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)
Supporting materials:
• Matter & Interactions I:
Modern Mechanics
mechanics;
integrated thermal physics
• Matter & Interactions II:
Electric & Magnetic
Interactions
modern 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 p  Fnet t where

p

mv
1 v / c
2
2
• 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 +
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
Week 3: A sample week
Chapter 3
The 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 3
The 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 3
The 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 3
The 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 3
The 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 = d
ks / m
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.
heat capacity
Students measure heat capacity of water in a microwave oven.
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…)
Student Programs
(these solutions to student homework are not included here)
Binary star
Damped oscillator
Charged rod
Cyclotron
Electromagnetic wave
Instructor Programs
(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 Mechanics
modern mechanics; integrated thermal physics
Matter & Interactions II:
Electric & Magnetic Interactions
modern E&M; physical optics
Ruth Chabay & Bruce Sherwood
John Wiley & Sons, 2002
http://www4.ncsu.edu/~rwchabay/mi