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Using math in physics - Reading the physics in a graph
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Highlights: a module to help students build physical intuition by learning to read the physics in graphs
Abstract: Graphs are a mathematical representation that builds on visual recognition to create a bridge between words and equations. If graphs are used appropriately, they can be a powerful tool in helping students learn to build the blend between physical concepts and mathematical symbology to develop their physical intuition and ability to think with math. This unit contains lots of materials to help students learn to put the physics into graphs: 9 short readings, 6 group learning activities, 115 homework problems with solutions and 50 exam problems from across the curriculum.
Resource Types: Instructor supplement, Restricted access, Student reading, In-class activity, Homework, Exam problem
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Using math in physics - Reading the physics in a graph

Using math in physics - Reading the physics in a graph

Using math in physics - Reading the physics in a graph - Introduction and Contents.pdf

Using math in physics - 6 - Reading graphs.pdf

Problems - Reading the physics in a graph - Table of contents.url

Problems - Reading the physics in a graph - Table of contents.pdf

2A.7. Reading the physics in a graph.pdf

2A.7.1 Example - reading the physics in a graph.pdf

3.4. Kinematics graphs.pdf

3.9. What's a derivative, really_.pdf

3.10 What's an integral, really_.pdf

3.16. Consistency of kinematics graphs.pdf

9.9. Interpreting mechanical energy graphs.pdf

15.3.1 Example_ Oscillator graphs.pdf

16.3.2 Example_ Velocity patterns in a pulse.pdf

16.6. Sinusoidal waves.pdf

Graph consistency.pptx

Physics to graphs.pptx

Electric forces.pptx

Reading energy graphs.pptx

Electric field and potential.pptx

Electric circuits.pptx

A diving gannet - in the water.pdf

Consistency of graphs.pdf

Juggling velocity.pdf

The perfect bouncer.pdf

Drawing kinematics graphs.pdf

Graph for a cart on a tilted airtrack - with spring.pdf

Graphs for a superball.pdf

Moving a vesicle.pdf

Rolling up and down.pdf

Straight line graphs of 1D motions.pdf

The motion of a red blood cell.pdf

A diving gannet - the fall.pdf

A diving gannet - the fall.url

Consistency of graphs.url

Juggling velocity.url

Drawing kinematics graphs.url

Graph for a cart on a tilted airtrack - with spring.url

Graphs for a superball.url

Moving a vesicle.url

Rolling up and down.url

The motion of a red blood cell.url

The motion of a red blood cell.url

A diving gannet - in the water.pdf

A remote controlled car.pdf

Drawing consistent graphs.pdf

Hitting a bowling ball.pdf

Force on a woodpecker.pdf

Nathan's train.pdf

Pushing a box - the details.pdf

Pushing a carriage.pdf

A diving gannet - in the water.url

A remote controlled car.url

Drawing consistent graphs.url

Force on a woodpecker.url

Hitting a bowling ball.url

Nathan's train.url

Pushing a box - the details.url

Pushing a carriage.url

Ball falling in oil.pdf

Balls up.pdf

Plotting a component of an electric force.pdf

Plotting the force between a charge and a dipole.pdf

Propelling a paramecium_ 1 -- Equations and graphs.pdf

Realistic spring graphs.pdf

Rolling up and down.pdf

Ball falling in oil.url

Balls up.url

Plotting a component of an electric force.url

Plotting the force between a charge and a dipole .url

Realistic spring graphs.url

Propelling a paramecium - 1 - Equations and graphs.url

Rolling up and down.url

Carts and graphs_ 1.pdf

Carts and graphs_ 2.pdf

Carts and graphs_ 3.pdf

Colliding carts.pdf

Random or not, here I come.pdf

Carts and graphs - 1.url

Carts and graphs - 2.url

Carts and graphs - 3.url

Random or not, here I come.url

Colliding carts.url

Blood flow and pressure.pdf

Measuring viscosity.pdf

Blood flow and pressure.url

Measuring viscosity.url

Energy skate-park 1.pdf

Energy skate-park 2.pdf

Kinetic energy and momentum graphs.pdf

Skateboarder energy graphs.pdf

Springy cart on a track.pdf

Sticky Carts.pdf

The perfect bouncer.pdf

The train, the hill, and the bumper.pdf

The bulldog on the skateboard - Graphs.pdf

The dipped track.pdf

The water-coat potential.pdf

Work-energy, impulse-momentum, and N2.pdf

Energy skate-park 1.url

Kinetic energy and momentum graphs.url

Energy skate-park 2.url

Skateboarder energy graphs.url

Springy cart on a track.url

Sticky Carts.url

The bulldog on the skateboard - Graphs.url

The dipped track.url

The perfect bouncer.url

The train, the hill, and the bumper.url

The water-coat potential.url

Work-energy, impulse-momentum, and N2.url

A molecular collision.pdf

An electron in a molecule.pdf

Bound states.pdf

Capture by photon emission.pdf

Chemical reaction toy model.pdf

Energy in photosynthesis - light and dark reactions.pdf

Going to a deeper well.pdf

Structure of the Lennard-Jones potential.pdf

The Gauss gun - Energy bar representation.pdf

Thermal to chemical energy transfer.pdf

Two atom bound state.pdf

A molecular collision.url

Bound states.url

An electron in a molecule.url

Chemical reaction toy model.url

Capture by photon emission.url

Energy in photosynthesis - light and dark reaction.url

Structure of the Lennard-Jones potential.url

Going to a deeper well.url

Two atom bound state.url

Thermal to chemical energy transfer.url

The Gauss gun - Energy bar representation.url

Opening a channel - perhaps.pdf

Opening a channel - perhaps.url

Adding up the energy stored in a capacitor.pdf

Charges near the origin.pdf

Debye length change.pdf

Details on dipoles.pdf

Electric field and potential from 4 charges.pdf

Electric field and potential near a water molecule.pdf

Electric fields in solution.pdf

Electric potential from a water molecule.pdf

Electrical loops in a membrane.pdf

Field and potential near points and sheets.pdf

Field and potential near a water molecule.pdf

Fields in a capacitor.pdf

Fields in a membrane.pdf

Orienteering in an electric potential.pdf

Potential near a dipole.pdf

Potential near a long molecule.pdf

Stuffing a capacitor.pdf

Tracking round a circuit 1.pdf

Tracking round a circuit 2.pdf

Tracking round a circuit.pdf

Adding up the energy stored in a capacitor.url

Charges near the origin.url

Debye length change.url

Details on dipoles.url

Electrical loops in a membrane.url

Electric field and potential from 4 charges.url

Electric field and potential near a water molecule.url

Electric fields in solution.url

Electric potential from a water molecule.url

Field and potential near a water molecule.url

Field and potential near points and sheets.url

Fields in a capacitor.url

Fields in a membrane.url

Orienteering in an electric potential.url

Potential near a dipole.url

Potential near a long molecule.url

Stuffing a capacitor.url

Tracking round a circuit 1.url

Tracking round a circuit 2.url

A bobbing bottle.pdf

Analyzing two oscillators.pdf

Diatomic vibrations.pdf

Diatomic vibrations step by step.pdf

Hanging mass on a spring problem.pdf

Oscillating energies.pdf

Oscillating graphs.pdf

SHO variables.pdf

SHO energies.pdf

Cosine graphs.pdf

A bobbing bottle.url

Analyzing two oscillators.url

Hanging mass on a spring problem.url

Diatomic vibrations step by step.url

Diatomic vibrations.url

Oscillating energies.url

Oscillating graphs.url

SHO energies.url

SHO variables.url

Cosine graphs.url

Action potential in motion.pdf

Action potentials on an axon.pdf

Adding pulses 1.pdf

Adding pulses 2.pdf

Adding pulses.pdf

An earthquake wave.pdf

Canceling pulses.pdf

Combining pulses.pdf

Complex wave shapes.pdf

Displacement and velocity patterns in waves.pdf

Graphing a pulse on a string 1.pdf

Graphing a pulse on a string 2.pdf

Graphing a pulse on a string 3.pdf

Making a pulse move.pdf

Motion in a standing wave.pdf

Moving a non-symmetric triangular pulse.pdf

Moving with the pulse.pdf

Overlapping pulses.pdf

Propagating a Gaussian pulse 1.pdf

Propagating a Gaussian pulse 2.pdf

Representations of elastic strings.pdf

Sinusoidal waves on a beaded string.pdf

Standing and traveling waves.pdf

Waves and velocities.pdf

Action potential in motion.url

Action potentials on an axon.url

Adding pulses.url

Adding pulses 1.url

Adding pulses 2.url

An earthquake wave.url

Canceling pulses.url

Combining pulses.url

Complex wave shapes.url

Displacement and velocity patterns in waves.url

Graphing a pulse on a string 1.url

Graphing a pulse on a string 2.url

Graphing a pulse on a string 3.url

Making a pulse move.url

Motion in a standing wave.url

Moving a non-symmetric triangular pulse.url

Moving with the pulse.url

Overlapping pulses.url

Propagating a Gaussian pulse 2.url

Propagating a Gaussian pulse 1.url

Representations of elastic strings.url

Sinusoidal waves on a beaded string.url

Spring vs string (graphs).url

Standing and traveling waves.url

Waves and velocities.url

Changing double slits.pdf

Interfering atoms.pdf

One and two slit patterns.pdf

Changing double slits.url

One and two slit patterns .url

Interfering atoms.url

Reading graphs - Quiz and Exam problems.docx

Reading graphs - Quiz and Exam problems.pdf

Using math in physics – Dimensional analysis.url

Using math in physics — Estimation.url

Using math in physics — Anchor equations.url

Using math in physics – Toy models.url

Using math in physics – Functional dependence.url

Exponentials for IPLS.url

INSTRUCTOR GUIDE


IMPLEMENTATION

Equipment required:  Computers / software

Specific equipment needed:  Computers needed to access the problems and readings, though they could be printed and distributed on paper.

Basic implementation tips & tricks:  Students often see graphs as something the instructor asks them to do — an answer they expect to memorize rather than a tool that can help them make sense of what's happening. In answering questions, both in class and in office hours, I'll often say, let's draw some graphs and see what they tell us. Or better yet, I ask the student to draw a graph and interpret it.

How does this resource fit into the flow of your course?  I bring graphs in to whatever topic is being discussed throughout the class. The readings are assigned during the section on kinematics. Whatever topics we are discussing, I explicitly use graphs for coding physical information in lecture, homework, quizzes, exams, and group learning activities.

PEDAGOGY

Pedagogical approach:  Collaborative problem-solving; Conceptually-oriented activities; Context-rich problems; Mathematically-focused activities

Skills / Competencies:  Multiple representations; Intuition building

What insights or realizations do you hope students gain from this resource?  that graphs are more than just a task assigned by an instructor — they are a valuable tool in analyzing and making sense of physical situations, and they are an important component both of building physical intuition and of complex problem solving

Why is this resource useful to life sciences students?  Life science students often have difficulty in seeing physical meaning in mathematical representations — graphs and symbols. Seeing how physical meaning is represented in graphs can help them learn to see the value of mathematical representations in reasoning about the physical world.

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SUBMISSION DETAILS


Copyright:   2024 Edward Redish

License:   CC BY-NC-SA - Attribution, No Commercial uses and Share Alike. Derivative works must have the same license.

Last Edit Date:  August 16, 2024

Vetted Library Publication Date:  October 4, 2023

Submission Date:  June 26, 2023

Version: 
Version 5, August 16, 2024
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