Pendulum Summer Project
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Summer vacation has long been associated with sleeping in, lazy days by the pool, hanging out with friends, learning the vocabulary of harmonic motion, constructing cheesy experiments, and graphing data. Summer 2012 will be no exception. First, I want you to read 3 pages on the internet (Step 1 in “Procedure” below). Then, I want you to print a worksheet from the internet (Step 2). You are to apply what you learned from reading by filling in the 29 boxes on the worksheet with as many correct answers as you can. Research on additional vocabulary may be required (for instance, what is an “independent variable”?) Next, I want you to apply what you learned from reading by constructing a simple experiment where you will carefully record measurements of length and time. You will also take a picture of you with your experiment (Step 19) You will then use your data to construct a graph (Step 21)
Lastly, you will answer questions about the results of your experiment, and put the pages of your completed report in the correct order. Since this is a summer project, you are to bring your completed report with you on the first day of school.
GRADING RUBRIC FOR THIS PROJECT: 100 points
a) At least 5 of the 7 pages turned in on time (first class meeting):7 points b) Report turned in complete (all 7 pages at the same time)7 points c) Data in Table 1 and Table 2 are unique, complete, and correct30 points d) The 12 questions on Page 1 and Page 2 are complete and correct:12 points e) The Graph on Page 3 has a title, labeled axes, and is plotted correctly:8 points f) The picture on Page 4 meets the requirements of Step 197 points g) The answers on the worksheet (Pages 5,6,7) are complete and correct29 points
1)Begin by reading 3 pages on the internet that I have selected for you. In particular, pay attention to the meaning of the following symbols – T, g, and l – and the definitions of the terms “acceleration of gravity”, “amplitude”, “length of a pendulum”, “period”, and “simple pendulum”
For this Wikipedia page, read 1, 6, 6.1, and 6.2 in the “Contents”: http://en.wikipedia.org/wiki/Pendulum 2)The link below takes you to a worksheet. At the top right is the “Printer Friendly Version”, click there and then print it. There are 29 boxes where answers should be recorded; you should be able to figure out most of the answers correctly; incorrect answers are – ½ point, missing answers are -1 point. For me, this worksheet prints as 3 pages; it is Pages 5, 6, and 7 of your project.
3)Gather the 9 items listed in a-i as follows (make every effort to borrow what you don’t have instead of spending money): a) about 10 foot of light string (thread, fishing line, dental floss, etc.) b) thumbtack or push-pin or tape with good adhesive, c) a few ounces of weight that can be tied/attached to the string (examples: car keys, Christmas tree ornament, padlock, anything compact and dense), d) tape measure, e) stopwatch that measures time to the nearest tenth of a second (0.1 sec) or hundredth of a second (0.01 sec); almost all cell phones have this as part of a tool or app, f) a chair or step-stool that is safe for you to stand on to touch a ceiling, g) scissors, h) camera (cell phone OK, but picture will have to forwarded to someone’s email account so it can be printed), i) graph paper (or you can plot your ordered pairs and print your graph at http://nces.ed.gov/nceskids/graphing/classic/ , select “line graph”) 4)IMPORTANT: this is a simple experiment.
The expectation is that the photo will show YOUR experiment in YOUR house, and that your photo and measurements will not be the same as another student’s. 5)Choose an indoor room where the ceiling is not particularly high, perhaps about 8 feet from the floor; a bathroom or bedroom is often a good choice. 6)Build a long pendulum; it will basically be like a kid on a swing at the park; here’s how: tie (or otherwise secure) the weight to one end of the string. Let the weight hang approximately six inches above the ground; tack or tape the other end of the string securely to the ceiling. Often, string is “twisted” as it is made, so the weight will spin for a while. Let the string unwind, wait until your pendulum hangs motionless. 7)Accurately measure the distance from the approximate center of the weight straight up to the ceiling. Record this distance above Table 1 below; if your tape measure shows centimeters, record the distance to the nearest whole or half centimeter. That is, if it looks close to 225 cm, try to decide if 224.5, 225.0, or 225.5 cm is the best reading. If your tape measure is in inches, record the distance to the nearest quarter inch. That is, if it looks close to 7 foot 6 inches, try to decide if 89.5, 89.75, 90.0, or 90.25 is the best reading.
Time as a function of amplitude
8)Pull the weight sideways about 2 inches and release it; notice that the weight swings back and forth for at least one minute. Therefore, there is plenty of opportunity to start a watch and measure the time needed to complete 10 back-and-forth swings. 9)Perform the time measurement; give the pendulum a small swing (sideways displacement about 2 inches) and ready the watch. It is important to count the swings correctly: when the weight is at the highest point, start the watch and say “zero”. When the weight returns to that same point, say “one”, etc. Stop the watch when you find yourself counting “10”. If you know you “botched” the measurement, clear the watch and start over. 10)If you felt like the measurement was done well, record the time as “Time 1” in Table 1 exactly as it appears on the watch, do not round or drop any digits. 11)Repeat the step above four more times until Time 2 –Time 5 in Table 1 is complete.
The five times should be pretty consistent, within 0.2 seconds of each other. If there is an obvious “outlier”, scratch it and repeat the step above again to get a better value. Once you have five good, consistent values, calculate their average and record it as “Average Time”. 12)Repeat Step 9, but this time give the pendulum a medium swing (sideways displacement of about 6 inches) 13)Repeat Steps 10 and 11; the second row of the data table should be complete. 14)Lastly, repeat Steps 9 through 11, but this time give the pendulum a large swing (sideways displacement of about 2 feet). 15)Use the results recorded in Table 1 to answer Questions 1 and 2.
Time as a function of length
16)Transfer the length and time data from the first row of Table 1 to the first row of Table 2. 17)Using the measuring tape to help you, snip the pendulum approximately 10 inches above the bottom of the string. Re-tie or re-attach the weight to make a shorter pendulum. Measure the length of this pendulum by repeating Step 4; record the length in the second row of Table 2. 18)In a well-designed experiment, only 1 variable is changed at a time. In this part, length is going to be made progressively shorter; therefore, the size of the swing must be kept the same. Using small swings (approx. 2 inches of amplitude), repeat Steps 9 through 11. Record the times in the second row of Table 2. 19)This would be a good time for the photograph. Make sure there is enough light so that you, the weight attached to the string, and some of the room is clearly visible in the photo. Print your photo and make it Page 4 of your project. 20)Complete Table 2 for the remaining rows by repeating steps 17 and 18 above until Table 2 is full OR the pendulum is less than 30 cm (12 inches) long.
21)Use Table 2 to construct your Graph. For the first data table, treat the “Length” and “Average Time” numbers as ordered pairs to be plotted on a coordinate grid. As shown in the last row of Table 2, the Graph must have (0,0) for an origin. Make “Average Time” the x-axis variable, and “Length” the y-axis variable. Label the x and y axes. Title the graph as follows: “Time for 10 swings as a function of pendulum length”.
A poor graph will lose points; I recommend making it on a computer (if you don’t know how, use the link in Step 3); however, if you choose to make it by hand on graph paper, decide how to number the grid so that the plotted points fit; however, I want the plotted points to take up about half a sheet of paper (that is, don’t make the graph too small).