when it finally becomes at 0Β°, we started gathering the required data. To get the initial height of the ballistic pendulum, the distance from the base to the center of the pendulum while at the reference point 0 is measured using the meter stick the In the second part. And while it is in the mean angle. The mass of the steel ball is used to compute for its velocity. This displacement was recorded. The vertical distance.) (Figure 4.pendulum was set up on to that angle. 2|Page . The pendulum bob was set to the computed average angle. The mass of the pendulum was also needed in order to compute for the velocity including the additional 100 grams in it. Setting the reference point to zero and measuring the initial height. y of the firing position which is the center of the hole of the spring gun on the table down to the floor was measured using the meter stick. The increase in height was then used for determining the velocity of the steel ball and the pendulum. (Figure 2. The bob was placed back to zero and then the steel ball was again fired. Measuring the initial height of the pendulum. the pendulum placed and locked upward so that the ball can be fired to the floor in horizontal direction. The spring gun was then placed at the end of the table. Measuring the final height of the pendulum based on the computed mean angle) The increase in height was calculated by subtracting the initial height of the pendulum from the final height of the pendulum. This part was done for a total of five trials. (Figure 3. The pendulum moved and made an angular displacement. the steel ball was loaded to the spring gun on the medium level which is said to be the second click heard and then fired to the pendulum holder. The final height of the pendulum was measured from the base to the center of the pendulum.) After getting the measurement. The mean or the average angle was computed by adding the five angles and dividing it by five. The group then placed a bond paper beneath a carbon paper. After the steel ball was fired. Measuring the vertical height of the firing position. (Figure 6.) 3|Page . Determining the horizontal distance from the tip of the spring gun to the tip of the table. the group launched the ball and knew which part it will land.travelled horizontally.) The computed velocity from the first part of the experiment was then used to predict in how far horizontally the ball will land and to test it further. a total of five trials was done. (Figure 7. it landed on the carbon paper which left a mark on the bond paper. For this part. The black marks in the bond paper will show how far the steel ball (Figure 8. Taped the papers securely which will be used to determine the horizontal distance of the ballβs landing since upon landing onto the carbon paper the ball will leave a black mark on the bond paper. Setting up the spring gun at the end of the table while the pendulum is placed upward.) The horizontal distances were measured carefully stating from the tip of the spring gun to the end of the table and from the end of the table to the black marks left on the bond paper using the meter stick. (Figure 5. Table 1. π’ = cm/s β2ππ¦ Velocity of the π£2 =0cm/s 5 26Β° pendulum before collision Velocity of the π£1 = steel ball before Average 375. The group then used the increase in height y. Getting the Initial Velocity of the Steel Ball. Upon completing the five trials. Ballistic Method (Figure 8. the group then calculated the increase in height by subtracting the initial height of the pendulum to the final height of the pendulum.875π + 241. m1 = 65.7 ππ β 8. the group calculated for the average angle.) These distances were recorded.5Β° pendulum Increase in height π¦= 3.5Β° + 26Β° + 26Β° + 26Β° π΄π£πππππ π΄ππππ = 5 π΄π£πππππ π΄ππππ = 25. The group then used the given formulas from the laboratory manual in order to compute for the initial velocity of the steel ball before its collision with the pendulum.6π 980ππ (β(2)( )(3. The average horizontal distance was then computed by adding all the five distances and also dividing it by five.9Β° π΄π£πππππ π΄ππππ = π¦ = π¦2 β π¦1 π¦ = 11.061 collision.2 ππ π’ = β2ππ¦ 980ππ π’ = β(2) ( ) (3.875π π 2 π£1 = 375.2ππ) π 2 π’ = 79.6g Trial Angle Initial height of the π¦1 =8. π£ = 1 Angle: 25. Upon completing the data to be gathered.875g Mass of pendulum.061 ππ/π 4|Page . in determining the change in potential energy which is also said to be the velocity of the steel ball and the pendulum right after collision.5cm 1 26Β° pendulum Final height of the π¦2 =11.2cm 3 26Β° π¦ = π¦2 β π¦1 Velocity of the steel ball and the π’= pendulum right 4 26Β° 79.196 after collision. m2 = 241. OBSERVATIONS AND RESULTS The first part of the experiment was focused in the determination of the velocity of the steel ball after the inelastic collision with the pendulum bob. The average horizontal distances and the measured vertical height was then used to compute for the velocity of the steel ball. Mass of the steel ball.2ππ) 65.5 ππ π¦ = 3.196 ππ/π π£1 = π£1 = π1 +π2 π1 (β2ππ¦) 65.9Β° (π1 +π2 ) cm/s β2ππ¦ π1 Sample computations: π1 + π2 + π3 + π4 + π5 5 26Β° + 25. Determining the horizontal distance travelled by the steel ball.7cm 2 25. After getting the average.513% DISCUSSION & CONCLUSION From the performed experiment. This is one way to know or confirm if the procedures were done properly so that the group will arrive with closely related results.113 ( ) 2 %ππππ = 3.4 cm π cm/s Average x: π£1 = π₯ β 2π¦ 154.The second part is mainly about validating the computed initial velocity of the steel ball through projectile motion.113 5 155. the final velocity of the two masses will be the same.24 cm Sample computations: π₯1 + π₯2 + π₯3 + π₯4 + π₯5 5 153. We have computed properly all that was required for the experiment too by using the appropriate formula for those.513% Sample Computation: % ππππ = |πΈπ1 β πΈπ2 | πΈπ + πΈπ2 ( 1 ) 2 |375.8 + 153. g = 980 cm/s2 Horizontal Height from Trial Distance. % diff = |πΈπ1 βπΈπ2 | πΈπ +πΈπ2 ( 1 ) 2 the Percentage Percent difference = 3. Since the collision was inelastic.9ππ) ( π£1 = 362. the average of the horizontal distance was then computed.24ππ)(β 980ππ ) π 2 (2)(88. we have validated the initial velocity of the steel ball through projectile motion.061 β 362. The group measured the vertical distance of the firing position which is from reference point to the ground. The velocity in the first part was used for predicting the horizontal distance. For the second part. By following the procedures stated in the manual properly gave us all the relevant data that are needed.24 ππ π΄π£πππππ π₯ = π π£1 = π₯ β 2π¦ π£1 = (154. I could say that it was a success.1 + 154. 362. After doing the five trials.4 π΄π£πππππ π₯ = 5 π΄π£πππππ π₯ = 154. Table 2. Difference Determining Percentage Difference. we have used the principles of conservation of energy and momentum in determining the velocity of the steel ball using a ballistic pendulum. When the ball was fired and landed to the carbon paper.7 + 155. This conclusion tells us that we have achieved the first objective of the experiment. In the first part of the experiment.7 cm π£1 = steel ball before collision.8 cm point to the cm ground 2 153. Trajectory Method Gravitational Constant. Table 3.113| % ππππ = 375. Getting the Initial Velocity of the Steel Ball.113 ππ/π The group then computed for the Percent Difference of the two computed velocities.2 + 154. 5|Page . the group then computed for the initial velocity using the given formulas in the laboratory manual.061 + 362.2 cm 3 154. x π¦ = 88. and all the necessary data. it left a black mark that will indicate the horizontal distance it covered after being launched.1 cm Velocity of the 4 154. Our data proves that the conservation of energy and momentum can be used in getting the velocity of the steel ball and pendulum bob.9 the reference 1 153. I believe that in terms of the errors made in the experiment. ACKNOWLEDGMENT & REFERENCE I would like to thank my groupmates for being so cooperative upon doing the experiment. Lastly. The sources of error can be from the measurement of the vertical and horizontal distances.513% which is considered as small difference. De Leon. 6|Page .. Jr. I thank him for instructing us on how we should set up the materials and equipment for our experiment. Since we manually measured these components. The percent difference we got was 3. MapΓΊa Institute of Technology. there is a high possibility that the measurements we got were inaccurate. our experiment will have a great chance of failure.The velocity in the first part was also used in this part for the determination of horizontal distance. Reference: Calderon. The result we got is really close from the initial velocity we got from the first part of the experiment. Ricardo F. (2000) College Physics Laboratory Manual. I also thank our professor. I appreciate all of their efforts since without their help. I would like to thank my family for supporting me in my studies as I pursue my degree in MapΓΊa. Prof. There were five trials and the average horizontal distance is what we used to compute for the initial velocity using the formula in the laboratory manual. Manila: Department of Physics. I also would like to acknowledge the lab assistants for reminding us how to handle the materials and equipment and telling us about the important things to remember such as the weights to be added. Jose C. it is somewhat minimal. for guiding all throughout the experiment. This only says that we have also achieved the second objective of the experiment. 7|Page .