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### Making Introductory Physics More Like Real Physics

Ruth Chabay & Bruce Sherwood

Department of Physics

North Carolina State University

This project was funded in part by the National Science Foundation (grants MDR-8953367, USE-9156105, DUE-9954843, and DUE 9972420). Opinions expressed are those of the authors, and not necessarily those of the foundation.

Two Big Ideas

- The atomic nature of matter, quantum physics, and relativity must be central to the introductory course
- Change the content, not solely the pedagogy
- The unity of physics
- Students should be led to see clearly that a few fundamental principles explain a very wide range of phenomena

What should we teach?

Physics education research: a large investment by teachers and students is required for effective learning.

What is important enough to be worth a large investment on the part of students and teachers?

Need clear goals on which to base decisions.

Goals

Involve students in the contemporary physics enterprise:

- Emphasize a small number of fundamental principles(unification of mechanics & thermal physics; electrostatics & circuits)
- Integrate 20th century physics(atomic viewpoint; connections to chemistry, biology, materials science, nanotechnology, electrical engineering, nuclear engineering, computer engineering, …)
- Engage students in physical modeling(idealization, approximation, assumptions, estimation)

(And, avoid simple repetition of high school physics)

- Matter & Interactions I: Modern Mechanicsmechanics; integrated thermal physics
- Matter & Interactions II:Electric & Magnetic Interactionsmodern E&M; physical optics

John Wiley & Sons, 2002

http://www4.ncsu.edu/~rwchabay/mi

Matter & Interactions

I: Modern Mechanics II: Electric & Magnetic Interactions

- Small number of fundamental principles
- Physical and computer modeling
- Atomic nature of matter: macro/micro
- Unification of topics
- Just-in-time desktop experiments
- Visualization / simulation software

Fundamental Principles

Modern Mechanics:

- The momentum principle
- The energy principle
- The angular momentum principle
- The fundamental assumption of statistical mechanics

How do we make these appear fundamental to the student?

The Momentum Principle

- Not central in traditional curriculum; comes very late in course
- In M&I, start with
- Concept central to the entire course

The Momentum Principle: Approximations

- When can we approximate p ≈ mv?
- First explicit approximation encountered by most students
- One component of building physical models

The Momentum Principle: The Newtonian Synthesis

- Initial conditions + principle + force law iterative update of momentum and position (time-evolution)
- One or two steps: on paper
- Orbits, oscillators, scattering: computer programs written by students
- Less emphasis on deducing forces from known motion

The Momentum Principle:

- Running students collide
- NEAR spacecraft encounters Mathilde asteroid
- Finding dark matter
- Black hole at galactic center
- Diatomic molecule vibration

Momentum + Energy Principles:

- Fusion
- Producing the D+

In 1997 the NEAR spacecraft passed within 1200 km of the asteroid Mathilde at a speed of 10 km/s relative to the asteroid (http://near.jhuapl.edu). Photos transmitted by the spacecraft show Mathilde’s dimensions to be about 70 km by 50 km by 50 km. It is presumably composed of rock; rock on Earth has an average density of about 3000 kg/m3. The mass of the NEAR spacecraft is 805 kg.

A) Sketch qualitatively the path of the spacecraft:

B) Make a rough estimate of the change in momentum of the spacecraft resulting from the encounter. Explain how you made your estimate.

C) Estimate the deflection (in meters) of the spacecraft’s trajectory from its original straight-line path, one day after the encounter.

D) From actual observations of the position of the spacecraft one day after encountering Mathilde, scientists concluded that Mathilde is a loose arrangement of rocks, with lots of empty space inside. What about the observations must have led them to this conclusion?

(week 2)

The Momentum Principle: Atomic Nature of Matter

- Ball-and-spring model of solid
- Macro-micro connection (Young’s modulus - interatomic spring constant)
- Apply momentum principle to model propagation of sound in a solid; determine speed of sound

Chapter 3The Atomic Nature of Matter:Modeling a Solid

Day 1(recitation)

Measurements

(a) Properties of spring-mass systems:

Students measure ks, T, m for a mass and spring

(b) Properties of solids:

Students measure Young’s modulus for aluminum

Chapter 3The Atomic Nature of Matter:Modeling a Solid

Day 2(lecture)

Ball-and-spring model for a solid; application to a stretched wire

(a) Students calculate effective interatomic spring stiffness ks from Young’s modulus for Al and Pb

(b) Newton’s second law applied to a mass on a horizontal spring

Chapter 3The Atomic Nature of Matter:Modeling a Solid

Day 3(recitation)

Students write a computer program:

(a) Model the motion of a mass on a spring, using day 1 data (numerical integration of Newton’s second law)

(b) Display an animation of the motion and a graph of x vs. t

(c) Compare measured period and computed period (very good agreement).

Chapter 3The Atomic Nature of Matter:Modeling a Solid

Day 4(lecture)

Analytical solution for spring-mass system

Students predict period for: 2 masses vs. 1 mass 2 springs vs. 1 spring 1 spring 2x as long, etc.

Test students’ predictions with demos

Chapter 3The Atomic Nature of Matter:Modeling a Solid

Day 5(lecture)

Atomic connection: static (Young’s modulus) and dynamic (speed of sound in a solid)

Demo: measure speed of sound in bar of aluminum

Students design computer program to predict speed of sound, based on ball & spring model of a solid

Run computer model (long chain of masses & springs), using ks for Al & Pb calculated by students during previous lecture

Dimensional analysis: v =

In an earlier problem we found the effective spring constant corresponding to the interatomic force for aluminum and lead. Let’s assume for the moment that, very roughly, other atoms have similar values.

(a) What is the (very) approximate frequency f for the vibration of H2, a hydrogen molecule?

(b) What is the (very) approximate frequency f for the vibration of O2, an oxygen molecule?

(c) What is the approximate vibration frequency f of D2, a molecule both of whose atoms are deuterium atoms (that is, each nucleus has one proton and one neutron)?

(d) Why is the ratio of the deuterium frequency to the hydrogen frequency quite accurate, even though the effective spring constant is normally expected to be significantly different for different atoms? (Hint: what interaction is modeled by the effective “spring”?)

In my opinion, the central idea in this chapter was to learn that atoms bonded to each other can be thought of as two balls connected to one another with a spring. Once we understood this concept, we could apply the models of springs from the macroscopic world to the atomic level, which gave us a general idea of how things work at the atomic level. Understanding that gave us the ability to predict vibrational frequencies of diatomic molecules and sound propagation in a solid.

It is absolutely amazing how we can use very simple concepts and ideas such as momentum and spring motion to derive all kinds of stuff from it. I truly like that about this course.

(S.H.)

The most central concept we’ve used is Newton’s second law. I have never used momentum this much ever. Somehow--it works as the defining factor of every equation or formula of motion to define how objects move and interact with each other. The most surprising thing to me, however, is not so much the law--but how important one single concept can be in so many varied problems.

(J.H.)

Week 14: Ball and spring model of a solid (Einstein model: independent quantized oscillators): students write a computer program to calculate the heat capacity of a solid as a function of temperature.

Students fit curves to actual data for Pb and Al, with one parameter, the interatomic spring constant ks. Values obtained are consistent with results from Week 3.

Students measure heat capacity of water in a microwave oven.

heat capacity

Modeling Physical Systems

Explain, predict, understand messy real-world phenomena

- Start from fundamental principles
- Idealize: Decide how to model a system
- Make assumptions and approximations
- Estimate quantities

Analyze a small number of phenomena, not a large number of repetitive problems

A hot bar of iron glows a dull red. Using our simple model of a solid, answer the following questions. The mass of one mole of iron is 56 g.

(a) What is the energy of the lowest-energy spectral emission line? (Give a numerical value).

(b) What is the approximate energy of the highest-energy spectral emission line?

(c) What is the quantum number of the highest-energy occupied state?

(d) Predict the energies of two other lines in the emission spectrum of the glowing iron bar.

(Note: the actual spectrum is more complex than this, and a more complex model is required to explain it in detail.)

(week 7)

Research Supporting Development

- Theoretical
- New views of standard physics
- Cognitive task analyses
- Predictions based on models of learning
- Experimental
- Analysis of students’ written work
- Think-aloud protocol analysis (video)
- Fine-grained assessments
- Large scale assessments
- Time Scale
- 14 years (and still going…)

(these solutions to student homework are not included here)

Binary star

Damped oscillator

Charged rod

Cyclotron

Electromagnetic wave

(See http://www4.ncsu.edu/~rwchabay/mi and http://vpython.org)

Speed of sound

Potential energy well

Rutherford scattering distribution

Path of an atom in a gas

Carnot engine

Magnetic field of a long wire

Helical motion in magnetic field

Gauss’s law

Two Big Ideas

- The atomic nature of matter, quantum physics, and relativity must be central to the introductory course
- Change the content, not solely the pedagogy
- The unity of physics
- Students should be led to see clearly that a few fundamental principles explain a very wide range of phenomena

Matter & Interactions I: Modern Mechanicsmodern mechanics; integrated thermal physics

Matter & Interactions II:Electric & Magnetic Interactionsmodern E&M; physical optics

Ruth Chabay & Bruce SherwoodJohn Wiley & Sons, 2002

http://www4.ncsu.edu/~rwchabay/mi

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