Pendulum Study: Period of Swing Materials Science Experimental Investigation ___________________________________________Signature of Sponsoring Teacher ___________________________________________Signature of School Science Fair Coordinator TeacherNathan Leong640 W. Scott St.Chicago, IL 60610Grade 8 Table of ContentsAcknowledgments Page 3Purpose and Hypothesis Page 4Background Research Page 5Materials and Procedure Page 10Results Page 7Conclusion, Reflection, Application Page 8Reference List Page 9 Acknowledgments An acknowledgement goes to Mrs. Machado-Schlossberg for signing and agreeing to the safety sheet for this experiment. 3Purpose The purpose for this project and experiment was to better understand pendulum motion and explore the functions of a pendulum. The experiment was to figure out what kind of effect changing the weight of a pendulum would have on the period of swing. Hypothesis After doing research, the hypothesis was that the weight would have a miniscule effect on the period of swing. A video from study.
com shows the equation to find a pendulum’s period of swing to depend only on the length of the pendulum string and the gravity. This and other sources state that these are the two most important factors for the period of swing. 4Review of Literature Throughout research for this project, there has been an accumulation of multiple sources across the Internet as well as a book written entirely on the topic of pendulums. All of these sources gave important and sometimes unanimous information about a pendulum’s period of swing and its motion. The first online source is from SparkNotes: SAT Physics, which is a credible source because it’s widely used by thousands of students across the nation studying for the SAT test. The main point taken from this site is that is the length of the pendulum string, so does the time it takes for it to oscillate back and forth. Also, the angle of displacement, the angle in which you remove the pendulum bob from the equilibrium position and drop it, does not play a role in its period of swing (Pendulums, 2001).
The next website can be another studying tool, which adds credibility to its information and their explanations of pendulum parameters and factors. Not only does it provide a clear, labeled diagram as SparkNotes did, but it also includes an equation as well as descriptions for the variables. It lists the equation for a pendulum’s period of swing to be T = 2??(L/g), and it explains what each variable, number, and symbol mean. At the end of the page, there is a summary to conclude all the information about time of swing as well as the parameters. The equation shows that the only two pieces of information needed are L, the length of the pendulum rod or string, and g, the acceleration due to gravity, which on earth is 9.8 meters per second (Equation for a Simple Pendulum, 2017). 5Moving over to a publication, another research source was The Simple Pendulum written by Dr.
James E. Parks, who had also done an experiment involving pendulums. Although it wasn’t the same as this experimental investigation, Dr. Parks did have strong thoughts and theories about pendulums. He understood restoring forces, motion, and pendulums quite well so he explained the equation at every step while he simplified. Dr. Parks also states, “the period of a simple pendulum depends only on its length and the value of the acceleration due to gravity.
“. This is information that has been listed in almost every source, and his understanding of physics and this subject of pendulum adds reliability it. Another helpful source was this educational video on study.com regarding the equations of a pendulum and how a pendulum functions. This video, titled Pendulums in Physics: Definition & Equations, was made in a group of lessons so it discusses other topics such as restoring forces and harmonic motion. Although this information wasn’t as useful in creating a hypothesis, it helped better understand a pendulum and how it works. As shown in previous sources, the equations The crucial part of this clip was when the voice over explained, alongside an animation, the role of the pendulum string or rod and the gravity on the bob.
The speaker states, “when you lift a pendulum to one side, the force of gravity wants to pull it back down, and the tension in the string wants to pull it left (or right)”. Both forces then work together to bring the pendulum bob back to the equilibrium position where it was lifted from. The next source is a page from physicsclassroom.com, and it holds extensive information about pendulum motion as well as force analysis of pendulums. This source is pretty credible due to multiple scientific subjects discussed on the rest of the site.
It labeled a pendulum’s motion to 6be periodic and that it would begin a back and forth vibration if displaced from the equilibriumposition as the other sources have highlighted. The force analysis paragraphs gave the most useful information because it, like other sites and texts, said “There are two dominant forces acting upon a pendulum bob at all times during the course of its motion. There is the force of gravity that acts downward upon the bob. It results from the Earth’s mass attracting the mass ofthe bob. And there is a tension force acting upward and towards the pivot point of the pendulum.”. These two forces were said to have the most impact and that a barely noticeable factor was the air resistance. It was important to take away that the weight of the pendulum bob wasn’t listed to have an effect on the period of swing.
Another physics related website was a helpful source and it is at webassign.net. The page titled Simple Harmonic Motion – Concepts actually doesn’t dive that deep into pendulums, but does cover harmonic motion such as pendulums experience. There is also, as the first couple sources had, a diagram that labels the directions of the forces acting upon the pendulum. It does state the equation though along with explanations as to why it is T = 2??(L/g).
Since the only two variables are still L and g, the “period of the simple pendulum does not depend on the mass”. This quote refers to the period of swing and backs up the equations further. To add on, the strictly educational page hyperphysics,phy-astr.gsu.edu explains simple pendulums, period of swings for pendulums, and pendulum motion. By understanding that pendulums experience simple harmonic motion, it made it easier for them to get into the equation.
This site has multiple diagrams of only pendulums, but the one that were most useful were the picture that showed the tension in the string and the direction of restoring force. Since 7 the pendulum has harmonic motion, the force is pushing the weight back to the equilibrium position. Because the pivot in this experiment will have some friction, that pattern of movement will come to an end regardless of weight.
The final online source is at khanacademy.org, and adds trigonometry into the explanations for pendulum movement. This website is almost entirely about learning across a wide range of subjects, which shows that it is a reliable source, but that there is a lot of information that lies in it. Although this time there isn’t an equation, there are simulations of a pendulum as well as a more mathematical approach to looking at how pendulums function. The first two diagrams are the most helpful because the first one shows, in the simplest form, what an average pendulum looks like at the equilibrium position. The one next to it, shows how the force of gravity comes into play when a pendulum is removed from the equilibrium position.
These were what was most important in researching for this experiment, even though there were more complicated explanations relating to trigonometry. Finally, at the end of all the websites and documents, a book titled The Pendulum: A Case Study in Physics had some pages that offered some supportive information. This book written by Gregory L. Baker and James A. Blackburn cover things from the history and origin of a pendulum to theoretical ideas of the pendulum.
These two authors seemed quite educated on the topics of pendulums and physics and had multiple sources at their disposal as well when writing this book. It was a helpful source because it broke down and simplified the equation for a pendulum’s period of swing, T = 2??(L/g), like the other sources have been able to do. It also 8talks about simple pendulums which are described as the ones we see most and what we see in this specific science experiment.
That is why this text was useful in researching and determining a hypothesis.In conclusion, all the nine sources gathered in the research stage contributed some informations or more in creating a prediction in the before beginning the experiment. 9 Materials In this experiment, the materials needed are:At least 1 foot of stringTape1 quarter1 eraser 1 box of cards1 protractor1 scale1 stopwatchThere can be alternative objects to the ones that have been listed such as a different coin or something of the sort. The string is crucial to the pendulum and the scale is to tell you the measurements of the objects that will be used. Procedure Tape one end of the string to a high surface so that at least 1 foot of the string hangs down 10Tape the quarter to the bottom end of the string so that the coin is 1 foot below the surface. If the piece of string extends over 1 foot, cut it so that it matches the measurement.
Using the protractor to measure the angle, pull the pendulum so that it is 60 degrees away from the equilibrium position.Let go and start the stopwatch at the same time until the pendulum returns back to the equilibrium position.Repeat steps 2-4 for the eraser and box of playing cards.Compare the periods of swing for each of the objects. 11Results The results of this experiment match with the predicted results stated in the hypothesis. After testing out two trials, the results came in almost identical both times with the period of swing coming in with the lowest being at around 13 seconds and a max of almost 21 seconds. There may have been some errors while I let go of the pendulum or when I had began the stopwatch, but both trials confirm each other’s results.
Even without any mistakes, the results could not have changed drastically, so the hypothesis still remains more correct than not. Data Table: Object Weight (grams) Period of Swing (min/sec) Trial #1 Period of Swing (min/sec) Trial #2 Quarter 51:14:191:13:47Eraser 91:15:381:17:11Deck of Cards 931:18:711:20:92 12Conclusion To conclude the ideas of this paper, this science project was about observing the effects of changing weights on a pendulum on the period of swing. Due to research in the beginning of the project, the hypothesis was that by changing the weights, there wouldn’t be a visible effect between the period of swings for each weight. After going through the experiment and gathering the results from both trials, it was clear that there was only a small difference between the periods of swing for each object. Like the results said, the biggest difference of time between both trials was less than 8 seconds, so it proves the hypothesis to be correct because it repeated the prediction that the weights would barely have an effect on the time of swing.
This specific experiment was to understand and confirm the idea that weight has a miniscule effect on a pendulum’s period of swing. 13Reflection To reflect, the test and procedure of this project were fair and it had all the variables in control except for the independent variable. With all the variables and materials in control, the results of this experiment were quite accurate, but things could still be changed about the procedure or materials.
For instance, the weight gap between the quarter and eraser was rather small compared to the box of card, but if this experiment was performed again, that would definitely be an alteration to make. Another helpful change could be if there was a third trial, but other than the materials, the experiment is legitimate. Now that the procedure is completed, the data has been collected and analyzed, there isn’t much left to explore. This is due to a lot of information regarding pendulums is online and has been studied already before, so it’s understandable why most of the ideas in this experiment are confirmed. 14Application Some people can apply the results of this experiment to their jobs if they work with pendulums or some pendulum-based timekeepers. Timekeeping is the most common use for a pendulum, but it’s still not commonly used at this time, so this experiment isn’t widely applicable or that useful.
For those who use and build clock pendulums, they can understand that the size of their pendulum bob can be changed if the want to customize it. According to the research, as long as the pendulum rod and the gravity on the bob are kept in check, the bob canbe customized to the owner’s liking and that’s something important for them to know. In terms of science though, this project of pendulums is in the field of materials science and motion. This experiment showcases the research that the only two factors that really factor into a pendulum’s period of swing. It explains how pendulums function with gravity and can show how a pendulum timekeeper works if applied to that. 15Reference List(2011) Pendulums.
Retrieved from http://www.sparknotes.com/testprep/books/sat2/physics/chapter8section5.rhtml Baker, G.
L., Blackburn, J.A. (2005) The Pendulum: A Case Study in Physics. https://books.google.com/books/about/The_Pendulum.
html?id=t4ISDAAAQBAJ=frontcover=kp_read_button#v=onepage=false Kurtus, R. (2017, June 19) Equations for a Simple Pendulum. Retrieved from http://www.school-for-champions.
com/science/pendulum_equations.htm#.WhDyPbaZPR1 Parks, J.E.
(2000, June) The Simple Pendulum. Retrieved from http://www.phys.
utk.edu/labs/SimplePendulum.pdf Pendulums in Physics: Definition & Equations.
Retrieved from http://study.com/academy/lesson/pendulums-in-physics-definition-equations.htmlPendulum Motion. Retrieved from http://www.physicsclassroom.
com/class/waves/Lesson-0/Pendulum-Motion Simple Harmonic Motion – Concepts. Retrieved from http://webassign.net/question_assets/ncsucalcphysmechl3/lab_7_1/manual.html Simple Pendulum. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html Trig and forces: the pendulum Retrieved from https://www.khanacademy.org/computing/computer-programming/programming-natural-simulations/programming-oscillations/a/trig-and-forces-the-pendulum 16