Introductory Physics for the 21st Century

Mark P. HauganDepartment of Physics

Purdue University

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.

With thanks to my collaborators at Purdue, NCSU and Georgia Tech

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

1900 1920 1940 1960 1980 2000

1910, Ganot

18th edition!

1928, 1938

Millikan et al.

1949

Sears & Zemansky

1960 Halliday & Resnick (from 1977)

2004 H&R/Cummings

2004 S&Z/Young

A Tongue-in-Cheek Overview of the 20th Century Evolution of Physics Textbooks

Steve Durbin, Purdue University

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?

21200 0.25 50

2V

2 2V

1.414 m/s to the rightV

We can certainly argue that a performance like this is evidence of some understanding, but …

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 *

21200 0.25 50

2V

2 2V

1.414 m/s to the rightV

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

, , , sys sys f sys i net on sys by surrp p p F 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*, , sys sys f sys i on sys by surrE E E W

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.

initial state

final state

Modeling builds equations that apply to specific situations by applying fundamental principles to 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.

2 2, ,

1

2net CofM trans sys CofM f CofM iF R K M V V

This implies a corresponding change in the skater’s translational kinetic energy expressed by the equation used earlier to “solve” the problem,

a useful “theorem” of Newtonian mechanics

particle 1 particle 2

F

F

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.

If you exert the same constant force on each particle during the same time interval Δt and then stop,

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 Larmor Radiation

2 20

6

Q aP

c

axially symmetric

Q3. How do the distances traveled by 1 and 2 during the interval Δt compare?

A) d1 > d2 B) d1 = d2 C) d1 < d2

*

*

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 atomic- level 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

x

y

z

sliderr

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.

slider sliderr v t

slider slider slider slider sliderp m v m v

net on slider ,0,0

,0,0

slider slider slider

sliderslider

slider

p F t F t m v

dv Fa

dt m

and so on.

even in the simplest cases

To motivate and reward such a careful approach analyze situations that are interesting and complicated (enough).

ES E Sr r r

ˆ / | |ES ES ESr r r

on by 2ˆ

| |E S

E S ESES

Gm mF r

r

E E ESp p F t

ESr

Er

Sr

x

y

/E E Ev p m

E E Er r v t

.

.

.

Vector Algebra and Geometry as a powerful tool

= <xE, yE, 0>

O

Orbital Dynamicsfrom visual import *

# Fundamental Constants [use MKS units throughout] G = 6.7e-11 # Newton's gravitational constant

# 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.m = 2.0e30 Etrail = curve(color=color.cyan)

# Set Earth initial velocity and momentum Earth.v = vector(0.0,29.865e3,0.0) Earth.p = Earth.m*Earth.v

# 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)

Newtonian Synthesis

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

When Possible Integrate Laboratory and Other Activities

Stretch a wire of length L and cross-sectional area A by pulling with a force of magnitude F on each end.

Discover that

wF k L

Note that in a simple model solid

( 1)layersL N d 2

atoms per layerA N d

L

d

y

x

on layer by next layer on layer by next layerˆ0 ,0,0layerPFi F F F

t

on layer by next layer 2| |w per layer a a

A d LF k L F N k s k

d L

A similar analysis for other atomic layers reveals that the bond stretch s is essentially uniform along the wire. So,

1 akF L

A Y d L

Apply the momentum principle, Newton’s 2nd law, to each layer of the wire in equilibrium under stress.

For this first layer,

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

a

a

kv d d

m

The Einstein Model Solid

quantized vibrational energy

and the low-temperature heat capacity of solids