Astronomical Laboratory Project Report
A. Author, B. Author, C. Author
Fall 2007
S EPTEMBER 2, 2007
In this section, describe the purpose of the experiment. For example, you might be testing the speed of sound formula using a Kuntz tube with different gases. The equation(s) to be tested would be inserted using the Mathtype equation editor (accessible by clicking on the ∑ symbol on the menu bar. Here's an example which you can double click to edit: v

 
 kT
Although you do not need to derive the equation(s), you should briefly summarize how they originate. Also, make clear which component(s) you will be testing. For example, in the Kuntz tube experiment, you would be measuring v as a function of gas species (i.e. the ratio

), but not the

or

dependence separately
1
. Also you are not (probably) testing the temperature dependence.
The primary questions you want to address and answer in the introduction are:
1.
What scientific question are we investigating?

If the experiment involves determining one or more properties of a substance using assumed correct physical law(s), what has been measured?

If the experiment involves testing a theoretical model (from known physical laws), what is it and where is it applicable?

If the experiment involves constructing an empirical model (based solely on observed dependencies among the measured variables), what variables will be measured and over what ranges?
2.
What general procedure has been used to answer the first question?
Incidentally, lists like the above are easily generated by using the numbered and bulleted list buttons in Word.
1 Greek symbols (among others) can inserted into text using Insert/Symbol. Inserting footnotes can be accomplished by positioning the cursor at the desired point in the text and using Insert/Footnote.
1

Physics II Lab Report 17.04.2020
In this section, describe the apparatus used to test the scientific model(s) in the first section. Figures would be quite useful here. They can be generated using any
Windows drawing program. A simple example is shown at right. To allow figures to 'float' so that text flows around them, select the figure and insert a frame (Insert,
Frame menu). The experimental procedure should be described in sufficient detail that an experienced experimentalist could reproduce your results using only the description of the experiment in your report.
The results are a presentation of both observed and derived quantities. For example, the speed of sound experiment involved measurements of the time delay at various separations of transducer and microphone. The observations were taken both with
Sequence
3
4
5
1
2
Average Speed
Table 1. Awesome Data.
Time difference
(msec)
Separation
(m)
0.30
0.38
0.44
0.54
0.65
330.2
0.10
0.14
0.18
0.24
0.32
Speed
(m/s)
325
336
351
328
311 air and Helium. The timing observations were then converted to speed using v=L/
 t.
These data could be presented in a table using the Table menu as shown below. I also used Table/Autoformat, inserted a title using Insert/Caption, and inserted a frame so the text flowed around it. I also fiddled a bit with the frame formatting parameters using
Format/Frame menu.
Many of the derived results you will obtain will be a result of least-squares fitting of the observed data. For example, suppose one has a series of measurements of shallow water wave speeds for a series of water depths. The relevant equation is v
 g h
2

Physics II Lab Report 17.04.2020 where g is the gravitational constant and h the height (note how variables in the text are italicized). Equations involving power-laws can always be transformed into simple linear equations of the form y=ax+b by taking the log of both sides. In this instance, we would have
 
2
 
2
By plotting log(v) versus log(h), a straight line can be fitted. The slope of the line is an measure of the h 1/2 dependence and the intercept is a measure of the gravitational acceleration g.
Least-squares fitting and plotting can be done most easily using MathCAD or
Graphical Analysis (GA). These program have the ability to copy plots into the Windows clipboard and paste them into Word documents (use the 'Edit/Paste' in Word).
In MahCAD, simply select the graph, select Edit/Copy, then Paste in the Word document.
In GA, use Edit/Copy Window (after selecting the graph window by clicking in it). A sample plot from GA is shown above.
3

Physics II Lab Report 17.04.2020
Data tables can also be pasted from GA into word by selecting the data windows, copying and pasting as with graphs. Here’s an example using the data shown in the GA graph above.
No experimental result is meaningful without a properly determined uncertainty calculation. For example, suppose one measures the average mass of ten male and female rats in a sample and obtains 1.42 kg and 1.37 kg respectively. One might naively conclude that male rats were on the average 3% more massive than female rats. But suppose also that the standard deviation of each set of measurements was +/- 0.1 kg.
Since the uncertainty in the measurements exceeds the difference in the means, one cannot conclude that there is any statistical difference.
The uncertainty in a measured quantity is typically estimated by the experimenter. For example, if you measure a length using a ruler, the uncertainty in a single measurement might be +/- 1mm. For measurements using instruments such as the
KIS interface, finding the standard deviation of repeated measurements is a good estimate of the uncertainty. For derived quantities , uncertainties must be measured using a propagation of errors calculation. Suppose one has a derived quantity F which depends on three measured variables x,y, and z. The uncertainty

F
is determined by the 'propagation of errors formula':

F
2 



F
 x
 2
 
 x
2 


F
 y


2
 y
2 



F
 z
 2
 
 z
2 where
 x etc. are the uncertainties in the variables x, y, z. As an example, suppose one has the equation v
 g h
The derived speed v is a function of a single measured quantity h ( g is a known constant). The uncertainty in the derived quantity v is given by
4

Physics II Lab Report 17.04.2020
 v
1
2 g h
  h
For derived quantities which are determined by least-squares fits, the uncertainties in the fitted parameters are more complicated. For a linear fit, the uncertainties in slope and intercept are calculated in the MathCAD routine mentioned above. For data with uniform uncertainties, GA calculates uncertainties.
A good discussion of both propagation of errors and the uncertainties in fitted parameters, see Chapter 6 in Bevington (Data Reduction and Error Analysis For the
Physical Sciences) or Chapter 2 of Lyons (Data Analysis for the Physical Science
Student).
The discussion section is an opportunity to describe both the significance and the limitations of your results.
This section is a succinct summary of your experiment, the main results, and their implications.
5