Experimental Methods and Physics Skills
/Astrophysical Skills and Techniques
Physics and Astrophysics Laboratory
Tutors:
Dr.A.Mahendrasingam (Singam)
a.mahendrasingam@keele.ac.uk
Dr.D.McLaughlin
d.e.mclaughlin@keele.ac.uk
Physics/Astrophysics Laboratory
Lecture Course
 Provide an education in the knowledge
required to become a Physicist/Astrophysicist
Laboratory Skills
 Educating students in some of the skills
required to be a Physicist/Astrophysicist
Physics/Astrophysics Laboratory
Module Structure: Two strands

Practical abilities to perform experiments
and the intellectual ability to analyse and
access the results of experiments (strand 1)

Basic computational skills (strand 2)
Physics/Astrophysics Laboratory
The experimental Methods Strand

Expected to perform 8 laboratory experiments
during the two semesters ( 5 in semester one, 3
in semester 2)

Your laboratory diary will be marked at the end
of each laboratory session. From this mark you
will receive a final mark for each completed
experiments

Each of these 8 experiments should take you 2
weeks ( 2 x 3 hour laboratory sessions)
Physics/Astrophysics Laboratory
The Computing Strand
Spreadsheets
 Programming

Physics/Astrophysics Laboratory
Assessment
Semester one
 Strand 1 ( 90 marks)
 Strand 2 ( 10 marks)
Semester two
 Strand 1 ( 90 marks)
 Strand 2 ( 10 marks)
Physics/Astrophysics Laboratory
Semester one
Experimental Strand
Bench work
(Lab diary for 5 completed experiments)
Mark
30
Report 1
Report 2
30
30
Computing Strand
Spreadsheet exercises associated with any two
Experiments
10
Total
100
Physics/Astrophysics Laboratory
Requirement to pass the Laboratory
 40 marks out of 100 available ( i.e. 40%)

Submit 4 (2 reports/semester) satisfactory
laboratory reports for strand 1

Laboratory contributes 20% to each lecture
modules.
Physics/Astrophysics Laboratory
Semester 1 Laboratory – Contribution to the
Lecture Modules
PHY-10022
20%
PHY-10024
20%
Semester 2 Laboratory – Contribution to the
Lecture Modules
PHY-10020
20%
PHY-10021/23
20%
Laboratory Class (Thursday 14:00 – 17:00)
Introduction to Laboratory Class – Friday (4/10/13) 10:00 – 11:00 in LJ 1.75
First lab session (Lecture on error and Data Analysis) – Thursday
(10/10/13) 14:00 – 15:00 in CBA 0.061
First lab session (Worksheet on error and Data Analysis) – Thursday
(10/10/13) 15:00 – 17:00 in LJ0.26 (Faculty Computing Lab)
Experiment
on (B) simple
Harmonic
Motion / Data
Analysis
and
Processing
10/10/13 – 24/10/13
Week 1
Week 2
Week 3
Week 4
Experiments A and C - M
Week 5
Maths test
2-3pm
Maths test
2-3pm
Lab
3-5pm
Lab
3-5pm
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Report #1
Deadline 4.00 PM 22/11/13
Week 12
Physics/Astrophysics Laboratory

Hardback notebook ( You should be able to buy the
notebook from the Stores (LJ0.36 or Phil )

Your copy of the Lab. Manual

Additional information about the laboratory can be found in
the module pages for PHY-10022/PHY-10024 on VLE
(http://students.keele.ac.uk)
Laboratory Notebook – Section
Front of your notebook should contain:
Name:
Address: School of Physical and Geographical Sciences

Each new experiment should start on a new page

Title of the experiment should be recorded at the start of the each new
experiment.

Date should be recorded at the beginning of each laboratory session

Results should be recorded with a short sentence which is sufficiently
explanatory that you or someone else can understand it

Record all your data/measurements as you take them
Laboratory Notebook
Always record the units of your measurements along with the
measurements themselves
If your data is taken for a certain period of time or a certain
number of oscillations etc. then always record this fact along
with the measurements themselves.
If you plot or fit your data using one of the computer
programs, make a printout of the program output (usually a
graph) and attach (glue, sellotape, staple) it into your
notebook.
If you use the spreadsheet to analyse the data, make a
printout of the spreadsheet and attach (glue, sellotape, staple)
it into your notebook.
Laboratory Notebook
If you decide that a set of measurements is incorrect for some reason
don’t obliterate it in your notebook. Instead simply draw one diagonal line
through it and make a note why you have discarded it. If at a later date you
change your mind (or if a staff supervisor or post-graduate demonstrator
persuades you to change your mind) you won’t have to re-take the data
again. As long as it can still be read it can be used.
Make a note of the pieces of apparatus that you are using in your
experiment, e.g. radioactive source B, A.C. circuit box G, a Farnell
oscilloscope serial number F831GBX etc. If for some reason a piece of your
apparatus is removed (it shouldn’t be but !) then we can recover it if we
know the number and you can continue your experiment without having to
start again.
At the end of your experiment you should summarise your results,
tabulating clearly the values you have obtained for any derived quantities
(and their error bars) with suitable notes explaining what each is.
Further details can be found in section 2.1 of the laboratory manual.
PC Lab (LJ1.27)
 You should able to logon to the computers in the PC Lab using your
university computer userid and password.
Also make sure that you save all your work on your network drive (S:).
The networked laser printer in the PC Lab can be used to print your work
in the laboratory. Initially you will be given a free 50 pages print quota.
Additional print quota can be purchased from Phil.
 A key is required to gain access to PC lab. You can obtain a key from Phil
by paying a refundable deposit.
You can also use the PCs in the PC Lab in
LJ0.026 (Faculty Computing Lab) using Keele
Card.
SAFETYBRIEFING FOR
PHYSICS/ASTROPHYSICS
STUDENTS
Safety
General safety policy
Emergency procedures
Dos and Don'ts
General Safety Policy
The School of Physical and Geographical Sciences must
Provide safe experiments in a safe environment
Establish emergency procedures
Provide safety information and guidance
It is your responsibility to
Take reasonable care for your own health and safety
Take reasonable care for others’ health and safety by complying
with the safety rules in the Lennard-Jones Laboratories
Emergency Procedures – FIRE ALARM
THE FIRE ALARM IS A CONTINUOUSLY SOUNDING SIREN
The entire building MUST be evacuated if the siren sounds
Leave either through the foyer or go right along the corridor and leave through
the rear building
DO NOT PANIC
DO NOT TAKE ANY PERSONAL RISKS
DO NOT USE THE SERVICE LIFT if the fire alarm sounds
Assemble on the grassed area outside the front entrance of the LennardJones Laboratories
re-entry to the building will not be allowed until Senior Fire Brigade Officer gives
permission to do so
YOU MUST NOT DO THESE
Smoke or drink in the laboratory
Drink the water from taps in the Laboratory – There
are Drinking Water taps in the toilets
Bring visitors into the laboratories AT ANY TIME
Put bags or coats on the tables
Remove the covers of any equipment or plugs, or use
equipment with broken or damaged mains leads
Work in the laboratory without supervision by staff
YOU MUST DO THESE
Store your bag/coats under the bench
Report any suspected faults in
equipment to the laboratory staff
Error Bars and the Scientific Process
(Lab Manual Section 2.2)
Aim of Science?
Advancement of knowledge, understanding nature,
etc….
How is this achieved?
Building theories/models and testing them by
experimental measurements.
Explaining the results of experiments by theoretical
models.
Comparing with theory/other experiments is clearly vital
to the scientific process – but how to do this objectively?
Error Bars and the Scientific Process
An error bar DX signifies our “confidence” in a value
that we measure
X± DX
“true” X lies within X- DX to X + DX ~66%
“true” X lies within X- 2DX to X + 2DX ~95%
“true” X lies within X- 3DX to X + 3DX ~99%
Error Bars and the Scientific Process
Error Bars and the Scientific Process
Comparing two values
Experiment and theory (X± DX) and (Y)
Experiment and Experiment (X± DX) and (Y± DY)
Does the value of X lie within the range of (Y± DY)
or
Does the value of Y lie within the range of (X± DX)
If YES then X agrees with Y within the limits of error or vice
versa
Error Bars and the Scientific Process
Examples
1. The SHM experiment – asked to compare the value of
spring constant k measured from Hooke’s law with value
measured from oscillations (SHM)
2. b-particle experiment – asked to compare measured value
of E (determined from R via Feathers equation) with
theoretical value of 2.26MeV
Systematic and Random Errors
Broad classification of errors into one of two classes
systematic and random
 Systematic errors are the same every time you make
a measurement.
 Random errors “fluctuate” every time you make a
measurement
Systematic Errors

Zero offset errors in equipment

Limits of measuring scales (e.g. Graduation on ruler/clock in SHM
experiment)

How to deal with systematic errors?

Careful calibration, re-calibration of equipment.

Use another piece of equipment to double check.

Reduce scale graduation errors by measuring a larger value. e.g.
In SHM experiment measure 10 oscillations instead of one, scale
limit on clock is 1 sec whether measure 1 oscillation or 10.

Use the graduation as error bar (sets limit to knowledge) or
estimate of offset value (whichever is bigger).
Random Errors
The measured values fluctuate about a true value due to
some random process, e.g.
 In b-particle experiment the count rate varies due to
nuclear fluctuations.
 In electrical circuit “noise” can lead to fluctuations in
measured voltages.
 In SHM experiment starting/stopping clock could be
different each time you measure 10 oscillations.
The effect of random errors can be treated statistically.
Random Errors
Measure N values x1, x2, x3,.....,xN
• Mean value

1
x
N
N
x
i 1
i
• Standard deviation for the fluctuations

1
2

( xi  x )

N  1 i 1
N

• The error in the mean
Dx 

N
Combining and Propagating Error Bars
 We have measured a quantity in an experiment, and
worked out its error bar ( call this raw data)
 Now we wish to process the value, i.e. use it in a formula.
 Since the raw value has an error bar, so must the
“outcome” from the formula.
 Example, in SHM experiment you measure T, the periodic
time and can get an error bar but what you need are
values of T2, what is the error in T2
 Even worse!!, in the b-particle experiment you measure
the count rate for thickness of Al, get an error bar in each
value and then you need the logarithm of the count rate.
What is the error in the logarithm???
The propagation of Errors Through Functions
( X  DX ) 2  ( X ) 2  2 X DX
( X  DX ) n  ( X ) n  n X n 1 DX
sin( X  DX )  sin( X )  DX cos( X )
cos( X  DX )  cos( X )  DX sin( X )
DX
log e ( X  DX )  log e ( X ) 
X
log e (10)
log10 ( X  DX )  log10 ( X )  DX
X
exp( X  DX )  exp( X )  DX exp( X )
10 ( X  DX )  10 X  DX log e (10)10 X
Combing Errors
Z  X Y
Z  X Y
 DX 
 DY 
DZ 
 DX   DY 
2
2
2
2
2
2
2
DZ
 DX   DY 
    
 X  Y 
Z
Z  X Y
DZ
 DX   DY 
    
 X   Y 
Z
Z  X Y
XY
Z 
UV
DZ 
2
DZ
=
Z
2
2
2
 DX 
 DY 
 DU 
 DV 
  +   + 
 +  
 X 
 Y 
 U 
V 
2
Example
A  r
2
DA   2rDr
DA 2Dr

A
r
DA  2rDr

2
A
r
Fractional error in A = 2 x Fractional error in r
or
% error in A = 2 x % error in r
In general
A  r
n
D A n Dr

A
r
Fractional error in A = n x Fractional error in r
or
% error in A = n x % error in r
Example
A  r
2
r  10.0  0.1m
What is the value for A?
A= x 10 x 10 = 314.16m2
Fractional error in r =0.1/10
Fractional error in A =2x0.1/10 =0.02
i.e. DA/A = 0.02
DA  A x 0.02 = 314.16 x 0.02 =6.28m2
A  314  6m
2
Error Bars and Slopes/Intercepts From Graphs
 Plot a graph of raw data points, each one has an error bar.
 Want to fit a straight line, get slope, use slope in formula.
 Since the data points have error bar so the slope of the
straight line will also have an error bar.
 “Theory” is called least squares data analysis.
 DON’T PANIC, leave the theory later.
 Computer program on PC’s in lab to fit straight lines and
work out error bars. (LineFit / Excel / KyPlot / DataStudio)
 Templates for Excel or Kyplot is available on the web in
the Physics/Astrophysics Laboratory web page.