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Physics Experiments for Mathematical Education Hans Kammer, Berner Maturitätsschule für Erwachsene, CH-3012 Berne, Switzerland

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Motivation for dealing with empiric Data in mathematical Education real world experiments engage students application in a practical field stimulates more than „grey theory“ alone well selected applications show beginners the enormous practical importance of mathematics managing great data volumes is a modern everyday application of mathematics (=>meteorology) working with practical experiments from physics, biology, sports etc. shows the interdisciplinar character of mathematics and first of all: calculator methods are simple!

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Evaluation of experimental Data: Procedure measuring physical data with sensors and calculator guessing the mathematical function describing these data fitting optically the measured data with this function varying its parameters with sliders or fitting by regression with a (limited) set of built in standard functions.

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What should you learn for your instruction? Handling of at least one sensor e.g. Temperature Data Acquisition with the TI-NspireCAS Handheld Calculator and Computer Software: Spreadsheet and Scatterplot in Graphs-Application Enter a Function and fitting it to the measured data by settings ist parameters with sliders automatic Data Regression with built in standard function Expanding the Regression Technique with Parameters/Sliders

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Subjects The Problem of Heating and Cooling: Newton‘s Law Harmonic Oscillations of a Pendulum Force Platform and more in the workshops …

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The Problem of Heating and Cooling: Newton‘s Law

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Experimental Setup

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The Problem of Heating and Cooling: Newton‘s Law

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Calculation: Finite Difference Equation (Spreadsheet)

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The Problem of Heating and Cooling: Newton‘s Law Calculation: Finite Difference Equation (Graph)

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The Problem of Heating and Cooling: Newton‘s Law Measurement: Response Time of an EasyTemp Sensor

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The Problem of Heating and Cooling: Newton‘s Law Measurement: Response Time („Optical Fitting“)

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The Problem of Heating and Cooling: Newton‘s Law Evaporation Heat of Pentane: Exponential Regression

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The Problem of Heating and Cooling: Newton‘s Law Evaporation Heat of Pentane or Acetone: Experimental Setup

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The Problem of Heating and Cooling: Newton‘s Law Evaporation Heat of Pentane ( ): Regression Graph

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Calculations: Harmonic Oscillations of a Pendulum

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Construction

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Workshop: Pendulum Experimental Setup

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Harmonic Oscillations of a Pendulum Sensors: Distance (ulrasonic, contactless), Acceleration

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Harmonic Oscillations of a Pendulum Measurement: Distance, Graph

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Harmonic Oscillations of a Pendulum Measurement: Distance, Spreadsheet, Regression

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Harmonic Oscillations of a Pendulum Measurement: Velocity, Calculated from distance data

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Harmonic Oscillations of a Pendulum Measurement: Acceleration, Calculated from velocity

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Force Plate (Clinic, Biomechanical Research, Sports) 3-d Professional Force Platform for Gait and Balance Analysis (Kistler 9285BA, piezoelectric)

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Force Plate (Kistler 9285 BA) Force Measurements and Photograhic/Cinematographic Recording of the Contact Surface from below

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Clinical Motion- and Gait-Analysis (Rehabilitation and prothesis enhancement, Kistler) Force Plate

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Gait Parameters: Forces vs. time (Kistler) Force Plate

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Motion and Gait Analysis (Kistler)

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Force Plate Take off Forces in Performace Diagnostics (Kistler)

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Force Plate Strain Gages instead of Piezoelectric Sensors (Vernier)

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Force Plate School Application: Newton‘s Law

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Force Plate Take off Forces during a Jump from the force plate (Vernier, Nspire)

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Force Plate Take off Forces: Calculation of Jumping height (Vernier)

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Force Plate Jump from the Force Plate: Data Analysis (Vernier, Nspire)

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And many other applications from natural and environmental sciences, sports, medicine …

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Thank you for your attention

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Physics Experiments for Mathematical Education: Workshop Hans Kammer, Berner Maturitätsschule für Erwachsene, CH-3012 Berne, Switzerland

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Subjects Discharging a Capacior with a Resistance Evaporation Heat of Pentane Pendulum: Distance and Acceleration R-L-C-Oscillator (Oscillating Circuit) Faradays Law of Induction Electric Characteristics (Diode, Bulb) Force Platform

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Workshop: Discharging a Capacitor Charging and Discharging Circuit

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Workshop: Discharging a Capacitor Capacitor, Resistor and 9-Volt Battery

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Workshop: Discharging a Capacitor EasyLink Interface and Voltage Probe

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Workshop: Discharging a Capacitor Nspire Discharging Scatter-Plot and Regression-Graph

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Workshop: Discharging a Capacitor Charging and Discharging Circuit

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Workshop: Evaporation Heat of Pentane Preparation of the Temperature Probe

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The Problem of Heating and Cooling: Newton‘s Law Evaporation Heat of Pentane or Acetone: Experimental Setup

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Workshop: Evaporation Heat of Pentane Optical Fit

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Workshop: Evaporation Heat of Pentane Regression

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Workshop: Pendulum Motion and Acceleration Sensors

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Workshop: Pendulum Measurement Procedure

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Workshop: Pendulum Experimental Setup

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Workshop: Pendulum Measurement Scatter-Plot, Spreadsheet

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Workshop: Oscillating Circuit Starting and Oscillating Circuit

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Workshop: Oscillating Circuit Experimental Setup

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Workshop: Oscillating Circuit Nspire Voltage Measurement (EasyLink)

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Workshop: Faraday’sLaw of Induction

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Workshop: Law of Induction Measurement: Voltage Probe and EasyLink

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Workshop: Law of Induction Measurement: 50 Hz R-C-Ripple Filter (if necessary)

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Workshop: Law of Induction Experimental Setup

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Workshop: Law of Induction Measurement: Voltage Surge (Coil 23’000 Turns)

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Workshop: Law of Induction Oscillating Magnet (turn by 90° for Measurement)

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Workshop: Law of Induction Oscillating Magnet: Experimental Setup

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Workshop: Law of Induction Oscillating Magnet (Coil with 23’000 turns) 2 Oscillating Modes

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Workshop: Characteristics (Bulb. Diode LED) Measuring Circuit: With 2 Nspires and 2 Voltage Probes

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Workshop: Characteristics Measuring: Characteristics of an ideal and a real Bulb

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Workshop: Characteristics Measuring: Characteristics of a LED (GaAS/GaP)

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Workshop: Force Plate Measuring: Vernier Force Platfrm (with Strain Gauges)

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Workshop: Force Plate Measuring: Nspire F vs. t Graph

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Workshop: Force Plate Calculations: Integral (Trapezoidal Rule)

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Thank you for your attention

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