1. 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?

2. From Theory to Experiment
Lab 1, Year 2, Term 1, 2015
Mr. Joseph Rendall

3. Term 1 Practical Lectures
Prepare yourself to develop an experiment based on a theme to be presented to you at a latter point

4. Topics to work-on this year continued from handout
Vote on:
Using instruments
Simple harmonic motion
Fluid Flow
Refraction
Magnetism
Electromagnetic induction
Atomic structure
Semi-conductors
Transistors
Cathode ray oscilloscope

5. Why does theory appear to be different than what I find in a practical?
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

6. 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

7. Review of some practical topics

8. Where does uncertainty come from?
The measuring instrument
The item being measured
The measurement process
‘Imported’ uncertainties
Operator skill
Sampling issues
The environment
instruments can suffer from errors including bias, changes due to ageing, wear, or other kinds of drift, poor readability, noise (for electrical instruments) and many other problems.
which may not be stable. (Imagine trying to measure the size of an ice cube in a warm room.)
the measurement itself may be difficult to make. For example measuring the weight of small but lively animals presents particular difficulties in getting the subjects to co-operate.
calibration of your instrument has an uncertainty which is then built into the uncertainty of the measurements you make. (But remember that the uncertainty due to not calibrating would be much worse.)
some measurements depend on the skill and judgment of the operator. One person may be better than another at the delicate work of setting up a measurement, or at reading fine detail by eye. The use of an instrument such as a stopwatch depends on the reaction time of the operator. (But gross mistakes are a different matter and are not to be accounted for as uncertainties.)
the measurements you make must be properly representative of the process you are trying to assess. If you want to know the temperature at the work-bench, don’t measure it with a thermometer placed on the wall near an air conditioning outlet. If you are choosing samples from a production line for measurement, don’t always take the first ten made on a Monday morning.
temperature, air pressure, humidity and many other conditions can affect the measuring instrument or the item being measured.
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

9. Examples of Measurement Uncertainty

10. Reducing Measurement Uncertainty
Calibrate your equipment to a known standard (i.e. length, concentration, resistance, ect.)

11. 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:
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

12. 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)

13. Relative Error
If the Actual Value (Xo) is unknown then take the error in your result as a percentage of your results
𝑔=9.9 ∓0.3 𝑚 𝑠 2
𝛿𝑥= ×100=3 %

14. 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.

15. Error Propagation
𝐴=𝜋 𝑟 2 D = 0.2 ± 0.05 m 𝐴 𝑚 = 22 7 × = 𝑚 2 𝐴 𝑚𝑎𝑥 = 22 7 × = 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦= −0.0314= 𝐴= ∓0.018 𝑚 2
0.018 different than 0.05

16. Sensitivity coefficients
𝑥=2𝑦+ 𝑧 2
𝑎 2 + 𝑏 2 = 𝑐 2
𝐴=𝜋 𝑟 2

17. Converting scales

18. 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?

19. Theory to data required
Coulombs’ law
𝐹= 1 4𝜋 𝐸 0 𝑞 1 𝑞 2 𝑟 2 𝑒
Fourier’s law
𝑄=−𝑘 ∆𝑇 ∆𝑥

20. 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?

21. 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