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

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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
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

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
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

Converting Wavelength to Frequency

- n=frequency (Hz)

- c= velocity of light (3x108m/s)

- l= 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
• n  Frequency of radiation
• n0 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=AeBx
• 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
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