LABORATORY
COURSE
PHYSICS 211
OBJECTIVES
 To test the validity of the fundamental ideas
(presented in PHY211) via quantitative or
qualitative experiments
 To master the error analysis and
statistical processing of experimental data
 To learn how to present scientific results in a
consistent, reasonable and clear manner
INSTRUCTOR
J. D. Roaden
j.d.roaden@uky.edu
Office:
CP 252
A Little About You
 Take out a sheet of paper and include the following:
 Name:
 Preferred Name:
 ID Number:
 Email:
 Year:
 Major:
 Where Are You From:
 Calculator Type:
 Lab Partners:
Required Materials
 RF Transmitter
 Lab Manual
 Graphing Calculator



TI – 84 series
TI – 83 series
TI – 84 Plus Silver is recommended
DOCUMENTATION
 Syllabus
www.pa.uky.edu/~ellis
 Lab Manual
www.johnnyprint.com
 Appendices
www.pa.uky.edu/~ellis
•Appendix A - CBR
•Appendix B - CBR Accuracy
• Description
Schedule
ofof
experiments
experiment
•Appendix
C - Error
Analysis
• Questions
Research
team
to be roles
answered
•Appendix
D - Measuring
Tools
• in
Lab
labreport
report
format
•Appendix
E - DataMate
•Appendix
-policy
Methodology
for
• Prelab
GradingFquestion
(if any)
Calculating Local g
•Appendix G - Standard Cover
Sheet
•Appendix H - Datagate
•Appendix I - Quick Start For
Vernier Photogate
Computers
 Username:
 Password:
phy211
4izrm165
 Programs:
 MS Office Suite
 Fundamental Science Skills
 Google Earth
 TI Connect
Who’s on First?
 Research Team Roles:
i. Principle Investigator
(1)Responsible for everything the Team does or
fails to do.
(2)Coordinates Team activities in Lab and during
the out of lab report completion process.
(3)Ensures that all team members contribute fairly.
(4)The PI develops and writes the “Results and
Conclusions” paragraph of the lab report
(5)Responsible for the integration of the report in
both style and content.
Who’s Second?
ii. Researcher
(1) Focuses on the in-class execution of the
experiment.
(2) Team’s expert on the systems used and
methods of data collection and recording.
(3) Develops and writes the “ Introduction” and
“Data and Calculations” paragraphs and the
raw data appendix.
Who’s on Third?
iii. Skeptic
(1)
Analyzes uncertainties associated with
measurements and procedures
(2)
Propagates uncertainties through the experiment
and correlates the relative contribution of each to
the uncertainty in the results.
(3)
Develops the “Analysis and Discussion”
paragraph and ensures consistency of thought and
flow of the key ideas into the “Results and
Conclusions” paragraph
GRADING POLICY
Section
Score
1. Introduction
10
2. Data and Calculation
20
3. Analysis and Discussion
4. Results and Conclusions
Lab report, Overall
30
40
100
Roles
Quiz &
PI
Pers
Prelab
10
40
10
Skeptic
40
Researcher
Principle
10 10 60
Investigator
GRADING POLICY
lab report grade  personal efforts 
final grade 


2
 Team report earned 10+19+30+35=94
 PI’s paragraph scored in 35
 PI’s quiz and prelab scored in 5
 PI points 8 out of 10
 Calculate percentage [(35+5+8)/60]*100=80
 Then PI’s total score (94+80)/2 =
87
Error Analysis
 Uncertainties
 Propagation of Uncertainties
 Standard Deviation
 Percent Error and Percent Difference
Uncertainty
 How certain you are about a given
measurement
 Cannot be smaller than half the smallest
division of the measuring device
 All results must be in the form x ± Dx, where
Dx is the uncertainty
Propagation of Uncertainties
 Rules can be found in Appendix C.
 Rule 1:
When adding or subtracting two
experimental values, the uncertainty
of this sum or difference is the sum of
the uncertainties of the two
experimental values.
Propagation of Uncertainties (cont.)
Calculate T = tf – ti
ti = 1.23 s ± 0.005 s
tf = 2.34 s ± 0.008 s.
 T = 2.34 s – 1.23 s = 1.11 s
 DT = 0.008 s + 0.005 s = 0.013 s
 Therefore, T = 1.11 s ± 0.013 s
Propagation of Uncertainties (cont.)
 Rule 2:
When multiplying or dividing two
experimental values, the relative
uncertainty of the product or quotient is
equal to the sum of the relative
uncertainties of the experimental
being multiplied and/or
values
divided.
 Relative Uncertainty is defined below
Uncertaint y of x Dx
Relative Uncertain ty of x 

Value of x
x
Propagation of Uncertainties (cont.)
Calculate F, where F=ma.
m = 0.531 kg ± 0.0005 kg
a = 9.79 m/s2 ± 0.005 m/s2
Rel. Unc.of F  Rel. Unc.of m  Rel. Unc.of a 
DF Dm Da



F
m
a
Propagation of Uncertainties (cont.)
DF Dm Da



F
m
a
m 

0.005
 0.0005kg  
s2 
 
 
m 

0.531
kg
9.79

 
s2 
 9.416210 4  5.107310 4
3
 1.452310
 0.0014523
Propagation of Uncertainties (cont.)
F = ma = (0.531 kg) x (9.79 m/s2) = 5.1985 N
Unc. of F = (Rel. Unc. of F) x F
DF = (DF/F) x F
= (0.0014523) x (5.1985 N)
= 0.0076 N
Therefore, F = 5.199 N ± 0.008 N
Standard Deviation
 For experiments with many measurements of the
same quantity we can obtain the error using the
statistical method known as standard deviation.
 In this lab there must be at least 10 data points
in order to use a standard deviation.
Dx 
1 N
2
( xi   x  )

N  1 i 1
Percent Error and Percent Difference
Percent Difference is to be used to compare two
experimental values
%d
2( x1  x 2 )

 100%
( x1  x 2 )
Percent Error is to be used to compare an experimental
value with a known value.
%e
( x a  xe )

 100%
xa
Lab Reports
 Introduction
 Data and Calculations
 Analysis and Discussion
 Results and Conclusions
 Draft
Introduction
 What did your group do?


Specifically who did what
Do not just repeat what is in manual
 Include a table of equipment used with UK
Inventory numbers.
 Include details of post lab meetings
 References including lab manual and
textbook if they were used
Data and Calculations
 Data is to be word processed and flow well
within the report
 Sample of each type of calculation should be
included using Equation Editor
 All calculated results are included
Discussion and Analysis
 Graphs (If applicable)
 Calculations of Error Propagation
 With explanation of why particular method was
used
 %e and %d with sample calculation (if
applicable)
 All errors must be discussed and labeled as
systematic or random and ranked from most
relevant to the experiment to the least
relevant
Graphs
 Include title and properly labeled axes

Should be a stand alone item.
 Plot data with xy scatter
 Include error bars
 If a trend line (best fit line) is used, include
slope equation and correlation value (R2)
Velocity of Fan Cart versus Time
12
Velocity (m/s)
10
y = 2.14x - 0.72
R2 = 0.9908
8
6
4
2
0
0
1
2
3
Time (s)
4
5
6
Results and Conclusions
 Include objectives of the experiment
 Answers to the Questions
 Present results in the proper form (x ± Dx)
 Compare results to accepted value or other
experimental values on a number line
 Draw conclusions from the number line

Comment on whether results are significantly
different, accuracy, precision, how and which
errors present effected your results.
 Were the objectives accomplished?
Draft
 Turned in 24 hours before the lab meeting
following the experiment
 Worth 20 points
 Must be word processed
 Include:




All tables, graphs, number lines, and figures
All calculations
Discussion of error
Basic outline for final lab report.
Draft (cont.)
 Must have signed raw data attached
 Must be attached as appendix to final lab
report
 Must be a nearly complete report.
 Is a guide, all mistakes cannot be caught
Number Line
Acceleration Due To Gravity
9.6 m/s2
9.7
9.8
9.9
10.0
Geographical Value
9.79 m/s2 ± 0.02 m/s2
Expt. Value using 13mm ball
9.85 m/s2 ± 0.05 m/s2
Expt. Value using 16mm ball
9.68 m/s2 ± 0.05 m/s2
Safety
 No food or drinks are permitted in lab.
 Clothing and Backpacks should be stored
under the benches.
 Emergency 911 cell phone and First Aid
Kit
 Gas Shut off valve
 Eye wash and shower unit
Assignment for next class
1. Split into groups
2. Read the description of “Free fall”
experiment (Lab manual)
3. Complete Pre lab for “Free fall”
4. Read Appendix C, Error Analysis
5. Register your clicker online.
Instructor
J. D. Roaden
Office Hours:
j.d.roaden@uky.edu
Tuesday, Thursday, & Friday
at 10 AM. (Potentially)
Office:
By appointment
CP 252