Transcript From Theory to Experiment

Quiz 1
• What is the purpose of a results table?
• What are some of the things you should include in a graph?
• What are some good factors to apply to axes scales?
From Theory to Experiment
Lab 1, Year 2, Term 1, 2015
Mr. Joseph Rendall
Term 1 Practical Lectures
• Prepare yourself to develop an experiment based on a theme to be
presented to you at a latter point
Topics to work-on this year continued from
handout
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Vote on:
Using instruments
Simple harmonic motion
Fluid Flow
Refraction
Magnetism
Electromagnetic induction
Atomic structure
Semi-conductors
Transistors
Cathode ray oscilloscope
Why does theory appear to be different than
what I find in a practical?
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Errors that arise from the practical
Changing physical conditions (environment)
Instruments used may me defaulting or used incorrectly
Lack of theory
Carelessness of person performing practical
Fear and poor background and lack of help from the lecturer
Misinterpretations of the instructions
Poor time management
Lack of practice
Wrong manipulation of data in table
Unidentified changes in small values
Inaccuracy of the instruments used
Instructions are not enough
Teacher responses
• Poor design
• Not careful when carrying out experiment (illegitimate errors)
• Theory is linked incorrectly (e.g. V = I/R)
• Measurement error is too large
• Sample size is too small
• Plotting errors
• Curve fitting errors (apply wrong curve fit)
• Equations appear to be abstract
Review of some practical topics
Where does uncertainty come from?
• The measuring instrument
• The item being measured
• The measurement process
• ‘Imported’ uncertainties
• Operator skill
• Sampling issues
• The environment
Measurement Good Practice Guide No. 11 (Issue 2)
A Beginner’s Guide to Uncertainty of Measurement
Stephanie Bell Centre for Basic, Thermal and Length Metrology National Physical Laboratory
Examples of Measurement Uncertainty
http://serc.carleton.edu/sp/library/uncertainty/examples/48909.html
Reducing Measurement Uncertainty
• Calibrate your equipment to a known standard (i.e. length,
concentration, resistance, ect.)
How to take good measurements
• Typical procedure for taking measurements
• Figure out how the device works
• Read the manual
• Cautiously “Tinker” with the device
• Calibrate the device to insure accurate readings
• Take note of any offsets
• Use the device to measure your system or object multiple times
• If there is an offset correct your readings to true values
• Determine the measurements uncertainty, for example:
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½ the smallest gradient discernable
½ of the decimal place past the digital read-out
The increment in which the digital read-out is fluctuating
Manufactures listed uncertainty
• Average your readings
• Record your uncertainty with units on measurements and average
Errors
• A systematic error (an estimate of which is known as a measurement
bias) is associated with the fact that a measured value contains an
offset. In general, a systematic error, regarded as a quantity, is a
component of error that remains constant or depends in a specific
manner on some other quantity. (Can be fixed by math)
• A random error is associated with the fact that when a measurement
is repeated it will generally provide a measured value that is different
from the previous value. It is random in that the next measured value
cannot be predicted exactly from previous such values. (Will be
significantly reduced by taking averages)
Relative Error
http://mathworld.wolfram.com/RelativeError.html
If the Actual Value (Xo) is unknown then take the error in your result as a percentage of your
results
𝑚
𝑔 = 9.9 ∓ 0.3 2
𝑠
0.3
𝛿𝑥 =
× 100 = 3 %
9.9
Indirect measurement
• Usually an electrical voltage or amperage output
• Measuring change of temperature to determine specific heat
• Measuring mass of water to determine volume
• Uncertainty in measurement is not the same as uncertainty in the
result.
Error Propagation
𝐴 = 𝜋𝑟 2
D = 0.2 ± 0.05 m
𝐴𝑚
22
0.2
=
×
7
2
2
= 0.0314 𝑚2
22
0.2 + 0.05 2
𝐴𝑚𝑎𝑥 =
×
= 0.0491
7
2
𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 0.0491 − 0.0314 = 0.0177
𝐴 = 0.0314 ∓ 0.018 𝑚2
Sensitivity coefficients
• 𝑥 = 2𝑦 + 𝑧 2
• 𝑎2 + 𝑏2 = 𝑐 2
• 𝐴 = 𝜋𝑟 2
Converting scales
Class Examples
• If you have collected data for resistance and voltage how would you
plot to determine current?
• If you have time and distance data, how would you plot to determine
speed?
• If you have diameter and height data how do you plot to find the
volume of a cylinder?
• If you have velocity and mas how do you find kinetic energy from the
slope?
Theory to data required
• Coulombs’ law
•𝐹=
1 𝑞1 𝑞2
4𝜋𝐸0 𝑟 2
• Fourier’s law
• 𝑄 = −𝑘
∆𝑇
∆𝑥
𝑒
How to design an experiment (questions to
ask yourself)
• What data can be collected? What instruments? What data cannot
easily be collected?
• What laws or law relate the data to the unknown (unmeasurable)?
• What is the expected result?
• What will be plotted?
• What procedures will need to be followed?
In groups of 5 (ask for help if needed)
• Pick a law
• Determine the data to be collected
• List the required materials/instruments for the experiment
• Determine what variables to plot