MAPUA INSTITUTE OF TECHNOLOGY Department of Physics
E202: CONSERVATION OF MOMENTUM: THE BALLISTIC PENDULUM DIZON, Joshua Dominic C. [email protected]
/2013150714/CE-2 PHY11L-A4 Group 2 Insert your photo here with the set-up of apparatus as background.
SCORE Signed Data Sheet (5)
Materials & Method (10)
Observations and Results (20) Discussion & Conclusion
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Acknowledgment & References (10) Performance (30)
February 05, 2015
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E202: CONSERVATION OF MOMENTUM: THE BALLISTIC PENDULUM DIZON, Joshua Dominic C.
OBJECTIVE The purpose of this experiment is to apply the principles of conservation of energy and momentum in calculating the velocity of a steel ball using a ballistic pendulum. The experiment was also done to prove the initial velocity of the steel ball through projectile motion. Understanding and application of law of conservation of momentum is really important. One of the most important applications is used in solving crimes and accidents. From simple car accidents to gun fights and murder, conservation of momentum is used in analyzing car collision and ballistic data from guns used in crimes. Ballistic tests helped solve many crimes all over the world. So here in this experiment, we intended to prove the law of conservation of momentum. Through this, we were able to determine the velocity of the steel ball. More details will be explained on the latter part of the report.
Figure 1. Setting the angle indicator of the ballistic pendulum to zero. After the angle indicator was set to zero degrees, the spring gun was set to medium then the steel ball was inserted inside. The launcher was then fired and steel ball was caught by the pendulum catcher.
MATERIALS AND METHODS For the first part, the velocity of the ball was calculated using the law of conservation of momentum. A ballistic pendulum and a steel ball with known mass were used. The spring gun will fire the steel ball which will be caught by the pendulum catcher. The pendulum catcher will then swing together with the pendulum bob which indicates the angle. Initially, the pendulum bob or the angle indicator was set to zero degrees and the height from the center of gravity of the pendulum to the surface of the table was determined. This was done to minimize the percent error and to avoid discrepancies with the results.
Figure 2. Releasing the trigger to fire the steel ball to the pendulum catcher. The angle and the height it displaced were then obtained. Several trials were done to get the average angle made by the pendulum. The average angle will then determine the final height made by the pendulum. When the final height was calculated, the change in height will then be determined by subtracting the initial height from the final height. Finally, the velocity of the steel 1|Page
ball before collision will then be calculated from the data obtained.
Figure 5. Determining the travelled by the steel ball. Figure 3. Determining the final height made by the pendulum. For the second and last part of the experiment, projectile motion was used. A carbon paper is needed for this part of the experiment to mark where the steel ball lands. The spring gun was set near the edge of the table and the pendulum catcher was then fixed upward to allow the ball to travel horizontally. The vertical distance was also measured beforehand.
Figure 4. Setting the launcher near the edge of the table and determining the vertical distance from the floor to the launcher. When the steel ball was fired, it followed a parabolic path. The horizontal distance the steel ball made was then determined from the mark the carbon paper made. Several trials were made to get the average horizontal distance. When all the data needed were obtained, the velocity of the steel ball before the collision will be calculated.
OBSERVATIONS AND RESULTS For the first part of the experiment, a table of data obtained is shown below: Mass of the steel ball, m1 = 65.8750 g Mass of the pendulum, m2 = 245.50 g TRIAL 1
Initial height of y1 = 6.1 the pendulum cm 27° 2 Final height of y2 = 9.1 the pendulum cm 27.5° 3 Increase in y = 3.0 height cm 27.5° 4 Velocity of the u = 76.68 steel ball and cm/s pendulum after collision 27.5° 5 Velocity of the v2 = 0 pendulum cm/s before collision Average angle: Velocity of the v1 = 27.5° steel ball 362.45 before collision cm/s Table 1. Data obtained to get the Initial Velocity of the Steel Ball by Ballistic Method For the first table, the mass of the pendulum and the steel ball was initially determined. The pendulum bob was set to zero to minimize the error. When the ball was fired, the pendulum catches the ball and it swings changing the angle from zero degrees to whatever the pendulum bob indicates. The angles were recorded and this procedure was done five times to get the average angle. The initial and final height was also recorded using a meter stick. For the increase in 2|Page
height, it was calculated by getting difference between the final and initial height. For the velocity of the steel ball and pendulum after collision, it was calculated by getting the square root of two times the gravity and the increase in height. And lastly for the velocity of the steel ball before collision, it was calculated by multiplying the velocity after collision to the division of the total mass of the steel ball and pendulum over the mass of the steel ball. Some sample calculations are shown below for further reference: u = velocity of the steel ball and pendulum after collision
For table 2, the vertical height was initially obtained by measuring the height from the reference point to the ground. After that, the horizontal distance travelled by the steel ball was determined. The marks made by the steel ball on the carbon paper served as the reference point for the horizontal distance. This procedure was done five times to get the average horizontal distance. And lastly, the velocity of the steel ball before collision was calculated by dividing the average horizontal distance to the time, which is computed by getting the square root of 2 times the vertical distance over gravity. Some sample calculations are shown below for further reference:
u = √2𝑔𝑦
v1 = velocity of the steel ball before collision
u = √2(980
𝑐𝑚 )(3.0𝑐𝑚) 𝑠2
v1 = x√
u 76.68 cm/s
v1 = velocity of the steel ball before collision
980 2 𝑠 2(90.0𝑐𝑚)
v1 = (156.84cm) √
(𝑚1 +𝑚2 ) √2𝑔𝑦 𝑚1
v1 = 365.96 cm/s
(65.8750𝑔+245.50𝑔) 𝑐𝑚 √2(980 𝑠2 )(3.0𝑐𝑚) 65.8750𝑔
Percentage Difference, % diff =
|𝐸𝑉1 − 𝐸𝑉2 | × 100% 𝐸𝑉1 + 𝐸𝑉2 ( ) 2
v1 = 362.45 cm/s
For the second part of the experiment, a table of data obtained is shown below: Gravitational constant, g = 980 TRIAL
Horizontal Distance, x 157.80 cm 158.00 cm
Percent difference = 0.96%
Height y = 90.0 from the cm reference 1 point to 2 the ground 3 156.10 cm Velocity v1 = of the 365.96 4 156.00 cm steel ball cm/s 5 156.30 cm before Average x: 156.84 cm collision Table 2. Data obtained to get the Initial Velocity of the Steel Ball by Trajectory Method
Table 3. Difference
For table 3, the percentage difference between the velocity of the steel ball before collision in ballistic method (𝐸𝑉1) and trajectory method (𝐸𝑉2) was calculated. The sample computation in getting the percentage difference is shown below: |𝐸𝑉1 −𝐸𝑉2 | % Difference = 𝐸𝑉1 +𝐸𝑉2 ( )
% Difference =
|362.45−365.96| 362.45+365.96 ) 2
% Difference = 0.96% 3|Page
DISCUSSION & CONCLUSION The experiment aims to prove the law of conservation of momentum. By using the law of conservation of momentum, we were able to determine the velocity of a steel ball. The conservation of momentum is a fundamental concept in physics. The conservation of momentum states that the total momentum of a collection of objects is conserved. This means that momentum is neither created nor destroyed, but it was only transformed through the action of forces. The conservation of momentum also states that the total momentum of a closed system remains unchanged. This means that when two objects collide, the total momentum of the objects before the collision is the same as the total momentum of the objects after the collision. On the first part of the experiment, the ballistic method demonstrated an inelastic collision. It means that the energy is not conserved. A high percentage of energy is lost. Projectile method can also be used in getting the velocity of the steel ball. By determining the mass of the steel and the horizontal distance it travelled as well as the vertical height of the spring gun, you can calculate for its velocity. But the projectile method is harder to do and it needs accurate measurement to have a small percentage error. I therefore conclude that the ballistic method is more accurate and practical method to use since it easier to do and there are fewer variables to consider. I also conclude that the reason we came up with results that are almost similar but not equal is because of the presence some errors and inaccuracy in measuring vertical and horizontal distances and other things. In projectile motion method, there are more assumptions could be done in measuring compared to the first method leading to more inaccurate measurements of horizontal distances travelled by the ball. Also, air resistance can affect the results making the vertical distance
shorter. So it is more practical to use the ballistic method than the projectile method. Lastly, since our percent error is very small and is less than one percent, I can say that our group did a very good job in performing the experiment. Our group made careful observations and measurements on necessary variables needed. Having a percent error less than one percent is a big accomplishment.
ACKNOWLEDGMENT & REFERENCE First, I would like to thank the Holy Father who guides me every day and give me the knowledge and strength to continue and strive to study hard. Second, I would like to thank my group mates, for allowing me to join with them in performing the experiment. Without them, I certainly cannot do this work alone. I also would like to thank our professor, Mr. Ricardo De Leon for sharing his knowledge and for his guidance during the experiment proper. Aside from that, I want to acknowledge the lab assistants who trusted us and lend us the materials used and for orienting us for proper care of those. And finally, I would like to thank my family for their love and support in my academic endeavors and fulfilling my dream to become an engineer. Here are the references I used to accomplish this report: - Halliday, D., Resnick, R. (2014). Principles of Physics (Tenth Edition). John Wiley & Sons Singapore Pte. Ltd. P. 129. -
Young, H., Freedman, R., University Physics with Modern Physics, 11th Edition, 2004