How will height of the bottom of a pendulum be affected if different weights are attached to the bottom of the pendulum?

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1 Home Abstract Our project involved attaching weights at 50 gram increments and observing the ways in which they affect the velocity and distance of a pendulum. To acheive this goal, we made a pendulum out of PVC pipes and PVC fittings and mounted various fishing weights to the bottom of it. We gathered our data using the ipad apps, Video Physics and Graphical Analysis. We found that an increase in weight did not have a significant effect on the velocity of the pendulum, but that greater weights did result in greater distances being traveled. Lab Lab Malcolm's Question: How will velocity be affected if different weights are attached to a pendulum? Kiera's Question: How will height of the bottom of a pendulum be affected if different weights are attached to the bottom of the pendulum? Independent Variable: Number of 50 gram fishing weights used Dependent Variable: Distance traveled and velocity of pendulum Controlled Variable: The pendulum and the distance from which it is initially dropped Malcolm's Hypothesis: If five weights at 50g increments are added to the bottom of a pendulum, then there will be a significant increase in velocity with each additional weight given that there is no change in position from where the pendulum is initially released. Kiera's Hypothesis: If five weights at 50g increments are added to the bottom of a pendulum, then the heavier it gets, the higher it will go given that there is no change in position from where the pendulum is released.

2 About Us Background Information Our topic involves the effects of various weights on the velocity and swing distance of a pendulum. We wanted to tie this topic into the real world by relating it to the functions of objects such as swings and certain amusement park rides. Just like a real swing, our pendulum utilizes kinetic energy when it falls and potential energy when it climbs (Lawrence). These two types of energy switch between one another to fit the situation. In our experiment, the weights we add to the pendulum are meant to represent the center of mass that would be brought about by a human being. Our experiment is not perfect because our fishing weights are not shifting balance like human weight could. While a human being can keep a swing moving indefinitely by shifting weight, our pendulum must eventually come to a stop. Although there are numerous things we could calculate with relation to our pendulum, we decided to focus on distance traveled and velocity. Velocity is typically referred to as "the rate at which an object changes position" (Speed). Velocity can be explained through the equation, V=d/t (Speed). In general, momentum describes the amount of effort needed to stop an object in motion (Momentum). In other words, the more momentum something has generated, the harder it will be to stop. Our experiment is intended to test the limitations of mechanisms like swings. By using fishing weights to simulate the scaled weight of a human being, we are attempting to determine how heavier or lighter people would effect the velocity and distance of a swing. If the data collected is accurate, we can use a ratio to determine the velocity or the distance traveled would be affected by simple plugging in a different weight and scalar properties. By doing this on a real life scale, you can determine if a larger swing would be safe for human use. An everyday example of a pendulum is the grandfather clock. The pendulum in the grandfather clock has to swing every two seconds so the weight has to be the right amount. A more recent and interesting function of a pendulum was the use of one in the stability of Taipei 101. This second largest building in the world was built closely to a fault line, so to stabilize it in the event of an earthquake, architects designed a system that holds up an 18 foot in diameter steel ball that weighs over 700 tons. This type of pendulum is called a damper and can be seen in action on windy days from observation decks that surround it. Because of this damper, Taipei 101 can withstand winds up to 216 km/hr by counteracting movements of the building either created by wind or earthquakes. You can also use the pendulum example for someone who is bungee jumping to see if there is any danger in swinging from a certain point. This data could be used for safety purposes or for creating a more cost efficient swing. Works Cited Lawrence, Stephen. "How Do You Go Up in a Swing?" How Do You Go Up in a Swing? N.p., n.d. Web. 28 Nov (an explanation of the different types of energies a swing utilizes)

3 "Momentum." Momentum. N.p., n.d. Web. 28 Nov (an explanation of momentum and the equations used to calculate it) "Speed and Velocity." Speed and Velocity. N.p., n.d. Web. 28 Nov (an explanation of velocity and the equations used to calculate it) "The 728-Ton Tuned Mass Damper of Taipei 101." Amusing Planet. Amusing Planet, 7 Aug Web. 28 Nov (gives a real life example of what a pendulum can be used for in modern architecture) "What Are Some Examples of Pendulums? + Example." Socratic.org. Socratic, n.d. Web. 02 Dec (Shows the different ways in which pendulums are used) Materials and Procedures Materials: * 5 fishing weights (50 grams each) * 1 ipad * 2 textbooks * PVC pipes (3/4", 1") * PVC tee fittings (two 1", one 3/4") * 1 roll of duck tape Procedures: 1. Acquire materials 2. Connect PVC pipes and tee fittings into a pendulum (reference image) 3. Mount pendulum on end of table and secure with duck tape and 2 textbooks 4. Cover bottom tee fitting with duck tape 5. Put a piece of a post-it note on the duck tape 6. Tape a meter stick to the side of the table 7. Mark part of table with tape or post-it note (this will be the position the pendulum is constantly dropped from) 8. Have a partner set up the ipad so that the camera captures both the pendulum and the meter stick 9. Move the pendulum to the starting point and release. Stop recording after the pendulum comes to a complete stop 10. Repeat steps 8-9 for another 4 trials 11. Remove tape and add necessary weights 12. Replace tape to secure weights 13. Repeat steps 8-9 for 5 trials with each additional weight 14. Analyze videos using video physics and graphical analysis

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8 Data and Graph Kiera s Data Kiera s Graph

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12 Malcom s Data Tables

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18 Malcom s Graphs

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25 Results and Conclusion Results Kiera: The results of my test was that the distance that the pendulum traveled slowly got larger up until the last weight. There was a strong positive linear correlation between the weights and the distance traveled. The equation of the best fit line for the average graph is y= x The Y- intercept tells me that the height when no weight is added should be Malcolm: My tests revealed that velocity was virtually unchanged as additional weights were added at 50 gram increments. Given this information, there was no true correlation between the weights and the velocity. Possibly due to human error, the graph of averages reveals a negligible linear correlation between the two. The equation of the best fit line for the average graph is y= x The y-intercept is about 1.08 meters per second. The slope is about.0123 meters per second.

26 Conclusion Kiera: For any lines if best fit, the equations are a linear regression lines where the equation is y= mx+b where m is the slope and b is the Y- intercept. The slope of shows that if you were to continue to add more weight at 50 g intervals, the distance from the lowest point will increase by each time. By conducting this experiment, I found that my hypothesis was wrong. This is because the average of the 250 g weight is less than that of the 200 g weights. I predicted that it would increase at each interval but when looking at the data, you can see that this is not true. Also the Y- intercept doesn't make sense because the control should be at the Y- intercept because there is no added weight. I predict that this is because the T joint on the bottom is what is skewing the data. Malcolm: For the line of best fit, a linear regression line equation is used in which y=mx+b. In this equation, m is the slope and b is the y-intercept. The slope of about.0123 indicates that for each additional weight added at increments of 50 grams, the velocity will increase by about.0123 meters per second. The y-intercept indicates that the average velocity of the pendulum should be about 1.08 meters per second when no additional weights are added. After conducting this experiment, I discovered that my hypothesis was incorrect. I hypothesized that for each additional 50 gram weight added to the pendulum, there would be a significant increase in velocity. The data revealed that the amount of weight made almost no difference to the velocity at all. While the y-intercept does make sense when considering the average of my control data, there were many points well outside of the 1.08 meter per second goal. This was likely due to human error. Error analysis and Next steps Kiera and I found that our data points did not always follow a common trend, and that some points were scattered more than otheres. Considering the fact that trials using the same amount of weight yielded differen't results, it is logical to blame human error. Although we had marked the height at which the pendulum would be released each time for consistency, we still required someone to support and release the pendulum at the start of each trial. Release times may have been milliseconds longer or shorter between each trial. To overcome this problem, we could develop a type of automated release. The weights also could have shifted between trials and skewed the results. We could fix this by creating a tighter holder for each individual weight. The last possible source of human error involves the Vido Physics app. As we tracked the movement of the pendulum manually, it is possible that some points were placed further out from the center of the pendulum than others. To overcome this, we could have marked the pendulum with a brighter color.