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These tips are useful for the experiments we do in class.
Identifying a Problem
Identifying a Problem
Every lab should be investigating something that should be written in a question form that can be answered through a controlled experiment. Some labs are verification labs (where we test a known relationship) while others are exploration labs (where we try to identify a relationship we did not already know), but the difference may not be apparent in the problem.
Examples:
What factors affect the rate of free-fall motion? (probably exploratory)
What is the acceleration due to gravity on earth? (verification -- it should be 9.8 m/s2)
Is energy conserved in an elastic collision?
Writing an outline of Data Collection Procedures
Writing an outline of Data Collection Procedures
Most of you have experience writing detailed formal procedures from your chemistry class and biology classes. I am glad they have helped you developed that skill, but in our class we will focus more out outlines of the essential characteristics of the procedures for two reasons. 1) Outlines require you to evaluate what the essential design elements of the lab are, which is a skill you ought to have. Many students lose track of the point of an experiment when they spend so much time considering the details. 2) Outlines save us time on lab writing and lab grading so we can get to more investigations.
Some people struggle to get this style down and don't know what to keep and what to leave out of the procedures when you outline them. Here are the required elements, which may be intermingled in your outline slightly:
Setup: Pair this with a diagram that has labels for tools being referred to and any key positions identified.
Measurements: Define measurements to be made (give symbol to be used, units are optional) and tool you'll use for any constants and variables measured (the variation description may be interwoven with this variation).
Variation: Describe how you will change your independent variable (make sure to define measurements and tools to be used for any new measurements here)
Reduce Uncertainty: repetition of measurements, measurements across a range of values, and trend analysis (using graphed data to identify trends) all help to reduce uncertainty and provide analysis information that can be used to understand the significan
Note some specific things that should not be included:
do not state to "gather materials" or steps like "hold the ruler against the side of the track." Assume that the audience knows how to use the tools - only describe steps that might be different for this lab in particular.
if the request is for "data collection" procedures you will stop with data collection and not describe the processing of the data. "Analysis procedures" include graph making, calculation, and graphical analysis techniques described below.
Example procedure outline
Example procedure outline
As an example to contrast with what you did in your chemistry class, I will apply the above principles to a titration lab.
Setup your apparatus with HCl in the burette and a flask below, as depicted in the diagram. [setup]
Use a graduated cylinder to measure 100 mL of SHA solution into the flask. [measurement tool described measuring constant]
Use the knob on the burette to drip HCl into the SHA, counting the drops added until the SHA changes color from colorless to green. [variation]
Rinse and repeat steps 2-3 for 3 trials. (alternate option: Rinse and repeat steps 2-3 adding an additional 150 mL of SHA until reaching 100 mL of SHA solution) [reduce error]
Writing an outline of Analysis Procedures
Writing an outline of Analysis Procedures
Like seen above with data procedures, we will focus more out outlines of the essential characteristics of the analysis rather than on the monotonous details. Most of this work can be automated in spreadsheets or calculators, so it does not make sense to require documenting individual calculations.
Some people struggle to get this style down and don't know what to keep and what to leave out of the procedures when you outline them. Here are the suggested elements, which may be intermingled in your outline slightly:
Plan for graph: Every graph should have which measurement (and unit) is to be plotted on which axis explained in an outline of procedures. If data is going to display a curve and would be easier to evaluate if linear, explain how data will be modified and why.
Plan for Graphical Analysis Techniques: Physics uses graphs to depict and evaluate relationships of independent and dependent variables, in addition to finding constants through use of graphical techniques like finding slope of a best fit line, intercepts, or asymptotes. The meaning of what these mean is established by comparing an equation with known Physics relationships to the mathematical equation of the data. You should refer to both the graphical technique and the equation of pure Physics quantities to assign meaning to the values of slope, intercepts, and asymptotes you plan to use in your analysis.
Plan for Calculations: Calculations should refer to how the calculation was planned based on basic Physics principles.
Plan for Summarizing Results: Refer back to the question of the lab investigation and figure out how your analysis will answer the question.
Example analysis outline
Example analysis outline
As an example to see the data collected at left of the cost to cover a square room with new flooring where the problem is to determine a relationship for the rate of flooring cost based on the length of the room.
Given that the cost of flooring will depend on the total area of the flooring and the area of a square room is A=l x l or A=l2, so we anticipate a curved graph of cost as a function of length. Instead, generate a column of data called "length of room squared (ft2)" and plot a graph of cost on the y axes and length squared on the x axis. [Calculation & linearization planned]
If the best fit line for the graph is directly linear that indicates a constant rate for the cost of flooring per square foot. Since a linear function is described by y=mx+b, and directly linear functions have b=0, then for our graph where Cost = m (squared feet), the slope must be the rate. [graphical analysis techniques and summarizing results]
Recording data and making observations
Recording data and making observations
All raw data is recorded in a table format. It is OK to use one format for data collection and include a place for averages there, then reformat the table to make analysis easier later. You should include both if you do that.
While recording your independent variable and dependent variable data in a table is essential, you should keep your eye out for any other observations that might affect your results or even just be interesting.
You can notate data points with an asterisk and make a note at the bottom of the data table
You can write a brief paragraph or include diagrams to indicate other observations.
examples to come
Reporting uncertainty:
Reporting uncertainty:
When you have random error, you report the average, but should really understand that any number that falls within the range of that data set would be considered to be statistically equal.
For example:
A motion is measured with the following times recorded for the same motion
The value to be reported would be 6.5 s ±0.3 s because the range of accepted measurements includes values up to 0.3 s off from the average.
You should not be required to report your measurements this way on all labs, but you should understand it and may choose to use it as a statistical tool when analyzing your own data.
Quantifying the quality of your results:
Quantifying the quality of your results:
Rather than use vague statements, like "pretty close" or "very accurate" you can find % difference or % error to give a numerical value to your statements. This is a much stronger way of supporting your claims than an opinion.
if 2 values are supposed to be the same or you are comparing them, use a % difference
if you are verifying a value (testing against a predicted value) use a % error
Analysis Calculations
Analysis Calculations
Always include a literal calculation that shows what the slope and/or area of the graph represent. If multiple values are referred to, create a new data table to summarize them.
For repeated calculations, show 1 example in long form (equation, substitution, answer with units) and then a data table summarizing results if you wish. Averages do not need work as long as they are in a logical place.
Show work for any values you will refer to in your analysis summary/conclusion.
Show % error or % difference calculations if used.
Conclusion should not introduce new data/calculations, but should refer to them
Error Analysis
Error Analysis
There are 3 types of error we often run into.
1) random error - average of measurements is close to true value (averaging multiple trials reduces error). All measurements have error, even electronically collected values, based on the limitations of the precision of the instrument.
ex. most stopwatch error could be either anticipating or delayed reaction. Averaging them is a good way to reduce error.
2) systematic error - true value is higher or lower than the average measurement (multiple trials do not help reduce, but results can be corrected if the systematic error is known)
ex. When measuring the speed of a car that curves between measured points the average of multiple trials measured is always less than true speed of the car because the actual distance traveled is further than the recorded value. Averaging will not reduce this error. We can either find a way to include the actual path or logically explain that our measured speed is too low.
3) blunders - these are goof ups that affect our results, like not zeroing a balance for one trial, allowing something that should be constant to change, or recording data incorrectly (445 grams instead of 455 grams).
An example Formal Lab Report
An example Formal Lab Report
Not all labs are the same, but here is an example lab I put together for students that were asked to design a lab about whether or not the projectile motion model accurately predicted projectile range.
example Formal Lab Report
example Formal Lab Report
While we rarely do a formal lab report, here is an example lab I put together for students that were asked to design a lab about whether or not the projectile motion model accurately predicted projectile range.
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