Description
Lab Summary – Follow the same 2-column format, general guidelines, and the “look and feel” of the example reports found here: all information is on the attached file.
Lab Summary – Follow the same 2-column format, general guidelines, and the “look
and feel” of the example reports found here: Report Help & Guidelines . However, do
not include a distinct Theory section or Background/Introduction section; it is
not required to include a Calculations Appendix. See expectations below for how to
structure a Lab Summary and reference the grading Rubric attached to this assignment.
To know what specific content to report on, be sure to follow the instructions in the
Experiment Manual for this experiment.
You must include all relevant data you recorded in some format as well as any results
(graphs, tables, etc.) you were told to produce. “In some format” should be interpreted
at your discretion. For example, if hundreds of data points were taken, placed in a table,
and then used to make a plot it makes most sense to include the final plot which is
representative of the data. You would not need to then also show the huge data table.
However, individual measurements like mass of an object, room air temperature, or
room pressure should always be included once somewhere if they were taken.
This is an individual assignment to be written and submitted by you reflecting
your own work, not that of a group.
Please upload a single PDF file which is organized and legible as your submission.
Be aware that all submissions will be checked and cross referenced for plagiarism
and uniqueness by Turnitin against internal and external references. Your report
should be the product of your work, not that of others, and not a modification of
others work.
Note: The file must be .pdf. If any attached files are not PDFs your assignment
submission will not be saved and no record of your attempt will be recorded. It is the
student’s responsibility to confirm their own successful submission within Canvas.
Structure and Rubric
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Title Area & Abstract o Title Area: Identifies Experiment Topic, Author, Lab Partners,
Course-Section, Instructor, Institution Affiliation, Date.
o Abstract: Summarize the overall paper in 8 sentences or less. State
purpose/objective of your work or what research problem was
investigated, the overall design and process of your experiment, the
major findings and results of your analysis including primary
numerical values, and conclusions from your study.
•
•
•
•
Statement of Purpose – In 4 sentences or less, define the goal or objective of
the experiment(s). Define scope of work.
Experimental Methods – In 300 words or less, briefly describe how the
experiment(s) was performed. Describe equipment and materials used to
perform experiment. Describes methods to operate equipment. Identifies
critical procedural steps needed to replicate experiment (setup, alignment,
calibration, things to avoid, etc.). Defines variables to be directly measured
and how they were measured. State any assumptions made related to
materials. Does not repeat/copy lab manual instructions.
Results – The bulk of your Lab Summary. To include any Results, Analysis, or
Discussion mentioned in the Experiment Manual. Also include any
graphs/plots and data tables asked to produce.
o Analysis of Data – Describe the data analysis and mathematical
processes used to manipulate your direct measurements into final
results. State any assumptions made related to math or physics
theory. Examples: were multiple trials averaged together, did you
use Excel, Matlab, or Pasco Capstone for analysis, was any data
removed or excluded and why, only positive values make sense so
negative values are ignored.
o Graphical Analysis – Includes Plots/Graphs as asked for in
Experiment Manual. Displays data graphically in a clear and logical
way. Formats data appropriately in graphs. Formats plots so axes
labels, values, units, data points, error bars are easily readable.
Gives additional context to graphed data through insightful labels
and captions. Demonstrates understanding of graphical analysis
technique used (curve fits, outlier data points, trendlines, etc.)
o Summary of Experimental Results – Gives principle numerical
results of experiment, as well as their uncertainties. Compares
numerical results to expected/reference values and/or theoretical
predictions by the process discussed in the Experiment Manual
(Discrepancy, % Difference, etc.). Interpret if results support physics
theory and expectations. Interprets if results are successful,
unsuccessful, or inconclusive with respect to Statement of Purpose.
Conclusions – Take away thoughts of the work you did. What likely impacted
your results, and what could be done to improve the work.
o Discussion of Uncertainties – Identify at least 2 likely sources of
uncertainty that you believe affected your results in a nontrivial way. Be specific in the source, what was affected, and how it
was affected (+bias, -bias, or +-random, etc.). Discuss how
significant you think each source of uncertainty is (does one have a
•
•
greater effect than others, does one have a small effect,
etc.). Review any assumptions made which now seem invalid or
possibly inappropriate.
o Thoughts for Improvement – Thinking back on how you
conducted the experiment and analysis, would you perform it the
same or would you do something different? Is there other
equipment you would want to try or use? Suggest at least 2
practical, non-trivial improvements you would make. Describe why
you think this would improve the experiment and better meet its
objectives.
Attribution to Reference Sources – Clearly indicates what information (text,
images, values, formulas) is obtained from a reference. Citations within report
body to reference listings. Bibliography of References List given, formatted
correctly. Examples of references include Lab Manual, websites, textbooks,
articles, blogs.
Data, Formatting, Other – Things not tied to any specific section or area of
the Lab Summary.
o Data & Data Tables – Displays data in labelled tables clearly and
logically. Formats data with correct and uniform decimal precision,
significant figures, units. Gives context to data through appropriate
use of labels, captions. Gives numerical uncertainties for values.
o Overall Formatting – General formatting guidelines are
appropriately followed: title area with single column abstract, 2column report body, additional supporting material contained in
labeled Appendix. Text is readable. Figures/Tables appropriately
sized, positioned.
o Optional Appendices – Any supporting information and
documentation you wish to include (or larger versions of graphs
and figures) should appear at the end of your Lab Summary in one
or more labelled Appendix.
Saving that PDF
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If you are writing up your report in MS Word, there is an option to save the
file directly as a PDF.
If you have something on a piece of paper that you need to attach to your
electronic document, you can scan it and save as a PDF, or you can take a
clear, high resolution photo of it and include the photo as a large, readable
image on a page at the end of your report. For scanning, you can use a
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physical scanner or a mobile app on your phone (saving the scan as a PDF).
Two free recommended options are Adobe Scan (iOS (Links to an external
site.)) or (Android (Links to an external site.)) and Microsoft Office Lens
(iOS (Links to an external site.)) or (Android (Links to an external site.)).
If you need to merge multiple PDFs into a single PDF (such as your report and
a scanned page from above) there are various ways to do
that. smallpdf.com (Links to an external site.) is an easy free way to do it
online.
Rubric
Lab Summary w/ Plots v2.0
Lab Summary w/ Plots v2.0
Criteria
Pts
This criterion is linked to a Learning OutcomeTitle Area &
Abstract
Title Area: Identifies Experiment Topic, Author, Lab Partners,
Course-Section, Instructor, Institution Affiliation, Date.
Abstract: Single paragraph, 8 sentences of less, states
purpose/objective, overviews work performed, summary of
results including primary numerical values.
5 pts
This criterion is linked to a Learning OutcomeStatement of
Purpose
Identifies the goal(s) or objective(s) of the experiment.
Defines scope of work.
5 pts
This criterion is linked to a Learning OutcomeExperimental
Methods
Describe equipment and materials used to perform
experiment. Describes methods to operate equipment.
Identifies critical procedural steps needed to replicate
experiment (setup, alignment, calibration, things to avoid,
etc.). Defines variables to be directly measured and how they
were measured. State any assumptions made related to
materials. Does not repeat/copy lab manual instructions.
12 pts
Lab Summary w/ Plots v2.0
Criteria
Pts
This criterion is linked to a Learning OutcomeData & Data
Tables (document wide)
Displays data in labelled tables clearly and logically. Formats
data with correct and uniform decimal precision, significant
figures, units. Gives context to data through appropriate use of
labels, captions. Gives numerical uncertainties for values.
12 pts
This criterion is linked to a Learning OutcomeResultsAnalysis of Data
Describe the data analysis and mathematical processes used to
manipulate your direct measurements into final results. State
any assumptions made related to math or physics theory.
Examples: were multiple trials averaged together, did you use
Excel, Matlab, or Pasco Capstone for analysis, was any data
removed or excluded and why, only positive values make
sense so negative values are ignored.
8 pts
This criterion is linked to a Learning OutcomeResultsGraphical Analysis
Includes Plots/Graphs as asked for in Experiment Manual.
Displays data graphically in a clear and logical way. Formats
data appropriately in graphs. Formats plots so axes labels,
values, units, data points, error bars are easily readable. Gives
additional context to graphed data through insightful labels
and captions. Demonstrates understanding of graphical
analysis technique used (curve fits, outlier data points,
trendlines, etc.)
15 pts
This criterion is linked to a Learning OutcomeResultsSummary of Experimental Results
Gives principle numerical results of experiment, as well as
their uncertainties. Compares numerical results to
expected/reference values and/or theoretical predictions by the
process discussed in the Experiment Manual (Discrepancy, %
Difference, etc.). Interprets if results support physics theory
and expectations. Interprets if results are successful,
unsuccessful, or inconclusive with respect to Statement of
Purpose.
15 pts
Lab Summary w/ Plots v2.0
Criteria
Pts
This criterion is linked to a Learning OutcomeConclusionsDiscussion of Uncertainties
Identifies various (but specific) sources of experimental
uncertainty that affected results in non-trivial ways. Is aware
of their affects on measurements and results. Gauges/ranks
their level of significance or impact on results. Review any
assumptions made which now seem invalid or possibly
inappropriate.
10 pts
This criterion is linked to a Learning OutcomeConclusionsImproves Experimental Design
Suggests insightful recommendations to improve experimental
design or analysis. Offers support of recommendations. States
how objectives can be better met.
8 pts
This criterion is linked to a Learning OutcomeAttribution to
Reference Sources
Clearly indicates what information (text, images, values,
formulas) is obtained from a reference. Citations within report
body to reference listings. Bibliography of References List
given, formatted correctly. Examples of references include
Lab Manual, websites, textbooks, articles.
5 pts
This criterion is linked to a Learning OutcomeOverall
Formatting
General formatting guidelines are appropriately followed: title
area with single column abstract, 2-column report body,
additional supporting material contained in labeled Appendix.
Text is readable. Figures/Tables appropriately sized,
positioned.
5 pts
Total Points: 100
PS253, Report Guidelines
5/7/2015 DPS
Report Format
As stated in the syllabus, the lab reports are meant to follow the format of most
professional journal publications. The sections of the report and their contents will
be outlined later. The title area and abstract should be centered at the top of the first
page, single column, justified to the margins, with the left and right margins equally
indented more than the margins of the full page. The body of the report and all other
typed material should be in two columns with a relatively thin center spacing, and
both columns should be justified. Format the page and body so that ~70 characters
fit per line in a single column. The only exception would be for large, detailed
images, figures, plots, or tables that simply cannot easily fit into a single column. For
these cases the large item should be placed at the top or bottom of a page with the
rest of the page back in two column format. Pages should be numbered with
numbering on the first page optional.
Clearly label each section of the report with a well-defined heading using your own
choice of consistent format throughout the report. You must include the minimum
required sections in the report as listed in the syllabus; you could include more if
you wanted to, or break one section up into two and rename them as you like, but it
should be clear what your intent is so the instructor knows how to grade it. Citations
within the body text should be clearly labeled and the label format consistent
throughout; the most common formats are numbered superscripts1 or (author,
year). Citation labels must directly correspond with items in the list of references.
The list of references (if titled it is up to you) should immediately follow the
‘Discussion of Results’ and come before extra stuff like the Calculations, plot data, or
raw data. References should follow a standard format (like MLA, APA, etc.) and be
consistent. Refer to the document Experiment Module Authors to see how to
reference the lab modules; these are considered to be works in an anthology,
reference, or collection. For more help on citation and reference format you can visit
this webpage:
Tables and Figures need to appear professional; they should be easily readable and
understandable and readily convey important information to the reader. Tables and
Figures should be labeled in numerical order as they appear in the report. Example:
Table II, Fig. 2. They must have captions that are not trivial, add value, and clarify
details not obvious from the information already present (a graph simply captioned
‘velocity vs time’ would be a poor choice). Graphs in particular should have data that
spans the entire area and is not ‘pushed’ to one side, x and y axis should be labeled
and display the units, the axis scales should be readable and appropriate for the
data, and if a line or function has been fit to the data the equation should be
displayed. See the document Excel Graphing & Analysis for specifics on graph format.
Equations presented in the text should be on their own line, not mixed in the middle
of sentences. Equations should be fully formatted by use of an equation editor.
The report should look polished, be clear and concise, well written, and easily
convey information to the reader. You can look at the Example Report files to
directly see how a report should be formatted.
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PS253, Report Guidelines
5/7/2015 DPS
REPORT OUTLINE
Your intended audience is another technically inclined student, though not
necessarily someone studying to be a scientist. You should write with enough detail
that the reader would understand how to do what you did in lab and be able to
follow along with every step of your analysis even if they had never done it before.
*Title and Abstract are single column at the top of the first page; mirrored, indented
left and right margins; justified alignment for Abstract; centered alignment for Title
Title Area
Name of the experiment
You (author) name, name of lab partner(s)
Course number and section number, name of instructor
Location/Affiliation, i.e. your department and the university and city
Date
Abstract
Usually a single, short paragraph very dense in specific information with one idea or
focus per sentence. Be as to the point as possible. Meant to capture attention.
What was the main aspect or goal(s) of the experiment?
What device or experimental method was used?
What was measured?
What was the main result(s)? If a specific quantity was measured state your
final value along with its error(uncertainty) and give the expected reference
value that it was compared to.
*From this point on, starting with the Background, everything is in two columns and
justified alignment. Format the page and body so that ~70 characters fit per line.
Background
Sets the scene for the reader, gets them ready to read the technical details to follow
Explain why you did the experiment.
What was the purpose? What were the goals?
Briefly give some background context and historical information.
Explain any deviations from expected procedure, especially parts skipped
for reasons like lack of time or equipment malfunction
Theory & Methods
Relatively short, but detailed section covering physical concepts, equations and
formula, experimental techniques and procedures used in the experiment.
Remember the reader should be able to figure out how to replicate your work.
State and explain important equations used in your analysis. These are
typically the main equations introduced in the lab modules or ones that you
are asked to derive. Do not just list equations! Remember citations!
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PS253, Report Guidelines
5/7/2015 DPS
Describe the variables used in equations, state constants and their values
and citations to a reference, highlight necessary conditions for Eq. to work
If an equation was derived describe what it was derived from and any
physics knowledge that was used, such as for simplification purposes
Briefly explain the main steps of the experimental procedure. Use your own
words, don’t rewrite the module procedure! The goal is to summarize to the
reader how you obtained your data. Point out important precautions and
technicalities of equipment or procedure, such as the limits of a given sensor
Results
This will be the most significant part of your report where you show and explain all
the hard work you did analyzing your data to get to your final results. It is in this
section that your level of intellect and comprehension will come across the most; in
most cases how you do in this section will separate the ‘A’ and ‘B’ reports.
Summarize your experimental results, normally the final value you were
looking for. This can be done in a sentence or two, or in a table if your results
are more complicated and include multiple final values. You should include
your experimental value, a theoretical(expected) value from reference, and
most likely a percent difference between the two. Order does not matter.
Example: “From our data taken in lab, we obtained a valve flow rate of 35±5
cm3/s compared to a manufacturer specified flow rate of 40. cm3/s [1]*citation
for this valve giving us a discrepancy of 13%.”
Your results should be given with the correct significant figures and you
should include your error analysis. Show the uncertainty, standard
deviation, or propagated error on your experimental values.
Compare your results to theory and expected values. Discuss any
discrepancies if they exist and what might have caused them.
If approximations or simplifications were made (say in theory like no
friction, or small angle) in order to make the analysis easier explain how
these might have affected your results.
Determine at least two possible sources of error(uncertainty); what kind of
error is it, what caused it, how large an affect it could have had, if you think it
significantly affected your results, if there is any way you could minimize it.
Be specific! Do not just list things! You need to justify your reasoning with
rough quantitative(numerical) and qualitative(logical) arguments.
Include tables, graphs, and figures when necessary to support your findings.
Format these professionally and make them as clear and informative as
possible. See the Format section of this document for more.
Answer all questions asked in the lab module. In the modules these tend to
show up as: “question:” or “for your report” or “for your analysis”. Do not
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PS253, Report Guidelines
5/7/2015 DPS
answer these in lists or numbered answers, you should be able to work your
answers into the overall flow of your discussion.
References
This section is straight forward. You should list the books, modules, websites,
papers, articles, databases, etc. that you used information from in order to make
your report. Keep in mind that a reference list should only include works that you
directly cited from in your report; a bibliography would be the only thing to include
other sources you didn’t directly quote or cite in your text but used as help.
Calculations
These may be done electronically and properly formatted using an equation editor
(there is a built in one in MS Word), or done by hand and must be neat and readable.
The objective is to show that you know how to do all the math needed
Include one complete example of every calculation done from start to finish
in order to obtain your final results. Approach it like a mathematical
cookbook so the reader can follow every step.
Include units throughout each calculation, not just on the answers
Significant figures should be correct on all answers, or at the end of a chain
of calculations if intermediate answers were not required for analysis
Make sure to show all error propagation in detail, showing each step
Make sure to show all derivations asked for, showing each step
If a calculation was performed many times (like in a spreadsheet) you only
need to work it out once, but use your own data values
Plot Data
This section only exists if you included in your report plots or graphs made from
your own data or calculated values. You should give data tables, normally 2 column
(x, y), properly formatted with clear labels, headings, and captions. Include the units
and variable names at the top of the columns, and values should be in correct
significant figures. This is a final check to make sure your graphs were made
properly, or in case it is too hard to read your graph. These must be typed.
Raw Data
The very last section! This is the data you took in lab during the experiment. It can
be saved electronically and printed later, or hand written and signed by the
instructor before you leave lab. Whatever you had from lab just attach it to the end
of the report, do not feel the need to rewrite it or take hand written stuff and make it
typed. It just needs to be present and readable.
You must have raw data attached or your report will not be graded!
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PS253, Report Guidelines
5/7/2015 DPS
Checklist for Writing a Good Report
Raw data sheet (typed or hand written) is attached to report
All work is your own original work!
One column title and abstract at top of first page
Everything else typed is in two columns (except very large figures or plots)
All numerical values in report have correct significant figures. This includes
within text, in data tables, and calculations. Uncertainties should also have
proper significant figures
All numerical values in report have correct units. This includes within text,
in data tables, and calculations
All measured values include associated uncertainty(error) Ex: 15±2 mm
All error propagation is done correctly, and if possible all calculated values
have associated uncertainties given with them Ex: 9.79±0.03 m/s2
Double check that all calculations are done correctly and you have an
example calculation for everything done in your analysis
Double check that all equations and formulas are correct and properly
formatted. Formulas should not be in line with text, but on their own line
and made with an equation editor (MS Word has a built in equation editor)
Make sure you are using terms correctly: accuracy vs precision,
uncertainty(error) vs discrepancy(deviation), etc.
Are all graphs formatted properly? Do they look professional, are they
numbered, do they have informative captions, are the axes labeled with
titles and units, are fit equations displayed, does the data ‘fill’ the graph?
Remember to check the Excel Graphing & Analysis document for help.
Are all figures and tables properly formatted? Are they numbered, do they
have informative captions?
Do you have a citation next to every single thing you used in the text from
another source? (quoted text, images, constants, equations from books,
website, articles, and lab modules) Are your citations properly formatted?
Does your reference list include all the sources you used and cited in your
report? Are your references properly formatted? Check Experiment Module
Authors document and here
Did you discuss at least two possible sources of error?
Your Plot Data section has a typed table for each graph in your report
Answer all questions asked in the lab module in your Discussion section
Review the ‘Guidelines’ page at the end of the lab module
Proofread your report! Make sure what you are writing makes sense.
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Introduction Part 1 Snapshot
09/30/2020 18:07:35
Theory Part 1 Snapshot
09/30/2020 18:07:39
Procedure 1.1 Snapshot
09/30/2020 18:08:21
Procedure 1.2 Snapshot
09/30/2020 18:09:18
Procedure 1.3 Snapshot
09/30/2020 18:09:21
Intro Snapshot
09/30/2020 18:12:38
Theory Snapshot
09/30/2020 18:12:41
Setup 2.1 Snapshot
09/30/2020 18:12:44
Setup 2.2 Level Check Snapshot
09/30/2020 18:12:48
Procedure Snapshot
09/30/2020 18:12:51
Analysis 2.1 Snapshot
09/30/2020 18:12:54
Data Snapshot
09/30/2020 18:12:57
Analysis 2.2 Snapshot
09/30/2020 18:13:01
Variable Release Angle
1
2
3
4
Pendulum Length (m) ±0.0005m
0.917
0.917
0.917
0.917
String Length (m) ±0.0005m
0.874
0.874
0.874
0.874
Pendulum Mass (kg) ±0.00001kg
0.488
0.488
0.488
0.488
Bob Hook Length (m) ±0.0005m
0.014
0.014
0.014
0.014
Bob COM Length (m) ±0.0005m
0.029
0.029
0.029
0.029
Vertical Displacement (m) ±0.0005m
0.077
0.1
0.12
0.14
Angle of Release (deg) ±0.05 deg
4.82
6.26
7.52
8.78
Mean Period (s)
1.93
1.93
1.93
1.93
0.00352
0.00112
0.0019
Run Number
Period Uncertainty (±s) 9.32*10^-4
le
Variable Pendulum Length
5
6
7
8
9
10
11
0.917
0.793
0.683
0.573
0.463
0.353
0.243
0.874
0.75
0.64
0.53
0.42
0.31
0.2
0.488
0.488
0.488
0.488
0.488
0.488
0.488
0.014
0.014
0.014
0.014
0.014
0.014
0.014
0.029
0.029
0.029
0.029
0.029
0.029
0.029
0.2
0.069
0.059
0.05
0.04
0.031
0.021
12.6
5
5
5
5
5
5
1.94
1.8
1.67
1.53
1.37
2.38
1.98
0.00166
6.78*10^-4
0.00331
0.00495
9.33*10^-4
0.0175
0.00469
ERROR RUNS
Variable Mass
12
13
0.917
0.917
0.881
0.882
0.199
0.0999
0.015
0.018
0.0215
0.0175
0.079
0.079
5
5
1.92
1.92
2.66*10^-4
4.92*10^-4
Lab Summary – Follow the same 2-column format, general guidelines, and the “look
and feel” of the example reports found here: Report Help & Guidelines . However, do
not include a distinct Theory section or Background/Introduction section; it is
not required to include a Calculations Appendix. See expectations below for how to
structure a Lab Summary and reference the grading Rubric attached to this assignment.
To know what specific content to report on, be sure to follow the instructions in the
Experiment Manual for this experiment.
You must include all relevant data you recorded in some format as well as any results
(graphs, tables, etc.) you were told to produce. “In some format” should be interpreted
at your discretion. For example, if hundreds of data points were taken, placed in a table,
and then used to make a plot it makes most sense to include the final plot which is
representative of the data. You would not need to then also show the huge data table.
However, individual measurements like mass of an object, room air temperature, or
room pressure should always be included once somewhere if they were taken.
This is an individual assignment to be written and submitted by you reflecting
your own work, not that of a group.
Please upload a single PDF file which is organized and legible as your submission.
Be aware that all submissions will be checked and cross referenced for plagiarism
and uniqueness by Turnitin against internal and external references. Your report
should be the product of your work, not that of others, and not a modification of
others work.
Note: The file must be .pdf. If any attached files are not PDFs your assignment
submission will not be saved and no record of your attempt will be recorded. It is the
student’s responsibility to confirm their own successful submission within Canvas.
Structure and Rubric
•
Title Area & Abstract o Title Area: Identifies Experiment Topic, Author, Lab Partners,
Course-Section, Instructor, Institution Affiliation, Date.
o Abstract: Summarize the overall paper in 8 sentences or less. State
purpose/objective of your work or what research problem was
investigated, the overall design and process of your experiment, the
major findings and results of your analysis including primary
numerical values, and conclusions from your study.
•
•
•
•
Statement of Purpose – In 4 sentences or less, define the goal or objective of
the experiment(s). Define scope of work.
Experimental Methods – In 300 words or less, briefly describe how the
experiment(s) was performed. Describe equipment and materials used to
perform experiment. Describes methods to operate equipment. Identifies
critical procedural steps needed to replicate experiment (setup, alignment,
calibration, things to avoid, etc.). Defines variables to be directly measured
and how they were measured. State any assumptions made related to
materials. Does not repeat/copy lab manual instructions.
Results – The bulk of your Lab Summary. To include any Results, Analysis, or
Discussion mentioned in the Experiment Manual. Also include any
graphs/plots and data tables asked to produce.
o Analysis of Data – Describe the data analysis and mathematical
processes used to manipulate your direct measurements into final
results. State any assumptions made related to math or physics
theory. Examples: were multiple trials averaged together, did you
use Excel, Matlab, or Pasco Capstone for analysis, was any data
removed or excluded and why, only positive values make sense so
negative values are ignored.
o Graphical Analysis – Includes Plots/Graphs as asked for in
Experiment Manual. Displays data graphically in a clear and logical
way. Formats data appropriately in graphs. Formats plots so axes
labels, values, units, data points, error bars are easily readable.
Gives additional context to graphed data through insightful labels
and captions. Demonstrates understanding of graphical analysis
technique used (curve fits, outlier data points, trendlines, etc.)
o Summary of Experimental Results – Gives principle numerical
results of experiment, as well as their uncertainties. Compares
numerical results to expected/reference values and/or theoretical
predictions by the process discussed in the Experiment Manual
(Discrepancy, % Difference, etc.). Interpret if results support physics
theory and expectations. Interprets if results are successful,
unsuccessful, or inconclusive with respect to Statement of Purpose.
Conclusions – Take away thoughts of the work you did. What likely impacted
your results, and what could be done to improve the work.
o Discussion of Uncertainties – Identify at least 2 likely sources of
uncertainty that you believe affected your results in a nontrivial way. Be specific in the source, what was affected, and how it
was affected (+bias, -bias, or +-random, etc.). Discuss how
significant you think each source of uncertainty is (does one have a
•
•
greater effect than others, does one have a small effect,
etc.). Review any assumptions made which now seem invalid or
possibly inappropriate.
o Thoughts for Improvement – Thinking back on how you
conducted the experiment and analysis, would you perform it the
same or would you do something different? Is there other
equipment you would want to try or use? Suggest at least 2
practical, non-trivial improvements you would make. Describe why
you think this would improve the experiment and better meet its
objectives.
Attribution to Reference Sources – Clearly indicates what information (text,
images, values, formulas) is obtained from a reference. Citations within report
body to reference listings. Bibliography of References List given, formatted
correctly. Examples of references include Lab Manual, websites, textbooks,
articles, blogs.
Data, Formatting, Other – Things not tied to any specific section or area of
the Lab Summary.
o Data & Data Tables – Displays data in labelled tables clearly and
logically. Formats data with correct and uniform decimal precision,
significant figures, units. Gives context to data through appropriate
use of labels, captions. Gives numerical uncertainties for values.
o Overall Formatting – General formatting guidelines are
appropriately followed: title area with single column abstract, 2column report body, additional supporting material contained in
labeled Appendix. Text is readable. Figures/Tables appropriately
sized, positioned.
o Optional Appendices – Any supporting information and
documentation you wish to include (or larger versions of graphs
and figures) should appear at the end of your Lab Summary in one
or more labelled Appendix.
Saving that PDF
•
•
If you are writing up your report in MS Word, there is an option to save the
file directly as a PDF.
If you have something on a piece of paper that you need to attach to your
electronic document, you can scan it and save as a PDF, or you can take a
clear, high resolution photo of it and include the photo as a large, readable
image on a page at the end of your report. For scanning, you can use a
•
physical scanner or a mobile app on your phone (saving the scan as a PDF).
Two free recommended options are Adobe Scan (iOS (Links to an external
site.)) or (Android (Links to an external site.)) and Microsoft Office Lens
(iOS (Links to an external site.)) or (Android (Links to an external site.)).
If you need to merge multiple PDFs into a single PDF (such as your report and
a scanned page from above) there are various ways to do
that. smallpdf.com (Links to an external site.) is an easy free way to do it
online.
Rubric
Lab Summary w/ Plots v2.0
Lab Summary w/ Plots v2.0
Criteria
Pts
This criterion is linked to a Learning OutcomeTitle Area &
Abstract
Title Area: Identifies Experiment Topic, Author, Lab Partners,
Course-Section, Instructor, Institution Affiliation, Date.
Abstract: Single paragraph, 8 sentences of less, states
purpose/objective, overviews work performed, summary of
results including primary numerical values.
5 pts
This criterion is linked to a Learning OutcomeStatement of
Purpose
Identifies the goal(s) or objective(s) of the experiment.
Defines scope of work.
5 pts
This criterion is linked to a Learning OutcomeExperimental
Methods
Describe equipment and materials used to perform
experiment. Describes methods to operate equipment.
Identifies critical procedural steps needed to replicate
experiment (setup, alignment, calibration, things to avoid,
etc.). Defines variables to be directly measured and how they
were measured. State any assumptions made related to
materials. Does not repeat/copy lab manual instructions.
12 pts
Lab Summary w/ Plots v2.0
Criteria
Pts
This criterion is linked to a Learning OutcomeData & Data
Tables (document wide)
Displays data in labelled tables clearly and logically. Formats
data with correct and uniform decimal precision, significant
figures, units. Gives context to data through appropriate use of
labels, captions. Gives numerical uncertainties for values.
12 pts
This criterion is linked to a Learning OutcomeResultsAnalysis of Data
Describe the data analysis and mathematical processes used to
manipulate your direct measurements into final results. State
any assumptions made related to math or physics theory.
Examples: were multiple trials averaged together, did you use
Excel, Matlab, or Pasco Capstone for analysis, was any data
removed or excluded and why, only positive values make
sense so negative values are ignored.
8 pts
This criterion is linked to a Learning OutcomeResultsGraphical Analysis
Includes Plots/Graphs as asked for in Experiment Manual.
Displays data graphically in a clear and logical way. Formats
data appropriately in graphs. Formats plots so axes labels,
values, units, data points, error bars are easily readable. Gives
additional context to graphed data through insightful labels
and captions. Demonstrates understanding of graphical
analysis technique used (curve fits, outlier data points,
trendlines, etc.)
15 pts
This criterion is linked to a Learning OutcomeResultsSummary of Experimental Results
Gives principle numerical results of experiment, as well as
their uncertainties. Compares numerical results to
expected/reference values and/or theoretical predictions by the
process discussed in the Experiment Manual (Discrepancy, %
Difference, etc.). Interprets if results support physics theory
and expectations. Interprets if results are successful,
unsuccessful, or inconclusive with respect to Statement of
Purpose.
15 pts
Lab Summary w/ Plots v2.0
Criteria
Pts
This criterion is linked to a Learning OutcomeConclusionsDiscussion of Uncertainties
Identifies various (but specific) sources of experimental
uncertainty that affected results in non-trivial ways. Is aware
of their affects on measurements and results. Gauges/ranks
their level of significance or impact on results. Review any
assumptions made which now seem invalid or possibly
inappropriate.
10 pts
This criterion is linked to a Learning OutcomeConclusionsImproves Experimental Design
Suggests insightful recommendations to improve experimental
design or analysis. Offers support of recommendations. States
how objectives can be better met.
8 pts
This criterion is linked to a Learning OutcomeAttribution to
Reference Sources
Clearly indicates what information (text, images, values,
formulas) is obtained from a reference. Citations within report
body to reference listings. Bibliography of References List
given, formatted correctly. Examples of references include
Lab Manual, websites, textbooks, articles.
5 pts
This criterion is linked to a Learning OutcomeOverall
Formatting
General formatting guidelines are appropriately followed: title
area with single column abstract, 2-column report body,
additional supporting material contained in labeled Appendix.
Text is readable. Figures/Tables appropriately sized,
positioned.
5 pts
Total Points: 100
Introduction Part 1 Snapshot
09/30/2020 18:07:35
Theory Part 1 Snapshot
09/30/2020 18:07:39
Procedure 1.1 Snapshot
09/30/2020 18:08:21
Procedure 1.2 Snapshot
09/30/2020 18:09:18
Procedure 1.3 Snapshot
09/30/2020 18:09:21
Intro Snapshot
09/30/2020 18:12:38
Theory Snapshot
09/30/2020 18:12:41
Setup 2.1 Snapshot
09/30/2020 18:12:44
Setup 2.2 Level Check Snapshot
09/30/2020 18:12:48
Procedure Snapshot
09/30/2020 18:12:51
Analysis 2.1 Snapshot
09/30/2020 18:12:54
Data Snapshot
09/30/2020 18:12:57
Analysis 2.2 Snapshot
09/30/2020 18:13:01
PS253, Report Guidelines
5/7/2015 DPS
Report Format
As stated in the syllabus, the lab reports are meant to follow the format of most
professional journal publications. The sections of the report and their contents will
be outlined later. The title area and abstract should be centered at the top of the first
page, single column, justified to the margins, with the left and right margins equally
indented more than the margins of the full page. The body of the report and all other
typed material should be in two columns with a relatively thin center spacing, and
both columns should be justified. Format the page and body so that ~70 characters
fit per line in a single column. The only exception would be for large, detailed
images, figures, plots, or tables that simply cannot easily fit into a single column. For
these cases the large item should be placed at the top or bottom of a page with the
rest of the page back in two column format. Pages should be numbered with
numbering on the first page optional.
Clearly label each section of the report with a well-defined heading using your own
choice of consistent format throughout the report. You must include the minimum
required sections in the report as listed in the syllabus; you could include more if
you wanted to, or break one section up into two and rename them as you like, but it
should be clear what your intent is so the instructor knows how to grade it. Citations
within the body text should be clearly labeled and the label format consistent
throughout; the most common formats are numbered superscripts1 or (author,
year). Citation labels must directly correspond with items in the list of references.
The list of references (if titled it is up to you) should immediately follow the
‘Discussion of Results’ and come before extra stuff like the Calculations, plot data, or
raw data. References should follow a standard format (like MLA, APA, etc.) and be
consistent. Refer to the document Experiment Module Authors to see how to
reference the lab modules; these are considered to be works in an anthology,
reference, or collection. For more help on citation and reference format you can visit
this webpage:
Tables and Figures need to appear professional; they should be easily readable and
understandable and readily convey important information to the reader. Tables and
Figures should be labeled in numerical order as they appear in the report. Example:
Table II, Fig. 2. They must have captions that are not trivial, add value, and clarify
details not obvious from the information already present (a graph simply captioned
‘velocity vs time’ would be a poor choice). Graphs in particular should have data that
spans the entire area and is not ‘pushed’ to one side, x and y axis should be labeled
and display the units, the axis scales should be readable and appropriate for the
data, and if a line or function has been fit to the data the equation should be
displayed. See the document Excel Graphing & Analysis for specifics on graph format.
Equations presented in the text should be on their own line, not mixed in the middle
of sentences. Equations should be fully formatted by use of an equation editor.
The report should look polished, be clear and concise, well written, and easily
convey information to the reader. You can look at the Example Report files to
directly see how a report should be formatted.
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PS253, Report Guidelines
5/7/2015 DPS
REPORT OUTLINE
Your intended audience is another technically inclined student, though not
necessarily someone studying to be a scientist. You should write with enough detail
that the reader would understand how to do what you did in lab and be able to
follow along with every step of your analysis even if they had never done it before.
*Title and Abstract are single column at the top of the first page; mirrored, indented
left and right margins; justified alignment for Abstract; centered alignment for Title
Title Area
Name of the experiment
You (author) name, name of lab partner(s)
Course number and section number, name of instructor
Location/Affiliation, i.e. your department and the university and city
Date
Abstract
Usually a single, short paragraph very dense in specific information with one idea or
focus per sentence. Be as to the point as possible. Meant to capture attention.
What was the main aspect or goal(s) of the experiment?
What device or experimental method was used?
What was measured?
What was the main result(s)? If a specific quantity was measured state your
final value along with its error(uncertainty) and give the expected reference
value that it was compared to.
*From this point on, starting with the Background, everything is in two columns and
justified alignment. Format the page and body so that ~70 characters fit per line.
Background
Sets the scene for the reader, gets them ready to read the technical details to follow
Explain why you did the experiment.
What was the purpose? What were the goals?
Briefly give some background context and historical information.
Explain any deviations from expected procedure, especially parts skipped
for reasons like lack of time or equipment malfunction
Theory & Methods
Relatively short, but detailed section covering physical concepts, equations and
formula, experimental techniques and procedures used in the experiment.
Remember the reader should be able to figure out how to replicate your work.
State and explain important equations used in your analysis. These are
typically the main equations introduced in the lab modules or ones that you
are asked to derive. Do not just list equations! Remember citations!
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PS253, Report Guidelines
5/7/2015 DPS
Describe the variables used in equations, state constants and their values
and citations to a reference, highlight necessary conditions for Eq. to work
If an equation was derived describe what it was derived from and any
physics knowledge that was used, such as for simplification purposes
Briefly explain the main steps of the experimental procedure. Use your own
words, don’t rewrite the module procedure! The goal is to summarize to the
reader how you obtained your data. Point out important precautions and
technicalities of equipment or procedure, such as the limits of a given sensor
Results
This will be the most significant part of your report where you show and explain all
the hard work you did analyzing your data to get to your final results. It is in this
section that your level of intellect and comprehension will come across the most; in
most cases how you do in this section will separate the ‘A’ and ‘B’ reports.
Summarize your experimental results, normally the final value you were
looking for. This can be done in a sentence or two, or in a table if your results
are more complicated and include multiple final values. You should include
your experimental value, a theoretical(expected) value from reference, and
most likely a percent difference between the two. Order does not matter.
Example: “From our data taken in lab, we obtained a valve flow rate of 35±5
cm3/s compared to a manufacturer specified flow rate of 40. cm3/s [1]*citation
for this valve giving us a discrepancy of 13%.”
Your results should be given with the correct significant figures and you
should include your error analysis. Show the uncertainty, standard
deviation, or propagated error on your experimental values.
Compare your results to theory and expected values. Discuss any
discrepancies if they exist and what might have caused them.
If approximations or simplifications were made (say in theory like no
friction, or small angle) in order to make the analysis easier explain how
these might have affected your results.
Determine at least two possible sources of error(uncertainty); what kind of
error is it, what caused it, how large an affect it could have had, if you think it
significantly affected your results, if there is any way you could minimize it.
Be specific! Do not just list things! You need to justify your reasoning with
rough quantitative(numerical) and qualitative(logical) arguments.
Include tables, graphs, and figures when necessary to support your findings.
Format these professionally and make them as clear and informative as
possible. See the Format section of this document for more.
Answer all questions asked in the lab module. In the modules these tend to
show up as: “question:” or “for your report” or “for your analysis”. Do not
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PS253, Report Guidelines
5/7/2015 DPS
answer these in lists or numbered answers, you should be able to work your
answers into the overall flow of your discussion.
References
This section is straight forward. You should list the books, modules, websites,
papers, articles, databases, etc. that you used information from in order to make
your report. Keep in mind that a reference list should only include works that you
directly cited from in your report; a bibliography would be the only thing to include
other sources you didn’t directly quote or cite in your text but used as help.
Calculations
These may be done electronically and properly formatted using an equation editor
(there is a built in one in MS Word), or done by hand and must be neat and readable.
The objective is to show that you know how to do all the math needed
Include one complete example of every calculation done from start to finish
in order to obtain your final results. Approach it like a mathematical
cookbook so the reader can follow every step.
Include units throughout each calculation, not just on the answers
Significant figures should be correct on all answers, or at the end of a chain
of calculations if intermediate answers were not required for analysis
Make sure to show all error propagation in detail, showing each step
Make sure to show all derivations asked for, showing each step
If a calculation was performed many times (like in a spreadsheet) you only
need to work it out once, but use your own data values
Plot Data
This section only exists if you included in your report plots or graphs made from
your own data or calculated values. You should give data tables, normally 2 column
(x, y), properly formatted with clear labels, headings, and captions. Include the units
and variable names at the top of the columns, and values should be in correct
significant figures. This is a final check to make sure your graphs were made
properly, or in case it is too hard to read your graph. These must be typed.
Raw Data
The very last section! This is the data you took in lab during the experiment. It can
be saved electronically and printed later, or hand written and signed by the
instructor before you leave lab. Whatever you had from lab just attach it to the end
of the report, do not feel the need to rewrite it or take hand written stuff and make it
typed. It just needs to be present and readable.
You must have raw data attached or your report will not be graded!
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PS253, Report Guidelines
5/7/2015 DPS
Checklist for Writing a Good Report
Raw data sheet (typed or hand written) is attached to report
All work is your own original work!
One column title and abstract at top of first page
Everything else typed is in two columns (except very large figures or plots)
All numerical values in report have correct significant figures. This includes
within text, in data tables, and calculations. Uncertainties should also have
proper significant figures
All numerical values in report have correct units. This includes within text,
in data tables, and calculations
All measured values include associated uncertainty(error) Ex: 15±2 mm
All error propagation is done correctly, and if possible all calculated values
have associated uncertainties given with them Ex: 9.79±0.03 m/s2
Double check that all calculations are done correctly and you have an
example calculation for everything done in your analysis
Double check that all equations and formulas are correct and properly
formatted. Formulas should not be in line with text, but on their own line
and made with an equation editor (MS Word has a built in equation editor)
Make sure you are using terms correctly: accuracy vs precision,
uncertainty(error) vs discrepancy(deviation), etc.
Are all graphs formatted properly? Do they look professional, are they
numbered, do they have informative captions, are the axes labeled with
titles and units, are fit equations displayed, does the data ‘fill’ the graph?
Remember to check the Excel Graphing & Analysis document for help.
Are all figures and tables properly formatted? Are they numbered, do they
have informative captions?
Do you have a citation next to every single thing you used in the text from
another source? (quoted text, images, constants, equations from books,
website, articles, and lab modules) Are your citations properly formatted?
Does your reference list include all the sources you used and cited in your
report? Are your references properly formatted? Check Experiment Module
Authors document and here
Did you discuss at least two possible sources of error?
Your Plot Data section has a typed table for each graph in your report
Answer all questions asked in the lab module in your Discussion section
Review the ‘Guidelines’ page at the end of the lab module
Proofread your report! Make sure what you are writing makes sense.
-5-
Pendulum Tests – Discovering What Variables
Affect a Pendulum’s Period
PS253 — Physics Laboratory for Engineers
Department of Physical Sciences
Embry-Riddle Aeronautical University, Daytona Beach, Florida
Introduction
Approach this assignment as an exploration of the unknown. The question to be answered
is: “What influences the period of a pendulum?” This is the same question that vexed
Galileo Galilei over four centuries ago during his early days of scientific experimentation.
The answers to this question helped to make pendulum clocks the first mass produced time
pieces both accurate and practical enough for keeping time across empires day or night, rain
or shine. Pendulum clocks remained the best timekeeping instruments for over 300 years
until well into the early to mid-1900s!
As you would expect, a quantitative technical analysis will be undertaken involving proper
experimental technique, measuring instruments, recorded data, and mathematical models.
The property of interest is the period of the pendulum or the time it takes to swing from one
side to the other and back again. By carefully changing only one variable at a time, initial
angle of release, pendulum mass, and length to the center of the mass, a controlled
experiment can be conducted whereby over many trials the correct relationship between
each variable and the period should be revealed. In the end you can report to your readers
how the pendulum reacted to changes in the variables.
Procedure
1. Use the triple beam balance to find the mass of 3 different pendulum bobs. Record the
bob masses and their measured uncertainties (±). We will assume the mass of the
string is negligible. Also record the height of each bob.
2. You will be performing multiple runs of the same experiment, varying only one
variable of interest at a time. To keep track of all the data, open an Excel spreadsheet.
Make column headings for Run Number, pendulum length L [m], pendulum mass m
[kg], displacement from vertical x [m], angle of release [θ], period T [s], and period
uncertainty [s]. All columns except the two period columns should have their
uncertainties given in the header row since they are constant for all measurements.
From now on you are expected to label and record your own data and uncertainties properly without
being given further instructions.
3. At your station there should be a vertical post with a crossbar near the top to suspend
a string and bob pendulum from. Near the bottom should be a photogate used to time
the passage of the bob. At maximum length, the pendulum bob should be able to hang
1.0m below the crossbar and still pass through the mounted photogate.
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Pendulum Tests
PS253 – Physics Lab for Engineers
If this is not already setup, proceed to set this up similar to Figure 1. Begin by using
the largest mass as the pendulum bob. Note that it is important to have the pendulum
oscillating in only one vertical plane passing through the photogate. This is more easily
achieved by securing a single string at two points along the crossbar and passing
through an attachment point on the pendulum, rather than only at one point on the
crossbar. The difficulty with this is making sure both sides of the string are the same
length and attached equidistant from the vertical line down to the bob.
Figure 1: Setup for simple pendulum test. (left) Illustration of basic setup. (middle)
Image of top crossbar setup. (right) Image of photogate setup and pendulum bob
attachment for spherical mass.
4. Plug the photogate into the Pasco interface’s Digital Channel 1. After logging in to the
computer connected to the interface, open the program Capstone.
5. When Capstone opens, in the left-side menu, click on the Hardware Setup button to open
a window where you can add your sensor.
6. Click on the virtual input where you plugged in the photogate and select Pendulum
Timer to add the photogate as a sensor.
The photogate works as on/off timer or switch using an infrared LED and infrared
photodiode on opposite sides of its gate. It records the state of the gate: blocked ‘1’, or open
‘0’. Thus it is a digital sensor. The software can use this information along with the time of
the gate events to determine many different things: velocity, time-in-gate, period, etc.
Pendulum Timer is a software preset which measures period by recording the time between
every third blocking event (start, reverse pass, forward pass & stop). The red LED on the
photogate will indicate when the gate is blocked.
7. Click the Timer Setup button below Hardware Setup and in the following drop-down
menu deselect Speed so that only the Period measurement will be visible.
8. Close the Timer Setup window when you are finished. In the central display area select
the option that gives you Table and Graph display windows.
a. In the Table display, set the first column as Period and delete the second column.
b. Using the Table display menu, click the Σ Show Statistics button and use the arrow
drop-down menu to display only Mean, Standard Deviation, and Count.
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Pendulum Tests
PS253 – Physics Lab for Engineers
c. In the Graph display, set the y-axis as Period and the x-axis as time.
9. Make sure that the length of your pendulum is ~1.0m, and if using a double crossbar
attachment point system, that both sides of the string are the same length and attached
equidistant from the vertical line down to the bob.
Then, use a meter stick to measure the vertical distance between the bottom of the
crossbar (where the top of the string is connected) to the top of the pendulum bob
(not necessarily where the string is attached). Add this length to half the height of the
bob to get L, the length of the pendulum to the center of mass.
We are assuming that the string is massless and that the bob’s center of mass is at its
geometric center.
10. Once the setup is complete, try a couple practice releases of the pendulum from small
angles to get a feel for the correct release. You want to pass the bob straight through
the photogate without hitting it, to have no rotation of the bob, and to impart no force
to the bob upon release. Practice now so you have more successful trial runs later.
11. For the first data run pull the bob ~5° from the vertical. As in Figure 1, set one end of
the long meter stick on the floor and make it as vertical as you can. Then pull the bob
to the side until 𝑥 ≅ 𝐿 sin 5° = ___ is reached. Remove the meter stick, click Record in
Capstone, and release the bob. Continue recording timings for a total of 19 periods,
clicking Stop after the 19th period. Record the mean period and its uncertainty (standard
deviation) in your spreadsheet. This is Run #1.
12. Without changing the string length, pull back the bob a few extra centimeters and
measure the new displacement x; also find the new release angle θ. Do not exceed a
release angle of 25°. Perform Run #2 with this new displacement from vertical
following the same procedure as in Step 11. This is Run #2.
13. Repeat Step 12 an additional three times, each time increasing the displacement from
vertical x thus increasing the release angle. These are Runs #3-5. You should now have
five runs for five different release angles.
You might need to brace or adjust the pendulum support stand for the larger angle
tests if it appears to start flexing or oscillating. Remember we are trying to allow only
one condition at a time to change so that we may infer any response in the period is
due to that variation alone.
14. Now, change the length of the pendulum by ≥10cm by adjusting the string. Measure
the new length as you did in Step 9 making sure to add this to half the bob height and
record this sum as L for Run #6. Perform Run #6 following the procedure of Step 11
doing your best to use a release angle as close to 5° as possible.
15. Repeat Step 14 an additional five times, each time varying the length by ≥10cm but
keeping a release angle of 5°. These are Runs #7-11, together with Runs #1,6 you have
seven runs for seven different pendulum lengths. All of these runs should have the
same mass and same release angle.
16. For the final two runs, Run #12,13 replace the largest mass bob with a different mass
bob using a different bob for each new run. Adjust the total pendulum length to be as
equal as possible to the total pendulum length L you used for Run #1. Remember this
was the sum of the vertical hanging length and half the bob height, each new bob likely
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Pendulum Tests
PS253 – Physics Lab for Engineers
has a different height so the string length must be adjusted slightly. Measure the length
as in Step 9 and perform runs #12,13 as in Step 11 using a 5° release angle.
Analysis
Note: You should only be comparing between runs with the same changing variable. For
example, when discussing if mass affects a pendulum’s period only look at Runs #1,12,13
(runs where mass actually changed, but everything else remained constant). When discussing
or plotting the effect of length on period only compare across Runs #1,6-11.
1. Describe how the mean period for each run varies, if at all, with different lengths,
vertical displacements, or masses. Make sure any variations are significant, that is it’s well
above the noise in the data (standard deviations of individual runs). From your data
and observations, what varying factors actually affect the period of a pendulum?
Explain what you are able to conclude from your experimentation.
2. Make plots of the following: period vs pendulum length, ln(period) vs ln(length), and
period vs vertical displacement. Review the plots. Do any show a significant change in
period with respect to the variable, is it a linear or nonlinear change? Do any show no
significant slope, i.e. is it constant and unaffected by changing that variable?
3. Let T = KLn be an exponential relationship where K and n are constants that fit the
data best, and take the natural logarithm of both sides:
ln 𝑇 = ln(𝐾𝐿𝑛 ) = ln 𝐾 + ln 𝐿𝑛
(1)
ln 𝑇 = 𝑛 ln 𝐿 + ln 𝐾
(2)
This is the equation of a straight line for a ‘y vs x’ graph where ln(K) is the y-intercept,
n is the slope, ln(T) is the y-variable, and ln(L) is the x-variable.
4. For your ln(period) vs ln(length) plot, fit a linear curve and equation to the data. Use a
Regression technique to find the slope and y-intercept of this line as well as their
uncertainties. Use these to find values for n and K.
5. Substitute your values for K and n into T = KLn. Assuming the data from the other
variables turned out well, you should have noticed by now that the only variable that
significantly affects the period of a simple pendulum is its length. So now we are building
an equation that can predict a pendulum’s period based on that information.
Without making educated guesses at what might be lurking behind these numerical constant
values, this is as far as we can go experimentally in determining a predictive equation.
However, it should be good enough to supply to other experimentalists if they wanted to
reproduce your work under similar circumstances.
Using some basic principles of physics and mechanics it is possible to derive an equation to
predict pendulum period directly from theory. This would reveal a more general equation
form where the numerical constants are replaced with physical constants, thus giving rise to
an even broader predictive equation that would be useful under a broader range of
conditions.
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Pendulum Tests
PS253 – Physics Lab for Engineers
6. As a comparison between theory and experiment compute the percent difference
between
a. K and
b. n and ½
2𝜋
√g
7. How might this experiment be improved upon to better illustrate the characteristics of
an ideal pendulum? For example, think of all possible sources of error and how you
might eliminate them, or how you might compensate for other physical properties that
might vary based on local conditions?
Remember in the procedure there were a few important parameters you did not want
to exceed certain limits. Might there be other effects that appear if you get too close to
these limits? There were also a few assumptions made during our experiment.
This is quite the simple pendulum we used. After all, continual advancements were
made over the course of 350 years to keep making better measurements of time using
ever more sophisticated pendulum systems!
8. Using the information given in 6.a from theory, it is possible to use data from timing
the period of pendulums to estimate the value of g, acceleration due to gravity on the
surface of the Earth. Use your K value to determine an experimental value of g, and
find the percent difference between your value and the reference value in Daytona
Beach, Florida of 9.79265(±3)m/s2.1
Pendulums were the instrument of choice for making extremely detailed measurements
of Earth’s surface gravity until very recently in the history of science (1950s-70s).
Earth’s surface gravity can vary naturally by 0.5% even after taking into account
elevation changes! Precise measurements with a well-designed pendulum system can
accurately detect these tiny changes in gravitational acceleration.
9. After you have answered all questions and completed your experimental analysis, could
you have guessed the theoretical equation governing the period of a simple pendulum
from your lab work? Refer to this in your Results section of your Lab Summary.
For your information, the theoretically derived equation for a simple pendulum’s
period is:
𝐿
𝑇 ≅ 2𝜋√
𝑔
(3)
Hopefully this gives you an appreciation for how difficult and time consuming it can be to
verify theoretical predictions, or discover new relationships from experimental results.
1
Provided by the US National Geodetic Survey via their online Surface Gravity Prediction Tool.
– 5 of 7 –
Pendulum Tests
PS253 – Physics Lab for Engineers
Pendulums: Lab Summary Guidelines
What to Include in a Lab Summary
To know what specific content to report on, be sure to follow the instructions in the
Experiment Manual for this experiment. Pay particular attention to the Analysis
instructions and any questions you are asked to answer. Statements like “for your Lab
Summary…” or “in your Lab Summary…” or “Discuss ___” are things that should
definitely appear in your Lab Summary. Include any graphs, plots, and tables you were
told to make in the manual’s instructions.
Include all the data you took in your Lab Summary, in some form (graph, table, image,
etc.). Anything that was recorded in lab including single measurements and repeated
trials. Generally included in Results section or in an Appendix if it is lengthy.
1-column abstract, 2-column for everything else (except large graphs, figures, tables at
the top/bottom of a page)
Correct units and sig-figs on all numbers
Cite and reference anything taken from the lab module
Cite and reference any text, values, equation, figures taken from anywhere else
How to Structure your Lab Summary, Overall Rubric
Title Area & Abstract o
Title Area: Identifies Experiment Topic, Author, Lab Partners, Course-Section,
Instructor, Institution Affiliation, Date.
o
Abstract: Summarize the overall paper in 8 sentences or less. State
purpose/objective of your work or what research problem was investigated, the
overall design and process of your experiment, the major findings and results of your
analysis including primary numerical values, and conclusions from your study.
Statement of Purpose – In 4 sentences or less, define the goal or objective of the
experiment(s). Define scope of work.
Experimental Methods – In 300 words or less, briefly describe how the experiment(s)
was performed. Describe equipment and materials used to perform experiment.
Describes methods to operate equipment. Identifies critical procedural steps needed to
replicate experiment (setup, alignment, calibration, things to avoid, etc.). Defines
variables to be directly measured and how they were measured. State any assumptions
made related to materials. Does not repeat/copy lab manual instructions.
Results – The bulk of your Lab Summary. To include any Results, Analysis, or
Discussion mentioned in the Experiment Manual. Also include any graphs/plots and
data tables asked to produce.
o
Analysis of Data – Describe the data analysis and mathematical processes used to
manipulate your direct measurements into final results. State any assumptions made
related to math or physics theory. Examples: were multiple trials averaged together,
did you use Excel, Matlab, or Pasco Capstone for analysis, was any data removed or
excluded and why, only positive values make sense so negative values are ignored.
– 6 of 7 –
Pendulum Tests
PS253 – Physics Lab for Engineers
o
Graphical Analysis – Includes Plots/Graphs as asked for in Experiment Manual.
Displays data graphically in a clear and logical way. Formats data appropriately in
graphs. Formats plots so axes labels, values, units, data points, error bars are easily
readable. Gives additional context to graphed data through insightful labels and
captions. Demonstrates understanding of graphical analysis technique used (curve
fits, outlier data points, trendlines, etc.)
o
Summary of Experimental Results – Gives principle numerical results of
experiment, as well as their uncertainties. Compares numerical results to
expected/reference values and/or theoretical predictions by the process discussed in
the Experiment Manual (Discrepancy, % Difference, etc.). Interpret if results
support physics theory and expectations. Interprets if results are successful,
unsuccessful, or inconclusive with respect to Statement of Purpose.
Conclusions – Take away thoughts of the work you did. What likely impacted your
results, and what could be done to improve the work.
o
Discussion of Uncertainties – Identify at least 2 likely sources of uncertainty that
you believe affected your results in a non-trivial way. Be specific in the source, what
was affected, and how it was affected (+bias, -bias, or +-random, etc.). Discuss how
significant you think each source of uncertainty is (does one have a greater effect
than others, does one have a small effect, etc.). Review any assumptions made which
now seem invalid or possibly inappropriate.
o
Thoughts for Improvement – Thinking back on how you conducted the
experiment and analysis, would you perform it the same or would you do something
different? Is there other equipment you would want to try or use? Suggest at least 2
practical, non-trivial improvements you would make. Describe why you think this
would improve the experiment and better meet its objectives.
Attribution to Reference Sources – Clearly indicates what information (text, images,
values, formulas) is obtained from a reference. Citations within report body to reference
listings. Bibliography of References List given, formatted correctly. Examples of
references include Lab Manual, websites, textbooks, articles, blogs.
Data, Formatting, Other – Things not tied to any specific section or area of the Lab
Summary.
o
Data & Data Tables – Displays data in labelled tables clearly and logically. Formats
data with correct and uniform decimal precision, significant figures, units. Gives
context to data through appropriate use of labels, captions. Gives numerical
uncertainties for values.
o
Overall Formatting – General formatting guidelines are appropriately followed: title
area with single column abstract, 2-column report body, additional supporting
material contained in labeled Appendix. Text is readable. Figures/Tables
appropriately sized, positioned.
o
Optional Appendices – Any supporting information and documentation you wish
to include (or larger versions of graphs and figures) should appear at the end of your
Lab Summary in one or more labelled Appendix.
– 7 of 7 –
Forces of Friction
PS216, Section 3, Donald Schumacher, Department of Physical Sciences
Embry-Riddle Aeronautical University, Daytona Beach, Florida
(March 2015)
The contact of two surfaces causes frictional forces that act on the motion of the
experimented object. In this experiment, the differences between static and kinetic friction were
analyzed using three different methods for comparison. Throughout all of the trials, it was found
that the coefficient of static friction and the force of static friction were consistently higher than that
of the kinetic friction taking place. The first method was found to be the most accurate when
comparing static and kinetic friction. The final coefficients for each value based on plotting them
against the normal force and taking the slope of that linear relationship had a percent difference of
1.14%. Since the angle of the surface for the normal force was flat, these values theoretically would
have the slightest of difference. A 13.6% difference was calculated between the coefficients for
kinetic friction in Method 1 and Method 3. Since the hanging mass was added for the third method,
it would be expected for a larger kinetic friction, however that was not the case based on the overall
experiment.
I.
INTRODUCTION
to test in this experiment. It was discovered by those
scientists that friction is completely independent to the
The force of friction vector acts in the opposite
size of whatever surface is making contact. With that
direction of the motion of the object causing the friction.
being known, the coefficient of the friction is
Any time there is contact made between an object and a
independent of the mass of the object being moved.
surface, the process of gravity pushing downward on
the object causing a friction connection on the surface
where that object makes contact. The normal force is
what balances out the force made my gravity on the
object, therefore contact is never lost in between the
object and the surface. The friction is proportional to the
normal force of the surface plane, thus a linear
relationship between the friction and normal forces can
be plotted. Before Newton’s force laws came about,
Leonardo Da Vinci and later Guillaume Amontons had
worked on the theoretical laws for friction that are put
II.
THEORY AND METHODS
Friction is the resistance to motion along a
surface. The three methods used to examine how the
frictional forces act on a surface included; sliding
various masses at an attempted constant velocity,
increasing the angle of the surface in which the normal
force acted on, and applying the forces of a hanging
mass to have a constant acceleration and increasing
velocity on the mass that the friction was being
analyzed from. The Data Studio application on the lab
computer was wired to a force probe on the object in
contact with the surface as well as a motion sensor at the
opposing end from the object’s directional velocity. The
motion sensor charted the carts position and velocity
graphs over time, while the force probe took in data for
the force being applied (after calibrating the sensor, or
‘zeroing’ the force scale out) to the object at the same
time instances that the position and velocity along the
Figure 2: To increase the surface incline angle, lab group members
stacked up various textbooks and folders while closely watching for
the threshold of static friction to transform into kinetic friction. The
angle of incline was then taken for data calculations.
surface were being plotted. Prior to each trial for each
separate method, the force probe had to ‘tare’ itself to
again by the press of a button to calibrate it for a new
trial to be performed.
The final method was setup as Figure 3 shows,
with a constant hanging mass (0.20kg) pulling the object
(.947kg) along the surface. For data collection, Data
Studio plotted the linear velocity curve and the force vs.
The mass of the object in contact with the
time curve (showing kinetic friction). By taking the
surface was varied for the first method for each
slope of the velocity, constant acceleration could be
individual trial. A table was made using Microsoft Excel
found, and used to find the coefficient of kinetic friction
to collect orderly data including; total mass on the
with Equation 6 below. This would then be compared
object, the normal force (calculated using Equation 2
the value found using Method 1.
below), static friction (final point on force vs. time plot
𝜇𝑘 =
that involved a stationary position, and the kinetic
𝑚2 𝑔⃑−(𝑚1 +𝑚2 )𝑎⃑
𝑚1 𝑔⃑
(6)
friction (averaged for constant velocity time period)
with standard deviation for kinetic friction (calculated
by Data Studio).
𝐹𝑁 = 𝐹𝑔 𝑐𝑜𝑠𝜃
(2)
Figure 1: The first method looked at both static and kinetic friction
at a constant velocity pulling by a consistent lab member. This figure
shows the force configuration after the object began moving along
the surface.
Figure 3: Set up for the third method consisted of modifying the
Atwood system with two masses for the friction experiment. This one
was designed to look at kinetic friction and its coefficient.
III.
DISCUSSION OF RESULTS
Data for the second method (finding angle of
The first method of finding values for friction
surface incline before kinetic friction takes place) was
(both static and kinetic) left much room for human
compiled by making a table of the angle measurement
error, since it was up to a lab member to pull the object
taken after resetting to a flat surface for each trial (Table
along the surface at a constant velocity (seen in Figure
1 on next page). These measurements could find the
4).
coefficient of static friction (using Equation 4 below)
and its standard deviation.
𝑠𝑖𝑛𝜃
𝜇𝑠 = 𝑐𝑜𝑠𝜃 = 𝑡𝑎𝑛𝜃
(4)
Figure 6: The linear relationship between kinetic friction and normal
forces has a slope that determines that coefficient of kinetic friction.
The R^2 value is further off from 1 than expected in an experiment
since it was difficult reading the resulting DataStudio graphs.
The second method of looking at static friction
took the coefficient of static friction based on the
Figure 4: The above figure is from the first method’s second run. The
green plot represents a constant velocity over time (extremely
zoomed out of scale in meters). The same set of points were taken to
analyze frictional forces (blue plot).
measured angle of incline and compared it to the static
By plotting both the static and kinetic friction
assumed that in Method 1 it was very difficult to find
points against the normal force that was calculated, the
the exact point that static friction broke due to the Data
linear proportion can be viewed. Thus, the slopes of the
Studio graphs being difficult to read. This method of
line of fit reveal the coefficient of static and kinetic
finding the angle would be the more accurate method
friction (Figures 5 and 6). These coefficient values will
for finding the coefficient of static friction (the least
later be compared to those found using the second and
human error, more consistent systematic error). More
third methods of this experiment.
trials would not necessarily make the second method
friction values found by using the first method. There
was an extreme percent difference of the two values
found using both methods, and therefore it was
better than it is with the current results because the
angle uncertainty is so large considering the scale of the
angle being measured. More trials by use of the first
method would double the data points to plot and would
affect the slope of the line in seen in Figure 5, making it
more accurate. Both cannot be made much more precise
since there are significant sources of error involved.
Table 1: Measurements for angle of the surface for each trial were
taken to help determine at what instance the static friction reached
the threshold just before kinetic movement began on the object.
Figure 5: Static friction and the normal force from the surface show
a linear relationship with the slope of the line of best fit to be the
coefficient of static friction. This experimentally came out to be
slightly greater than that of kinetic friction.
Run
Angle (degrees)
1
10
2
9.9
3
4
10
9.8
5
10
For looking at the kinetic friction force, the third
second method that involved finding the angle at which
method has less room for human error. Therefore, this
static friction was at the threshold of becoming kinetic
is the method for most accuracy. In Figure 7, a standard
friction was difficult to get varied results. The angle
deviation of 0.02 of the continuous friction force was
uncertainty (0.1 degree) based on the measurement
taken from a certain time period of data across the
device was too large to detect much difference in the
position, velocity, and force plots from Data Studio. The
frictional changes over the five trials taken. Also,
coefficient of kinetic friction would have a greater value
‘eyeballing’ the object for the exact point in which
in the third method rather than the first, since the inertia
kinetic friction was applied and static friction ceased to
is greater (due to the added hanging mass), and
exist was not the most accurate way this method could
acceleration is constant in the opposite direction of the
have been done.
kinetic friction force. Experimentally, this proved to be
true as well. The coefficient of kinetic friction was .227
for the first method (smaller inertia), whereas it was .198
for the third method. The difference of the kinetic
friction coefficients is calculated to be 13.36%. Based on
IV.
standard deviation (used for Method 1) and error
1.
REFERENCES
Schumacher, Donald, Prof. “Force of Friction”
propagation (used for Method 3), the third method also
Physics Lab Packet. ERAU, Daytona
proves to be the most precise method to use when
Beach, FL. 10 March. 2015. Reading.
performing kinetic friction experiments.
2.
Physics Lab #8. 10 March.
2015. Raw Data. ERAU, Daytona
Beach, FL.
3.
“History.” Friction: History. Davidson
University, n.d. Web. 20 Mar. 2015.
4.
N. “Static and Dynamic Friction.” Lab 4: Static
and Dynamic Friction (n.d.): 1-3.
Physics Dept. Clark University. Web.
20 Mar. 2015.
5.
F. PHY 251 Lab 5 – Friction (n.d.):
Mississippi College. Web. 20 Mar.
2015. .
Figure 7: These graphs show the position (red) of the frictional object,
the velocity of the object that increases (green), and the kinetic
friction force plot (blue) over the same time period.
Sources of error came about in the three
different methods that were attempted to be avoided as
much as possible. When doing the first experiment, a
lab group member considered it difficult to pull the
massed object with a constant velocity along the surface.
Therefore, to avoid this harming the data being
collected, a best fit of the data points was taken from the
velocity curve, and those same instances were then
taken from the force plot over the same time period. The
V.
CALCULATIONS
Method 1: Static & Kinetic Friction
𝐹𝑓𝑟𝑖𝑐 = 𝐹𝑠,𝑘 = 𝜇𝑠,𝑘 𝐹𝑁
(1)
𝐹𝑁 = 𝐹𝑔 𝑐𝑜𝑠𝜃
(2)
𝜃 = 0° (𝑓𝑙𝑎𝑡 𝑠𝑢𝑟𝑓𝑎𝑐𝑒)
(3)
Method 2: Static Friction
𝑠𝑖𝑛𝜃
𝜇𝑠 = 𝑐𝑜𝑠𝜃 = 𝑡𝑎𝑛𝜃
(4)
Method 3: Kinetic Friction
𝜇𝑘 𝑔 = 𝑎
𝜇𝑘 =
(5)
𝑚2 𝑔⃑−(𝑚1 +𝑚2 )𝑎⃑
𝑚1 𝑔⃑
(6)
Error Propagation for Kinetic Friction
2
𝛿𝜇𝑘
2
𝜕𝜇𝑘
𝜕𝜇𝑘
𝜕𝜇𝑘
(𝛿 ))
= √(
(𝛿𝑚1 )) + (
(𝛿𝑚2 )) + (
𝜕𝑚1
𝜕𝑚2
𝜕𝑎 𝑎
𝛿𝜇𝑘 = .00347
2
VI.
PLOT DATA
Table 2:
Method 1 involved using a lab member to pull the massed object along the flat surface at a constant velocity.
Method 1: Sliding Friction Equalities
Run #
Total Mass (kg)
Angle (degrees)
Normal Force (N)
Static Friction (N)
Kinetic Friction (N)
σ(Fk)
1
2
3
4
5
6
7
Avg
0.9466 1.444 1.1953 1.0463 1.295 1.0958 1.6927 N/A
0
0
0
0
0
0
0
0
9.26721 14.1368 11.702 10.2433 12.6781 10.7279 16.5715 12.19
2.02
1.73
0.08
2.7
2.31
0.13
2.42
2.23
0.17
1.91
1.71
0.13
2.49
2.32
0.13
1.91
1.65
0.15
3.61
3.39
0.14
2.437
2.191
0.133
Table 3:
Method 2 found the threshold for the static friction just before it escalated into kinetic friction force based on the incline angle.
Method 2: Angle of Friction
Run #
1
2
3
4
5
Avg
Total Mass (kg)
Angle (degrees)
0.9466
10
0.9466
9.9
0.9466
10
0.9466
9.8
0.9466
10
N/A
9.94
ms
0.64836 0.51455 0.64836 0.39388 0.64836
0.5707
σ(Fs )
0.10248
Table 4:
The third method found the coefficient of kinetic friction by applying a hanging mass to the other end of pulley system.
Method 3: Modified Atwood with Friction
Run #
1
2
Total Mass 1 (kg)
0.947 0.947
Hanging Mass 2 (kg) 0.2
0.2
Acceleration (m/s2)
mk
0.116
0.12
0.197 0.196
3
4
5
6
7
Avg
0.947 0.947
0.2
0.2
0.947
0.2
0.947
0.2
0.947
0.2
N/A
N/A
0.101
0.092
0.098
0.109 0.105
0.199
0.199
0.197 0.198
0.1
0.198 0.198
1. Specific Instruction on how to complete the Lab
Summaries are at the end of the Lab Manual and in
the Rubric for the assignment
2. Abstract: Summary of the report, and most
importantly a summary of your results ( in this case
the average velocities and uncertainties, present
this for example in the form of 4.03 +- 0.02 m/s),
and if you were successful or not. It is not a
methods section.
3. Experimental Methods: Talk about physically how
you did the lab with setup and execution and with
what materials/
measuring devices
4. Results: Talk about how you went from measured
values to calculated results, assumptions made in
physics, and present results neatly through
tables/graphs, and talk about them.
5. Conclusions: Don’t just present possible source of
uncertainty, but think about if it would be random
or systematic. If it’s systematic, would it over or
under estimate calculated results for velocity?
6. Lastly, having a reference section is great but
please use the reference somewhere. This would
probably be useful for the methods section at least
1. Specific Instruction on how to complete the Lab
Summaries are at the end of the Lab Manual and in
the Rubric for the assignment
2. Abstract: Summary of the report, and most
importantly a summary of your results ( in this case
the average velocities and uncertainties, present
this for example in the form of 4.03 +- 0.02 m/s),
and if you were successful or not. It is not a
methods section.
3. Experimental Methods: Talk about physically how
you did the lab with setup and execution and with
what materials/
measuring devices
4. Results: Talk about how you went from measured
values to calculated results, assumptions made in
physics, and present results neatly through
tables/graphs, and talk about them.
5. Conclusions: Don’t just present possible source of
uncertainty, but think about if it would be random
or systematic. If it’s systematic, would it over or
under estimate calculated results for velocity?
6. Lastly, having a reference section is great but
please use the reference somewhere. This would
probably be useful for the methods section at least
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