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Purpose: In this activity you will investigate various properties of a pendulum.
Materials: Pendulum apparatus Stop watch
Meter stick Various bobs for pendulum
Balance Graph paper or Graphical Analysis
Background:
A pendulum is a classic example of periodic motion, which is a motion that is repetitive, redundant, keeps repeating itself, keeps going back and forthoh, Ill stop now. A pendulum only works when there is gravity, and of course can be used as a clock. It is also an example of circular motion, which means there is a net centripetal force. Because we are studying gravity and are moving towards circular motion, we will try to figure out the basic properties of a pendulum and see how we can combine gravity and circular motion together in a few different ways, whether it is a pendulum, an amusement park ride, or satellite motion. Keep the force diagram for a pendulum in mind (what does it look like?).
Procedure:
You will be trying to determine the best way of obtaining answers to the questions below. Keep in mind, you should always be thinking of estimating errors on all measurements (in any experiment you ever do!) as well as how to minimize those errors. Think about what might be the best way of measuring a given quantity. Also, do not forget to include units on all measurements, along with a reasonable estimate of the uncertainty of all measurements! For anything measured in trials, think standard deviation.
For your write-up: Purpose, Materials, Procedure, Data Tables, Questions and Analysis (with appropriate graphs; these should be titled and labeled with quantities being graphed and units! Graphs need to be done on the computer.).
Definitions:
Period = time it takes the pendulum, when released from rest, to swing over and back to where it started, or the time for one round-trip.
Length = length from the point where the string is free to swing to the center of mass of the bob at the end of the string.
Questions/Analysis:
For a constant length and constant mass of the pendulum, gather data for a graph of period as a function of angle (as measured from the vertical). Your measurements should range from a few degrees (small angles) up to 90o. Estimate errors on measurements and include them as error bars on your graph. The error bar for period measurements (some number of trials) should be the standard deviation of the mean.
Interpret your graph of period vs angle in a couple of sentences; what relationship(s), if any, do your data suggest? Direct or inverse? Linear, flat or something different? Include in the discussion how your interpretation depends largely on the error bars.
For a constant length and constant small angle (less than 10 degrees) of the pendulum, investigate whether the period of the pendulum is dependent on the mass of the bob. Use five different masses to do this. Make sure to adjust the length so they are always the same. For instance, when you hang a larger mass on the string, you will need to shorten the string a bit since the object will be longer. Try to estimate errors to see if any discrepancies are significant or not. Graph period as a function of mass, and explain your data and draw conclusions about such a dependency based on the data. Include estimated error bars on the periods.
For a constant mass and constant small angle (less than ten degrees), collect data for a graph of period as a function of length of the pendulum. Plot your data using Excel, Graphical Analysis or your calculator and see if you can obtain a fit to the data to get an idea of the relationship. Include the point (0,0) on your graph and in your fit.
From your graph of period vs length, what type of relationship is suggested for period as a function of length? Is it linear or non-linear? Explain your answer in a few sentences based on your fit to the data.
If you were to do this experiment on the moon, what changes in your data would you expect to find, particularly in your period measurements? Make sure to explain your answers in some detail; you dont have to do any calculations necessarily, but conceptually what might you expect would change?
There are only three significant forces acting on the weight at any time, those being tension, gravity and air friction. Which of these are constant, which are non-constant? If any are non-constant, when are they the strongest, and when are they the weakest? Explain, and include a force diagram/free-body diagram.
Solve the following problem: For a pendulum of length 75 cm, what is the maximum speed (neglecting air resistance, etc) of the bob if the pendulum was started at rest at a 12o angle relative to the vertical? Where in the swinging motion is the maximum speed reached? Why? Hint: Think of energy conservation. PE = mgh and KE = mv2.
Using your graph in #4, how long should a pendulum be in order to have a period of 1.0 sec? How long should a pendulum be to have a period of 2 seconds? Use interpolation and/or extrapolation to estimate your answers.
10. What exactly does Fcentripetal = mv2/R mean? What does the value of mv2/R tell us, and what does it depend on specifically for a pendulum? Consult the book for assistance.
Write a brief, to-the-point (i.e. one paragraph) summary of your findings/conclusions about what the period of the pendulum depends on and how it depends on specific quantities.
Lab Trial: Guinea Pigs (You and your partners) at Using Photogates for Pendulum (
Purpose: Collect Data using a Vernier photogate and a Vernier LabPro Interface, and use the Logger Pro software to accurately measure the period of a pendulum. In addition, do graphs and fits using Graphical Analysis.
When in Logger Pro, in order to get the timing software set, we need to calibrate the system for Pendulum Timing. Go to Experiment, go to Calibrate, and then to Lab Pro. Go to the Calibration Setting box, and select Pendulum Timing. The measurement will be on the main page, under the toolbars.
Questions/Analysis:
For a constant length and constant mass of the pendulum, gather data for a graph of period as a function of angle (as measured from the vertical). Use a photogate to do so, which gives a much more precise measurement than what you got before with stopwatches. Your measurements should range from a few degrees (small angles) up to 90o. Graph your data using Graphical Analysis, and do a fit to the data to see what the actual function looks like (something we were not able to do before).
For a constant mass and constant small angle (less than ten degrees), collect data for a graph of period as a function of length of the pendulum. Plot your data using Graphical Analysis see if you can obtain a fit to the data to get an idea of the relationship. Include the point (0,0) in your fit. See how close you can get to a square root.
Your take on it: Does this work better than using stopwatches? How user-friendly did you find Graphical Analysis to be?
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