Controlling Experimental Variables Names:
Honors Physics – Olenik
Introduction:
A great number of science students struggle with proper experimental design. One reason for these struggles is lack of experience; hence, this lab is designed to step you through proper experimental design and give you some practice selecting and controlling variables. You will also get some practice presenting your results in a variety of ways to show trends, and then you will use these trends and your knowledge of mathematics to make predictions of pendulum behavior.
Most of you are probably at least somewhat familiar with pendulums. They have been, and continue to be, used to help keep time in certain clocks. The period of the pendulum is very important when it comes to keeping time. The period of a pendulum is defined as the time it takes for the pendulum bob to swing away from and then back to its starting position. If a pendulum has a period of one second, it will make an effective timekeeper. In this lab you will analyze a simple pendulum to determine what variables affect the period of a pendulum and which do not, and then you will use your powerful intellect to design a pendulum timer with a period equal to one second.
Step 1. Brainstorming Variables:
There are many variables that could effect the period of a pendulum. In this section you need to brainstorm at least six of these variables. At this point, you have not done any research so don’t worry too much about not being exactly correct. Just think and write your ideas down. When you are done, we will discuss each of your ideas with the class. (6 points)
1.
2.
3.
4.
5.
6.
Step 2. Forming Initial Hypothesis.
In this step you need to form a hypothesis(es) about which variable(s) you think affect the period of a simple pendulum. Your hypothesis(es) should be in standard “if/then” format, so you state which variables will affect the period and how they affect the period. (6 points) Then, in the justification section, you then need to detail why you formed the hypothesis you did (i.e. you need to really contemplate this and then thoroughly and clearly articulate your thought process) (6 points)
Hypothesis(es):
Justification:
Step 3. Doing Research and Revising Hypothesis.
In this step you need do a small amount of research and reading to help transform your original hypothesis from just a guess to more of an “educated guess”. Spend no more than 20 minutes on this task; however, obtain evidence that you have done the research necessary (make sure to correctly cite the origination of this evidence). You can use whatever resources are most time efficient for you. Evidence (3 points). Citation (2 points). Revised hypothesis(es) (3 points).
Evidence:
Revised Hypothesis(es):
Step 4. Designing Procedures to Test Your Hypothesis
In this, the most difficult step by far, you need to design a set or sets of procedures to ultimately determine/prove what factor(s) affect the period of a pendulum. I do realize that, if you have done your research, you may think you already know the answer to this question; however, what is most important at this point is that you are able to thoughtfully design a procedure that isolates and controls variables.
To aid in this process, I have found a simulator that I would like you to use. It will save on class time and materials. The simulator can be found at
http://phet.colorado.edu/simulations/sims.php?sim=Pendulum_Lab
*Simulator tips to help make your life easier.
- use the mouse to manually manipulate the variables using the sliders (don’t type numbers in box, please!)
- selecting the photogate timer in the lower part of the green box will allow you to measure the period of your pendulum.
Make sure that your procedures are sequential, fair, and detailed enough that someone else could repeat exactly what you did. In science, it is very important that others can repeat exactly what you have done and verify your results. This is how the scientific community makes sure that new discoveries are valid. Having topic headings in your procedures for each variable is very helpful as well. Also, you may want to take a peak at the data tables in the next section before you write your procedures. (15 points total or 5 points for each variable)
(Insert Procedures here)
Step 5. Collecting Data
Data collection and organization is of the utmost importance in scientific endeavors. One must collect adequate amounts of data (too little can cause incorrect conclusions and too much can be cost prohibitive) and organize that data so others can understand and analyze it. Once you have collected your data, organize it in the tables below (use all the data cells to make sure you have collected an adequate amount of data). Make sure to vary your variable over a wide range to make your data more comprehensive (i.e. don’t pick numbers very close to each other for each of your variables). (12 points)
Table 1. Variable 1 versus Period Variable 2 = Variable 3 =
Variable 1 (unit) / Period (seconds)Table 2. Variable 2 versus Period Variable 1 = Variable 3 =
Variable 2 (unit) / Period (seconds)Table 3. Variable 3 versus Period Variable 1 = Variable 2 =
Variable 3 (unit) / Period (seconds)Step 6. Graphing Data
Graphing data helps show trends in the data and helps the observer to make conclusions from the data. So, we are now going to make x-y scatter graphs of the data. For each variable, period (the dependent variable) will be graphed on the y-axis and the respective independent variable will be graphed on the x-axis (see example below).
Period (seconds)
Variable (units)
When completing these graphs, make sure to include a title, label the axes, and include units. Make sure that the scale on each of the axes starts at zero (this can be done in Excel by clicking on axis, then selecting format axis, then selecting scale); if the computer auto scales the data, sometimes the graphs can be deceiving. (15 points or 5 points for each graph)
(Insert graphs with out any curve fitting included here)
Step 7. Analyzing the Graphs
Once you have completed the three graphs, you should notice one has more variance than the other two. This different graph should represent the variable that most dramatically effects the period of a pendulum.
What variable did your graphs show most dramatically effected the period of a pendulum? (3 points)
(Insert Answer Here)
Did it agree with what you found in your research? Describe how it did or didn’t. (5 points)
(Insert Answer Here)
Because several assumptions have to be made to derive the equation for the period of a pendulum, the equation for the period of a pendulum you found in your research works only for small angles of release. When the pendulum bob is released at higher angles it begins to slightly tweak the period; hence, release angle has an effect on the period of a pendulum that is not apparent in the formula.
Do some research and briefly explain these assumptions in the derivation of the pendulum equation and why they cause greater differences in calculated values as the release angle is increased. A simple sketch will be very helpful in your explanation. (5 points)
(Insert Answer Here)
Now we will really use our brains. No matter how much you manually vary the three variables on the simulator, the shortest period you can obtain is 1.5533 seconds. (I do realize that you can type smaller numbers into the boxes, but I am going to ask you to refrain from doing so. This will allow us to utilize some of your high-powered mathematical skills). This is because the simulator will not allow you to vary the one important variable low enough to obtain a shorter period. One of our goals for this lab was to design a pendulum timer that has a period of one second. The fact that the simulator will only allow us to go down to 1.5533 seconds is therefore somewhat problematic. This is where we use our graph and our brains to look for a trend in that graph. If we can determine a trend in the graph, then we can use that trend to infer points that might not be included in our original data (a process called extrapolation).
Excel has a function to help you fit a curve to your data (just like you have done in Algebra II and Pre-Calc with your calculators). Although you can use your calculators to fit this curve, I would like you to use Excel so you can print out your results in a professional looking manner. If you want to check the results, I invite you to do so. In Excel, click on the chart of the variable that affected the period of a pendulum the most and then select “add trendline” in the “Chart” menu at the top of the page. Select “Power” under type and then select “options”. Under “options”, forecast your curve backward until it intersects with the time equal to one second. Don’t worry about fitting a curve to the variable that has not affect on period; however, I would like you to fit a curve to the release angle graph. You will have to select a “Polynomial” type fit for this graph.
Now, Use your graph to determine what a pendulum with a period of one second would look like? Briefly explain how you reached this conclusion attach a copy of the graph with a curve fit to it that has been forecast backward. (10 points)
(Insert Answer Here and Insert Graph Here)
Use the equation you found in your research to determine what a pendulum with a period of one second should look like (show work). (5 points)
(Insert Answer Here)
How did your prediction from your graph compare to the value obtained from the equation? (3 points)
(Insert Answer Here)
What are some reasons for any differences (list and describe at least two)? Hint: include the graph of period versus release angle with a curve fit to it. (6 points)
(Insert Answer Here)
Step 8. Verifying Accuracy of Simulator
Now use the pendulums in the lab to verify the accuracy of the simulator. Design and record a detailed procedure (that is repeatable) to determine how actual recorded values compare to the simulator-derived values. Try to design your procedure to minimize the human error that is now going to be a factor in your results! (6 points)
(Insert Procedures Here)
How did the actual pendulum compare to the simulator? Include a titled data table showing how the results from the simulator and your actual pendulum compare. (6 points)
(Insert Answer and Data Table Here)
Describe two specific things you did to try to minimize human timing error? Make sure to describe how one of these strategies helped reduce the percent error in timing. (4 points)
(Insert Answer Here)