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Introductory Physics for
the 21st Century
Mark P. Haugan
Department of Physics
Purdue University
With thanks to my collaborators at Purdue, NCSU and Georgia Tech
Our work is supported by the National Science Foundation
award 0618647. Opinions expressed here are those of the
author and not necessarily of the NSF.
Why a New Introductory Physics Curriculum?
Case 1: Integrating aspects of contemporary physics
i ) emphatically demonstrates the power of physics principles and
develops knowledge that can ease students’ transition to more
advanced study.
ii) explicitly portrays physics as the vibrantly alive science that it is.
We can modify traditional treatments of the principles of dynamics using
momentum and energy concepts so that it can be combined with a few
contemporary ideas, e.g., a system’s internal energy contributes to its
rest mass and is quantized, to make principled presentations of many
20th century discoveries.
Nuclear Atom
Nuclear Fission and Fusion
Particle Decay and Reaction Energetics
Spectral-Line Emission and Absorption
Dark Matter
Supermassive Black Holes
Aspects of Low-Temperature Thermal Physics
A Tongue-in-Cheek Overview of the 20th
Century Evolution of Physics Textbooks
Steve Durbin,
Purdue University
2004 H&R/Cummings
1960 Halliday &
Resnick (from 1977)
1910, Ganot
18th edition!
1949
Sears &
Zemansky
1928, 1938
2004 S&Z/Young
Millikan et al.
1900
1920
1940
1960
1980
2000
Why a New Introductory Physics Curriculum?
Case 2: The knowledge and skills that too many students take away
from traditional physics courses is superficial, at best.
i ) evidence from research studies
ii) our own assessments based on subsequent student performance
A skater of mass m=50 kg,
initially at rest, pushes
away from the side of a
skating rink by exerting a
force perpendicular to
the boards of constant
magnitude F=200 N.
The force stops when she
has moved 0.25 m and her
hands lose contact with the
boards.
What is her final velocity?
1
200  0.25   50  V 2
2
V2 2
V  1.414 m/s to the right
We can certainly argue that a performance like this is evidence of some
understanding, but …
1
200  0.25   50  V 2
2
V2 2
V  1.414 m/s to the right
Q1. Does any force do significant work on the skater in this situation?
A. Yes, the force she exerts on the boards
B. Yes, the force the boards exert on her
C. Yes, the net force exerted on her by the boards, ice and Earth
* D. No
Intuitive, even naïve, knowledge and the matching of equations to
physical situations can be useful resources, even for us. They must,
however, be disciplined by more principled knowledge and reasoning.
The Matter & Interactions (M&I) Curriculum
The preceding problem is a typical physics problem in that it asks the
student to explain or predict something about the structure or the
behavior of a physical system, the skater, in some specific situation.
Faced with such a task, what does a physicist do, when they are
proceeding with care?
They appeal to fundamental physics principles and construct a model
representation of the physical situation, they run the model to make
their explanation or prediction and, finally, they assess the adequacy
of the result.
M&I fosters the development of richly structured physics knowledge and
the ability to use it flexibly and reliably by having students approach
problem solving in this way. A handful of fundamental definitions
and principles are the core of this knowledge structure.
The Momentum Principle
psys  psys , f  psys ,i  Fnet ,on sys by surr t
The change in momentum of a system during a time interval Δt is equal
to the net force exerted on the system by its surroundings.
The time interval Δt must be small enough that the net force is
essentially constant during it.
The net force acting on a system at an instant is the vector sum of all
forces exerted on the system by objects in its surroundings.
The Energy Principle*
Esys  Esys , f  Esys ,i  Won sys by surr
The change in the energy of a system is equal to the work done it by
its surroundings. The work done on a system …
The parallel form of these principles, repeated again in the form of the
Angular Momentum Principle, and the analogous ways they are used
when constructing models facilitates students’ learning and their use of
what they’ve learned.
The Matter & Interactions (M&I) Curriculum
Based on their experience in a traditional HS physics course, the M&I
approach to physics and to problem solving may not be what they
are expecting.
They may, therefore, find it helpful for you to talk a bit about how
equations they may have memorized and used to answer questions
about some kind of physical situation emerge in the new approach.
Such equations are built efficiently and with physical meaning when we
use our fundamental definitions and principles to construct a model
of the situation of interest.
There are many opportunities to point out when this happens.
Modeling builds equations
that apply to specific
situations by applying
fundamental principles to
initial
final
state
state
systems involved and by
making situation-appropriate assumptions and idealizations.
Applying the energy principle to the system consisting of the skater and
making the reasonable approximation that the frictional force exerted
by the ice on the skater’s skates is negligible, we conclude correctly
that no work is done on the skater in this case.
Applying the momentum principle to the system consisting of the skater
and making the same approximation, we conclude that net force
exerted on the skater by her surroundings is equal to the force exerted
on her by the boards and that her momentum changes accordingly.
This implies a corresponding change in the skater’s translational kinetic
energy expressed by the equation used earlier to “solve” the problem,
Fnet  RCofM  Ktrans 
1
2
2
M sys VCofM
, f  VCofM ,i 
2
a useful “theorem” of
Newtonian mechanics
For fun(?) and to emphasize that this sort of approach has value far
beyond introductory physics:
Consider particles 1 and 2 far from other objects and initially at rest.
Both have the same mass M. However, particle 1 is uncharged while
particle 2 has charge Q.
F
F
If you exert the same constant
force on each particle during
the same time interval Δt and
then stop,
particle 1
particle 2
Q2. how do the final speeds (much less than c) of particles 1 and 2
compare?
A) v1 < v2
* B) v1 = v2
C) v1 > v2
Q3. How do the distances traveled by 1
and 2 during the interval Δt compare?
A) d1 > d2
B) d1 = d2
0Q 2 a 2
Larmor
P
Radiation
6 c
*C) d1 < d2
axially
symmetric
The Matter & Interactions (M&I) Curriculum
Students’ intuitive ideas about motion and
mechanism are refined and extended to
yield more formal, fundamental definitions
and principles of physics.
Perhaps surprisingly, addressing the atomiclevel structure of matter can facilitate
understanding of traditional material while
injecting contemporary physics content.
How can the
boards exert
a force on
the skater?
Sense of Mechanism
What is thermal energy?
Introduce Fundamental Concepts and Principles Early
and Use Them Consistently
even in the simplest cases
rslider  vslider t
y
rslider
pslider  mslider vslider  mslider vslider
z
x
pslider  Fnet on slider t  F , 0, 0 t  mslider vslider
 aslider
dvslider
F


, 0, 0
dt
mslider
and so on.
In this way, special cases are embedded in and reinforce the target knowledge
structure from the beginning and equations are connected to physical meaning
in physical situations by model construction.
To motivate and reward such a careful approach analyze
situations that are interesting and complicated (enough).
y
from visual import *
Orbital
Dynamics
# Fundamental Constants [use MKS units throughout]
G = 6.7e-11 # Newton's gravitational constant
Vector Algebra and Geometry
as a powerful tool
# Place Sun and Earth in their initial positions
Earth = sphere(pos=(1.5e11,0.0,0.0), radius=4.0e9,
color=color.blue)
Earth.m = 6.0e24
Sun = sphere(pos=(0.0,0.0,0.0), radius=8.0e9,
color=color.yellow)
Sun.mES
= 2.0e30
Etrail = curve(color=color.cyan)
r
r = <x , y , 0>
# Set Earth initial velocity and momentum
E E
E
Earth.v = vector(0.0,29.865e3,0.0)
Earth.p = Earth.m*Earth.v
rS
O
rES  rE  rS
rˆES  rES / | rES |
Fon E by S  
GmE mS
rˆES
2
| rES |
pE  pE  FES t
# Predict the Earth's motion
t =0.0
dt = 864.0
while 1:
r_ES = Earth.pos - Sun.pos
rhat_ES = r_ES / mag(r_ES)
F_ES = -(G*Sun.m*Earth.m/mag(r_ES)**2)*rhat_ES
Earth.p = Earth.p + F_ES*dt
Earth.v = Earth.p/Earth.m
Earth.pos = Earth.pos + Earth.v*dt
t = t + dt
Etrail.append(pos=Earth.pos)
x
Newtonian Synthesis
vE  pE / mE
rE  rE  vE t
.
.
.
When Possible Integrate Laboratory and Other Activities
Model interatomic interactions using
a linear (spring) force law for small
displacements from equilibrium
separation, d, the atomic diameter.
The Model Solid
atomic diameter
from density
and molar mass
Stretch a wire of length L and
cross-sectional area A by pulling
with a force of magnitude F on
each end.
Discover that
F  kw L
Note that in a simple model solid
L  ( N layers  1)d
A  Natoms per layer d 2
d
L
y
Apply the momentum principle,
Newton’s 2nd law, to each layer
of the wire in equilibrium under
stress.
For this first layer,
x
Player
t
 0   Fiˆ  Fon layer by next layer   F  Fon layer by next layer , 0, 0
A similar analysis for other atomic layers reveals that the bond stretch s is
essentially uniform along the wire. So,
 A   d L 
 F  kw L | Fon layer by next layer | N per layer ka s   2  ka 

d
L
  

F 1  ka  L
   
A Y d  L
Micro-Macro Connections Increase Coherence
The Speed of Sound in Solids
disturbances propagate
After analyzing the harmonic
oscillation of mass-spring
systems we use dimensional
analysis to obtain an analytic
expression for this speed
ka
v  d 
d
ma
The Einstein Model Solid
quantized
vibrational
energy
and the
low-temperature
heat capacity of solids