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 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? 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 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

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: 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 𝑔=9.9 ∓0.3 𝑚 𝑠 2 𝛿𝑥= 0.3 9.9 ×100=3 %

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=𝜋 𝑟 2 D = 0.2 ± 0.05 m 𝐴 𝑚 = 22 7 × 0.2 2 2 =0.0314 𝑚 2 𝐴 𝑚𝑎𝑥 = 22 7 × 0.2+0.05 2 2 =0.0491 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦=0.0491 −0.0314=0.0177 𝐴=0.0314 ∓0.018 𝑚 2 0.018 different than 0.05

Sensitivity coefficients 𝑥=2𝑦+ 𝑧 2 𝑎 2 + 𝑏 2 = 𝑐 2 𝐴=𝜋 𝑟 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 4𝜋 𝐸 0 𝑞 1 𝑞 2 𝑟 2 𝑒 Fourier’s law 𝑄=−𝑘 ∆𝑇 ∆𝑥

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