The purpose of this project is for students to explore a real application of physics that has some personal significance. The student will produce a unique report in which actual data for a moving object is graphed and analyzed. The subject must be a singular moving object or an interacting set of objects (though a single moving object will be best). There are three phases to this project. In phase one the student will collect, research, or simulate data for the chosen subject. In phase two the student will produce and analyze graphs of the data. In phase three the student will write a concluding statement in which the results of the project are interpreted, scrutinized, and evaluated. Each phase is described in more detail below.
In order to produce the required set of graphs (see phase two) the student will need to produce or obtain an adequate quantity of data. In general at least 5 data points are needed to make a reasonable graph. However, it is desirable to have closer to 10 or more data points. The student has three options for obtaining data: direct experimentation and measurement of the subject, computerized simulation of the subject, or research and citation of published data for the subject.
In the case of direct measurement, the student will design and perform an actual experiment in which data is collected using appropriate scientific instruments. The student will have the option of using the school’s scientific equipment under the instructor’s supervision. The finished report must include a detailed description of the experimental procedure that was used to collect the data.
In the case of research, the student will find a reliable published source of data. Possible sources would include internet sites, books, magazines, journals, etc. The finished report must include appropriate bibliographic information and a description of how the data was produced or measured.
In the case of computerized simulation, the student will chose an appropriate model which is capable of matching at least two known data. Or in other words it must be a simulation of some actual known event and not just a simulation purely for the sake of generating some graphs. The student may write a program for the computer or calculator or use Interactive Physics or some similar program. The finished report must include a detailed explanation of the model that is chosen and the source of the known data for the subject.
In any of these cases it is permissible to use one set of data to calculate a second or third set of data provided that an example or explanation of this process is included in the report.
The finished report shall contain a set of three graphs based on the collected data. Depending on the topic chosen for the report these graphs will have various x and y variables. The three graphs should be chosen not only to illustrate the interesting aspects of the data but also to show how the data confirm physics principles, laws, equations, theories, etc. Graphs based on experimentation or research should include an equation and curve of best fit. Graphs based on simulation should include known data points in addition to the model results.
The last aspect of this project is for the student to evaluate the data, graphs, and curve fits. This last section of the report will be a written conclusion not to exceed two pages in length. In this section the student will reflect on the results of the project. The purpose of the conclusion is to explain how the data, graphs, and calculations support or exemplify the science of physics. Appropriate material for the conclusion would include: calculation of error and/or deviation, discussion of sources of error, comparison of results to physics concepts learned in the course, explanation of physics concepts learned in the process of doing the report (that are beyond the scope of the course), and explanation of the significance of resulting values such as slopes, constants, y-intercepts, etc. The conclusion can take on a variety of forms depending on the subject of the report and the content of the graphs. However, in all cases the student is expected to show evidence of critical and original thought.
Each report will be graded on the basis of the given rubric. This table establishes point values for specific components and aspects of the end product. In this way it is hoped that the resulting grade will be objective and fair. On the other hand, it should be recognized that the instructor will make judgements as to how well the report fulfills the requirements and may give partial or no credit for any of the stated point values. The student should strive to produce a coherent and flowing report that meets or exceeds the requirements in an appropriate fashion. A report in which the student has clearly pieced together a product that minimally meets the requirements in a disjointed manner may not receive full credit. The student should strive to meet the “spirit” of the rubric – not just the literal words. Put another way, the student should not strive to find technical “loopholes” in the grading criteria.
The finished report consists of the following (bound in a folder and in this order):
1. A brief introductory paragraph explaining choice of subject.
2. Documentation explaining source(s) of all data.
3. Three data tables.
4. Three graphs – each with curves and equations of best fit.
5. Conclusions
Detailed information about each section of the report (corresponds to rubric):
· Introduction/Topic Choice – In this section describe your choice of topic and explain why it is significant to you personally. Choose a topic that interests you or relates to your life somehow. The topic must be related to the concepts that you learn in the course but should also illustrate physics concepts that are beyond the scope of the course.
· Documentation of Data – Regardless of the type of project you must explain
or otherwise document where the data comes from and how it was measured.
For direct measurements that you make yourself, explain exactly what and
how you measured. A sketch of your experimental setup is a good
idea. For researched data found in a book, magazine, web site, etc, state
the source in which you found the data and any details you can find about how
the data was originally measured or determined. For simulated data
produced by a computer or calculator, state the program and/or equations that
were used and give the source of the known information for whatever you are
simulating.
If you use one set of data to calculate another, you must explain and show how
this was done. It is acceptable to give an example of each type of
calculation (you don’t have to show the calculation of every single data
point).
· Data Tables – All data should be put in neat, well-labeled tables with titles and units. Include data that is to be graphed but also any other data that is relevant or that was used by you in any way.
· Graphs –
Produce three unique graphs based on your data. Each graph needs
appropriate title, scales, labels, and units. Choose x and y variables
appropriately. Each graph must be on graph paper or printed with a grid
of horizontal and vertical lines. For each graph you must determine an
equation of best fit and draw a corresponding line or curve. Variables
and units for the equation must be adequately defined.
If you determine the equation yourself then show the work that you did in order
to find the equation’s coefficients.
If you use a computer or calculator, label the result as a “regression
equation” and give the correlation coefficient R or R2. If you
choose to do this you must actually use the regression equation to plot the
line or curve of best fit. Include a small table showing some x and y
values that were calculated with the regression equation. The purpose of
this is to confirm that the regression equation does indeed correspond to the
data and line or curve of best fit.
· Conclusions – In this section evaluate and analyze the results. Discuss in specific and scientific terms how the graphs, equations, tables, coefficients, etc. relate to appropriate physics concepts. Evaluate experimental error by discussing or calculating deviation and/or error. In order to calculate error you must have an accepted value. In some cases there may be no accepted value but should still be able to assess how reasonable your results are. Discuss any relevant physics concepts that are illustrated by your results – including any that are beyond the scope of what was learned in class. Do not make claims that are not supported by your results!
· Format/Grammar – The entire report will be graded for correct format, spelling, and grammar. When assembling into a folder please try not to cover up anything with the binding. Also please do not use plastic covers for the pages as this interferes with grading.
Project Scenarios
Described below are three hypothetical project choices:
Scenario 1 - Direct Measurement
John is interested in the effect of air on a falling object. This is something discussed only in general terms in class – we basically ignore the effect of air in high school physics. So John decides to perform his own experiment in which he measures the motion of a falling object on which there is significant air resistance. He decides to measure a falling balloon. He is able to use one of the school’s Calculator Based Rangers. He does three trials on the balloon in which the balloon is filled with different amounts of air. In his report he has three data tables each showing velocity versus time for the balloon filled to a certain size. He makes three corresponding graphs and does appropriate analyses.
Scenario 2 – Research
Susan is interested in the performance of dragsters. This is not a suitable topic for performing her own experiment and making direct measurements. However, she is able to find a published data table in a magazine showing velocity versus time for a certain racecar. Using this one data table she is able to calculate two more tables of values: one showing force versus time and another showing power output versus velocity. She makes three corresponding graphs and does appropriate analyses.
Scenario 3 – Simulation
Jane is interested in satellites that have elliptical orbits. Obviously this is not a case where a direct measurement can be made. Nor is she able to find any published data that would be suitable for graphing. She is able to find some limited information about the Chandra X-ray Telescope indicating values of its perigee and apogee altitudes. She uses a program on her calculator to perform a simulation of the Chandra satellite. The program produces simulated data showing the satellite’s altitude and speed versus time. Using this simulated data Jane is able to calculate a third set of data showing the satellite’s kinetic and potential energy. She makes three corresponding graphs and does appropriate analyses. The graphs include both the simulated data and the limited known values for the satellite.