Transcript here
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
[email protected]
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
9.416210 4 5.107310 4
3
1.452310
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:
[email protected]
Tuesday, Thursday, & Friday
at 10 AM. (Potentially)
Office:
By appointment
CP 252