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PH15720

PH15720. Laboratory Techniques - An Introduction to MATHCAD. Introduction. Review of Last Week Arrays, Vectors and Matrices Simple matrix & vector maths Statistics Plotting & analysing data with vectors. Review of Last Week. Entering data with the Input Table

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PH15720

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  1. PH15720 Laboratory Techniques - An Introduction to MATHCAD

  2. Introduction • Review of Last Week • Arrays, Vectors and Matrices • Simple matrix & vector maths • Statistics • Plotting & analysing data with vectors

  3. Review of Last Week • Entering data with the Input Table • Extracting columns from a matrix • Creating simple X-Y graphs • Formatting graphs • Slope & Intercept

  4. Resistor Example from Lecture 4 #1 Input table as before Extract Voltage to vector & apply units Same for current

  5. Resistor Example from Lecture 4 #2 • Check on values of vectors

  6. Resistor Example from Lecture 4 - Plotting

  7. Error Bars #1 • Add to graph to show uncertainty in y values. • Create vector of ‘High’ values • Create vector of ‘Low’ values • Add as traces to y-axis • Add extra x-axis variables • Format as error bars

  8. Error Bars #2 • Use vector maths to get ‘high’ and ‘low’ vectors Huge error for illustration only

  9. Error Bars #3 • Add to graph

  10. Error Bars #4 • Format traces as Error Error type Hide Arguments&Show Legend

  11. Error Bars – Completed Graph

  12. Pre-Processing Data • Use vector maths to pre-process data before graphing • Use knowledge of physics to get data into a straight line format

  13. Photoelectric Effect #1 • Photoelectrons emitted from metal surface under illumination • Illuminate metal with light of different wavelength • Measure energy of emitted electrons (Stopping Potential) • Keller, Gettys & Skove p976

  14. The Photoelectric effect hv A e- VStop

  15. Photoelectric Effect #2 • Equation given in terms of frequency • Experimental data given in wavelength  convert Planck’s constant StoppingPotential Electronic Charge e Threshold Frequency Applied Frequency

  16. Converting Wavelength to Frequency - n=frequency (Hz) - c= velocity of light (3x108m/s) - l= wavelength (m) - Valid for all electromagnetic radiation

  17. Photoelectric effect #2 • Use resource centre for physical constants • Watch for confusion of e & q • Useful functions (look-up in help system) • slope(vx,vy)  slope of line • intercept(vx,vy)  intercept with axis

  18. Stopping Potential Equation • Vs  Stopping Potential • n  Frequency of radiation • n0 Threshold frequency • h  Planck’s constant • q  Electron Charge

  19. Photoelectric Effect #3 Curves for two different metals shown Slope of lines = h/q Intercept with x-axis (Vs=0) at Threshold Frequency (Different for each metal)

  20. Power Law • Systems in the form:Y=AeBx • Examples: • Cooling • Radioactive Decay • Compound Interest • B is time constant or rate constant

  21. Power Law • Take logs of Y values straight line • intercept gives ln(A) • slope gives B

  22. Power Law Example #1 • Data in input table as before • Extract Columns

  23. Power Law Example #2- Normal Plot Useless – No Information

  24. Power Law Example #3- Format y scale log • Straight line => power law • Need to get slope & intercept

  25. Power Law Example #4 • Take log of y data • Calculate slope & intercept • Display A&B • Create model

  26. Power Law Example #5Compare model vs data

  27. Review of Data Handling#1 • Use of Input Table • Column Extract Operator M<> • Add units if needed • Plot vector vs vector • Add Error bars

  28. Review of Data Handling#2 • Extract Information from data • slope() • intercept() • Pre-processing • Handling power law data • Create model & compare with data

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