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 Extracting columns from a matrix Creating simple X-Y graphs Formatting graphs Slope & Intercept

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

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

Resistor Example from Lecture 4 - Plotting

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

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

Error Bars #3 Add to graph

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

Error Bars – Completed Graph

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

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

The Photoelectric effect A hv e- VStop

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

Converting Wavelength to Frequency - =frequency (Hz) - c= velocity of light (  3x10 8 m/s) - = wavelength (m) - Valid for all electromagnetic radiation

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

Stopping Potential Equation Vs  Stopping Potential  Frequency of radiation   Threshold frequency h  Planck’s constant q  Electron Charge

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)

Power Law Systems in the form: Y=Ae Bx Examples: –Cooling –Radioactive Decay –Compound Interest B is time constant or rate constant

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

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

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

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

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

Power Law Example #5 Compare model vs data

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

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