Science Investigative  Project |
Swinging Pendulums |
Lum Qian Wei (20) |
210 |
Ms Tan Beng Chiak
Lab book URL: http://qwscienceinvestigativeproject.blogspot.com/
Table of Content
Table of Content
Sections | Page |
Abstract | 1 |
Introduction | 1 |
Apparatus & Materials | 3 |
Methodology | 4 |
Results | 5 |
Discussion | 6 |
Conclusion | 7 |
Further Improvements | 8 |
Acknowledgement | 8 |
References | 8 |
Appendix A- | 9 |
Appendix B- | 10 |
Abstract
This study is about the factors affecting the movement of the pendulum. 2 experiments are conducted to measure the period of oscillation of different pendulums and pendulums in different external conditions – The first with varying lengths of the pendulum and the second one with pendulums place in liquids of different viscosity. From the experiments, results show that the longer the length of the pendulum, the longer the period of oscillation. Also, the more viscous the liquid, the longer the period of oscillation. These results show the relationship between the variables and the movement of the pendulum, and further extends research done in the past.
Introduction
This study was performed to further investigate the effects of viscosity on movement. From the experiment, “Swimming in Syrup” conducted by the Myth Busters, the results were not very accurate due to human error of people’s different swimming speeds. With the use of a pendulum, the amount of force acting on the pendulum to make it move should be constant. (Research interest) Thus this study of pendulums’ period of oscillations through liquids of different viscosity (1, 10, 20, 30 cSt) is conducted to obtain more accurate results and a clearer conclusion. The independent variable will be the viscosity of the liquid the pendulum moves through, while the dependent variable is the period of oscillation. The temperature of the liquids, length of pendulum, height pendulum is raised to and the amount of liquid being used, are kept constant. (Research interest)This research extended to other variables affecting the period of oscillation and a side study on how the length of the pendulum (5, 10, 15 cm) affects the period of oscillation was conducted. The (Independent variable) lengths of the pendulum are varied, and the (dependent variable) period of oscillations are measured. Other variables like the height the pendulum is raised to are kept constant. (Side aim) For both experiments, the data is also analysed to find out if the independent variable affects the period of oscillation proportionally.
Viscosity is a measure of the resistance of a liquid to flow, or in other words, the amount of friction the liquid acts on the moving object. The more viscous the liquid, the larger the amount of friction acting on the pendulum. The hypothesis will therefore be: the higher the viscosity of the liquid the longer the period of oscillation. As for whether the effect on the period of oscillation will be proportional, the hypothesis is that it will be proportional. With reference to Newton’s second law of motion, F = ma (where F = force, m = mass and a = acceleration), the friction acting against the pendulum should affect the acceleration of it proportionally. Since viscosity is a measure of friction in a liquid against flow, F = viscosity. M = mass of pendulum (25g). The equation will then be Viscosity = 25a, and in order to find the deceleration (due to friction) of the pendulum, the equation will be a = viscosity/25, where a = deceleration. a will therefore increase proportionally as m is kept constant. (E.g. a = 10/25, a = 2/5. a = 20/25, a = 4/5. 4/5 is twice as much as 2/5 which is proportional to the doubling of viscosity.) [Loo Wan Yong and Loo Kwok Wai. 2007. Physics Insights. Pg 65.]
To measure viscosity, Zahn cups were used. Zahn cups are cups with orifices (holes) of different sizes, depending on the range of viscosity being tested. Zahn cups measure viscosity by measuring the amount of time required for 44ml of the liquid to flow out through the orifice. The viscosity of the liquid can then be calculated using a formula. This experiment will require Zahn cup #1, which has a orifice size of about 0.198cm (2mm), as it can measure up to 56 cSt. (I only require viscosity of up to 40 cSt.) The formula is: Viscosity = 1.1(Time-29). [Zahn Cup. Retrieved from Weber Scientific.
Based on Galileo Galilei’s research, he concluded that the weight, amplitude and material of the pendulum do not affect its period of oscillation. Amplitude refers to the angle which the pendulum is raised to before release. The period of oscillation is only affect by the length of the pendulum; the longer the pendulum, the longer the period of oscillation. [Andrea. (1997). The Pendulum.]
This is due to the fact that the longer pendulum has to travel a longer distance, thus requiring more time to travel the larger distance. The pendulum is not affected by the other variables as they do not appear in the equation:
T = 2π(L/G) Where T = Period of oscillation L = Length of pendulum G = Acceleration of gravity [The Pendulum.Retrieved from AIAA.]
(Hypothesis) Therefore, the longer the pendulum, the longer the period of oscillation. (Hypothesis) The length of the pendulum should not affect the period of oscillation proportionally. With reference to the equation T = 2pÖ(L/G), the length of the pendulum will not affect the time proportionally. For example, 2pÖ(5/981) = 0.449 (to 3 s.f.), 2pÖ(10/981) = 0.634 (to 3.s.f.). Based on the calculated values, the period of oscillation of the 10cm long pendulum does not double that of the 5cm long pendulum.
Apparatus and Materials
Pre-experiment Zahn Cup Set-up: (Appendix B Fig 1.)
- 2 styrofoam cups
- 1 transparent plastic container
- 1 measuring cup (44ml)
- 1 screwdriver
- 1 sheet of cardboard
- 1 ruler
- 1 pair of scissors
- 1 mathematical compass
- 1 stopwatch (times up to milliseconds)
- 1 string
- 1 calculator
Experiment 1 - Length of pendulum: (Appendix B Fig 2.)
- 1 pendulum (5cm)
- 1 pendulum (10cm)
- 1 pendulum (15cm)
- 1 stopwatch (up to milliseconds)
Experiment 2 - Viscosity: (Appendix B Fig 3.)
- 1 litre of water (viscosity 1)
- 1 litre of honey water (viscosity 10)
- 1 litre of honey water (viscosity 20)
- 1 litre of honey water (viscosity 30)
- 1 pendulum
- 1 measuring beaker (1 litre)
- 1 stopwatch
- 1 plastic container
Methodology
Experiment 1- Length of Pendulum
To find the relationship between the length of the pendulum and the period of oscillation, I measured the time the pendulum takes to complete 5 oscillations, and calculate the period of oscillation by dividing the value by 5. I conducted this experiment with 3 different pendulums of different lengths, 5cm, 10cm and 15cm long. The weight of the pendulum of 25g and the amplitude of 90ºC were kept constant in the 3 set-ups.
Procedure:
1. Raise the 15cm long pendulum at least 15cm from the ground.
2. Clamp it to a support.
3. Raise the weight, parallel to the ground and make sure the string is straight.
4. Release the weight and start the stopwatch simultaneously.
5. Stop the stopwatch after 5 oscillations are completed.
6. Repeat the experiment 4 times more for more accurate results.
7. Repeat steps 1-6 with the 10cm and 5cm long pendulums.
Experiment 2 – Viscosity of Liquids*
To find the relationship between the viscosity of the liquid which the pendulum swings through and the period of oscillation, I measured the time the pendulum takes to complete 5 oscillations and calculate the period of oscillation by dividing the value by 5. I conducted this experiment with 4 different liquids of varying viscosity, 1cSt (water), 10cSt (77% water 23% honey), 20cSt (51% water 49% honey) and 30cSt (26% water 74% honey). The amount of liquid poured into the container was kept constant at 1 litre in all 4 set-ups. The temperature of all liquids was kept at 20ºC as the experiment was conducted in an air-conditioned room. Also, the pendulum’s length and weight was the same, at 10cm and 25g.
Procedure:
1. Using the measuring beaker, pour 1 litre of water into the container.
2. Allow the water to reach the temperature of the air-conditioned room (20ºC).
3. Use the thermometer to check the temperature.
4. Position the chopsticks above the beaker such that the pendulum (string included) is fully submerged.
5. Raise the pendulum till it is just touching the surface of the water.
6. Release the pendulum and start the stopwatch at the same time.
7. Stop the stopwatch after 5 oscillations.
8. Repeat the experiment 4 times more for more accurate results.
9. Repeat steps 1-8 with honey water (10, 20, 30 cSt) instead of water.
*Refer to online lab book (blog) for experiment preparations to obtain percentages of honey and water.
Results *Refer to appendix A for raw data.
Experiment 1 – Length of Pendulum (Fig 1.)
Fig 1 shows that the average time taken for 5 oscillations increased with increasing length of the pendulum, resulting in an increasing trend in the period oscillation.
Experiment 2 – Viscosity of Liquids (Fig 2.)
Fig 2 shows that the average time for 5 oscillations increased with increasing viscosity of the liquid the pendulum moves through, resulting in an increasing trend in period of oscillation.
Discussion
Experiment 1 – Length of Pendulum
The longest pendulum (15cm) took the longest time to complete 5 oscillations, 4.696s, resulting in the largest period of oscillation of 0.9392s. The shortest pendulum (5cm) took the shortest time to complete 5 oscillations, 2.876s, resulting in the shortest period of oscillation of 0.5752s. The 10cm long pendulum had a period of oscillation of 0.79s. Although the period of oscillations are not equivalent to the values derived from the equation: T = 2pÖ(L/G) (0.4486, 0.6344, 0.7769), the values still increase as the length of the pendulum increases. This proves that my hypothesis is right: The longer the length of the pendulum, the longer the period of oscillation.
The period of oscillation of the pendulums of varying lengths do not increase proportionally. For example, the 10cm long pendulum does not have a period of oscillation that is twice as long as that of the 5cm long. Likewise, the period of oscillation of the 15cm long pendulum does not triple that of the 5cm long pendulum. This has proven the hypothesis right: The length of the pendulum does not affect the period of oscillation proportionally.
The assumptions made are that human error in starting and stopping the stopwatch has to be taken into account.
Experiment 2 – Viscosity of Liquids
The pendulum that moved through the most viscous honey water that had a viscosity of 30cSt took the longest time to complete 5 oscillations, 5.234s, resulting in the largest period of oscillation of 1.0468. The pendulum that moved through water that had a viscosity of 1cSt (least viscous), took the shortest time to complete 5 oscillations, 4.07s, resulting in the shortest period of oscillation of 0.814s. The pendulum in the honey water of viscosity 10cSt had a period of oscillation of 0.862s, while the pendulum in the honey water of viscosity 20cSt had a period of oscillation of 0.964. The period of oscillations increase as the viscosity of the liquid increases. This proves that my hypothesis is right: The more viscous the liquid, the longer the period of oscillation.
The period of oscillation of the pendulums in varying viscosities of liquids do not increase proportionally. For example, the pendulum in the honey water of 10cSt does not have a period of oscillation that is ten times as long as that of the pendulum in water. Likewise, the period of oscillation of the pendulum in honey water of 30cSt, does not triple that of the pendulum in honey water 10cSt. This has proven my hypothesis wrong. I have failed to consider that although the deceleration caused by friction may be proportional, the acceleration is kept the same and the resultant acceleration might not be proportional.
The assumptions made are that the liquids’ temperature did not change during the experiment and that human error in starting and stopping the stopwatch has to be taken into account.
Conclusions
The longer the length of the pendulum, the longer the period of oscillation. Also, the length of the pendulum does not affect the period of oscillation proportionally. The more viscous the liquid, which the pendulum moves through, the longer the period of oscillation. The viscosity of the liquid does not affect the period of oscillation proportionally. These conclusions are valid only with the assumptions mentioned in the discussion.
Further improvement/ future plans
If I were given extended time for this project, I would like to investigate how the amplitude affects the period of oscillation, Although research have shown that small amplitudes (angles below 45º) do not affect the period of oscillation, large amplitudes do affect the period of oscillation to a certain extent.
Acknowledgement
Many thanks to Ms Tan Beng Chiak, my Science teacher, for guiding me through this project and giving me feedback on my project.
References
Web Site
Andrea. (1997): The Pendulum. Internet:
<http://muse.tau.ac.il>.
Book
Loo Wan Yong and Loo Kwok Wai. 2007: Physics Insights. Pearson Longman.
Web Site
Weber Scientific: Zahn Cup. Internet: <http://www.weberscientific.com/products/instructions/Zahn%20Cup-instruct.pdf>.
Web Site
AIAA: The Pendulum. Internet: <http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/pendulum_exp.htm>.
Appendix-A
Experiment 1 – Length of Pendulum Raw Data:
Length of pendulum/cm | Time taken for 5 oscillations/s | Period of oscillation/s |
5 | 2.81 | |
2.69 | ||
2.98 | ||
3.06 | ||
2.84 | ||
Average time taken for 5 oscillations/s | 2.876 | 0.5752 |
10 | 3.95 | |
3.97 | ||
3.93 | ||
3.95 | ||
3.95 | ||
Average time taken for 5 oscillations/s | 3.95 | 0.79 |
15 | 4.69 | |
4.69 | ||
4.8 | ||
4.48 | ||
4.82 | ||
Average time taken for 5 oscillations/s | 4.696 | 0.9392 |
Experiment 2 – Viscosity of Liquids Raw Data:
Water (20ºC) | Viscosity/cSt | Time taken for 5 oscillations/s | Period of oscillation/s |
1 | 4.09 | ||
4.04 | |||
4.07 | |||
4.09 | |||
4.03 | |||
Average time taken to complete 5 oscillations/s | 4.07 | 0.814 | |
Honey water (20ºC) | 10 | 4.35 | |
77% water | 4.25 | ||
23% honey | 4.3 | ||
4.26 | |||
4.39 | |||
Average time taken to complete 5 oscillations/s | 4.31 | 0.862 | |
Honey water (20ºC) | 20 | 4.82 | |
51% water | 4.86 | ||
49% honey | 4.89 | ||
4.72 | |||
4.81 | |||
Average time taken to complete 5 oscillations/s | 4.82 | 0.964 | |
Honey water (20ºC) | 30 | 5.21 | |
26% water | 5.32 | ||
74% honey | 5.24 | ||
5.18 | |||
5.22 | |||
5.234 | 1.0468 |
Fig 1. Zahn Cup Set-up
Fig 2. Experiment 1 Set-up
Fig 3. Experiment 2 Set-up
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