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course phy 231
revision
labanalysis1#$&*
course phy 231
quicklab1#$&*
course phy 231
Brief pendulum experimentUses: washer, thread, analog clock, ruler or meter stick
Construct a pendulum using washer and thread. Make 1-minute counts for pendulum lengths (measured from the position at which the thread is held to the center of the washer) equal to three different lengths:
• the the distance from your wrist to your fingertips
• the distance from your elbow to your fingertips
• the distance from your shoulder to your fingertips
Be sure to measure the length of each pendulum you time.
Report the pendulum lengths and the corresponding numbers of counts:
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Wrist to fingers: 8 inches, 63 full swings in 1 minute
Elbow to fingers: 18 inches, 41 full swings
Shoulder to fingers: 28 inches, 35 full swings
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Analysis:
Graph your 1-minute count vs. length, and sketch a smooth curve representing the trend of your data.
Using your graph estimate the number of counts for a pendulums of length 52 cm, and another of length 13 inches. Estimate also the lengths corresponding to pendulum counts of 30 and 50.
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Using my graph, for 52 cm length, I got 16.3 full swings
Using the graph, for 13 cm length, I got 52 full swings
For 30 counts using the graph, the required length would have to be 31 cm
For 50 counts, the length would have to be
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Determine the period of each of your three pendulums, i.e., the time required to complete 1 oscillation. A oscillation is from extreme point through equilibrium to opposite extreme point.
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For the 8 cm length, a period was .95 seconds
For the 18 cm length, a period was 1.46 seconds
For the 28 cm length, a period was 1.71 seconds
Inches rather than centimeters, according to your data report; the periods look just about right if lengths are in inches.
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Sketch a graph of period vs. length, showing your three points, and sketch a smooth curve to fit your graph.
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The curve y=-.0013x^2+.085x+.355 fits well
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Use your graph to estimate the period of a pendulum whose length is 26 cm, and also the length for which the period would be 1.2 seconds.
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Using the graph for length of 26 cm, the period should be 1.7 seconds
For period of 1.2 seconds, the corresponding length should be 12.2 cm
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What is the uncertainty in the number of counts made, and to what do you attribute the uncertainty?
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Counts? I’m confused. What do you mean by counts?
You originally counted the number of cycles in a minute, for each length.
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I don’t think there was much uncertainty. I would think I may have not started each pendulum swing from the same point. Also, I counted whole cycles, so if it took 61 seconds to do 40 cycles, I would say 40 cycles, instead of 39.5 in 60 seconds
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What is the approximate average percent uncertainty in your counts?
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Around 2 percent
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Do your sources of uncertainty result in the same expected percent uncertainty for all counts?
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No. for the first length, 2 percents sounds right, and with each cycle being longer for longer length, there was more potential to round more. So I would say 3 percent, saying one full cycle off
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Good. However see my last note and submit a revision. Only those last three questions need to be answered.
&#Please see my notes and, unless my notes indicate that revision is optional, submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
If my notes indicate that revision is optional, use your own judgement as to whether a revision will benefit you.
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@& You still haven't given a satisfactory answer for the uncertainty.
Your first count was 63 cycles in 1 minute.
However there were not exactly 63 cycles in exactly 1 minute. There is some uncertainty in the number of cycles that actually occurred in exactly 1 minute.
Do you think that the way you counted the cycles, the uncertainty in the actual number of cycles in a minute was more or less than +- 10 cycles? Almost certainly, you will say that you did better than that.
Do you think it was more or less than +- 0.1 cycle? Almost certainly you cannot conclude that your count was that accurate.
What are the possible sources of uncertainty in that count? Just how accurate was that count, and on what specific assumptions do you base your estimate?
Your second count was 41 full swings. Your third was 35 full swings.
Do you believe your uncertainty in the number of counts for each of these trials was the same as before? Why would it be the same, or why would it be different? What are your estimates for the uncertainties?
What therefore are the percent uncertainties in your data?
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