About your lab report: You'll submit both a word-processed report and a Logger Pro file.
Measure the acceleration due to gravity to 3 significant figures by using the relationship between the length and period of a simple pendulum
We generally use 9.80 or 9.81 N/kg (or m/s2) as the value of the gravitational field, termed g. This is also the value of the acceleration of a free-falling object at the surface of the Earth. The actual value, however, depends on your location. The purpose of this lab is determine--subject to certain constraints--the value of the gravitational field at your school. The primary constraints are that you must use a simple pendulum, your timer must be a manual stopwatch, and you're expected to achieve 3 significant figures in your value of g. However, you won't be penalized for achieving less than three figures assuming that you've designed and executed your experiment well with the materials that you have available.
You've measured g in a previous lab using a different method. In L04, you used video analysis to measure the acceleration of a lead-weighted racquetball in a long fall. Air friction was small enough in that situation that you were able to obtain a value for g close to what was expected.
The present lab provides a standard way to measure g to high accuracy and, in the process, to see the interplay between theory and experiment. The period, T, of a simple pendulum in the small-angle approximation is T = 2p(L/g)1/2, where L is the length of the pendulum. One can use this formula to calculate g, given measurements of T and L. The general plan will be to measure T as a function of L, re-express variables appropriately to obtain a linear fit, and determine the value of g from a coefficient of the fit. You've used this method many times before.
The precision and accuracy of the measurement of g with a simple pendulum depends on the smallness of the angle as well as the measurements of T and L. Here are some design considerations:
As you can see from the above, there's much to think about in designing an experiment to give precise and accurate results even with the simplest equipment. While we spent much time discussing experimental design above, the remaining instructions are brief. By this time, we expect you to be well-versed in collecting and analyzing data.
Setting Up and Taking Data
You should be ready now to set up your equipment to take data. In addition to setting up the equipment, prepare a data table that will allow you to present all of your data in an organized way. Think about how you will do this in order to provide a logical display and make the table easy to read. Before beginning to record data, practice your timing technique. Come up with a technique that you think will minimize your starting and stopping errors. When your preparations are complete, take your data. If you're working with a partner, you can both use the same pendulum, but you must do your own timings. Also, check each other out on measuring the length of the pendulum.
Analyzing the Data
Use Logger Pro to analyze the data. Use the standard process of re-expressing variables to obtain a linear fit. Provide a matching table and equation of fit, and show how you determine the value of g using the results of the fit. The correct method is to use a numerical coefficient from the fit and equate that to the expected physics expression for that coefficient. You obtain the latter from the theoretical expression for period as a function of length. If you don't use this method, you'll receive no credit for the analysis. By this time in the course, the method should be second nature to you.
Writing Your Report
While you'll submit your analysis in a Logger Pro file, your report will be a word-processed Word document. This is to be a complete report as described in the lab guide. All sections listed in the guide are required. Here are some specifics about particular sections.
Theory: In this section, describe the method of graphical analysis that you use to determine the value of g.
Method: Describe specifically how you addressed the various design considerations described above in setting up and carrying out the experiment. Make a list lettered as above (a-h). Each response must be complete in of itself without having to refer to these instructions in order to see what design point you're addressing.
Data: Present all your data in a logical and easy-to-read format with complete labels. You will need to include deviations and means.
Graph/fit, matching table and equation of fit: Copy and paste your graph, including the fit, in your Word report. To review how to write a matching table and equation of fit, see the FAQ for labs.
Sample Calculations: Show how you use one of the coefficients of your fit to determine a value for g.
Submitting your report
Submit your files as requested.