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

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!

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.

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

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

The Problem of Heating and Cooling: Newton‘s Law

Experimental Setup

The Problem of Heating and Cooling: Newton‘s Law

Calculation: Finite Difference Equation (Spreadsheet)

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

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

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

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

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

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

Calculations: Harmonic Oscillations of a Pendulum

Construction

Workshop: Pendulum Experimental Setup

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

Harmonic Oscillations of a Pendulum Measurement: Distance, Graph

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

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

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

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

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

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

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

Motion and Gait Analysis (Kistler)

Force Plate Take off Forces in Performace Diagnostics (Kistler)

Force Plate Strain Gages instead of Piezoelectric Sensors (Vernier)

Force Plate School Application: Newton‘s Law

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

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

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

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

Thank you for your attention

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

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

Workshop: Discharging a Capacitor Charging and Discharging Circuit

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

Workshop: Discharging a Capacitor EasyLink Interface and Voltage Probe

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

Workshop: Discharging a Capacitor Charging and Discharging Circuit

Workshop: Evaporation Heat of Pentane Preparation of the Temperature Probe

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

Workshop: Evaporation Heat of Pentane Optical Fit

Workshop: Evaporation Heat of Pentane Regression

Workshop: Pendulum Motion and Acceleration Sensors

Workshop: Pendulum Measurement Procedure

Workshop: Pendulum Experimental Setup

Workshop: Pendulum Measurement Scatter-Plot, Spreadsheet

Workshop: Oscillating Circuit Starting and Oscillating Circuit

Workshop: Oscillating Circuit Experimental Setup

Workshop: Oscillating Circuit Nspire Voltage Measurement (EasyLink)

Workshop: Faraday’sLaw of Induction

Workshop: Law of Induction Measurement: Voltage Probe and EasyLink

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

Workshop: Law of Induction Experimental Setup

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

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

Workshop: Law of Induction Oscillating Magnet: Experimental Setup

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

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

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

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

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

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

Workshop: Force Plate Calculations: Integral (Trapezoidal Rule)

Thank you for your attention