Re-conceptualizing Introductory Physics

Mark A. Peterson

Mount Holyoke College

May 9, 2007

Is there any alternative to …?

• Physics starts with Newton, and F=ma.

• Its subject is the motion of point particles.

An alternative view …

• Physics starts with Archimedes and Galileo

• Its subject is proportionalities in Nature

• One of its main goals and uses is common-sense estimation, using known proportionalities, dimensional analysis, and a few important data, including natural constants

Laboratory 1: Scaling in Bones

A suggestion of Galileo:

The length L and diameter D of homologous bones in animals should scale as D ~L The argument is that the required bone strength goes as L , but the actual bone strength goes as D . These should grow together.

3/23

2

Log-log plot of femur diameter D vs. length L

How is this starting point unusual?

• It is biological, and complex

• It is approximate, not precise

• It emphasizes proportionality (here in the form of a power law), via geometry (volume and area)

• It draws on history in a serious way, not as something merely supplementary

• It is an interesting, open-ended problem

Geometrical Optics

• Proportion and geometry, in a theory of how we see.

• Historical reference: perspective in Renaissance painting

• Mathematics: angles, small-angle approximation

• Utilitarian interest: optical instruments

Time

• Clocks: angular clocks; oscillator clocks; logarithmic clocks (decay)

• History: longitude, pendulum, GPS system

• Mathematics: sine and cosine as functions

• Mathematics: the effect of small perturbations (binomial approximation)

Equilibrium: forces and torques

• proportion again: Archimedes’ law of the lever

• Hooke’s Law, elasticity theory, geometrical factors (recall bones lab)

• Microscopic picture: springs in parallel and series, and the forces between atoms

Equilibrium: Energy

• An alternative conceptual picture of mechanical equilibrium: Minimization of potential energy.

• Kinetic energy and speed

• Conservation and non-conservation of mechanical energy: approach to equilibrium

Fluids

• Density, pressure: geometrical factors again, volume and area

• Archimedes’ principle, buoyancy

• Phenomenology of moving fluids

• Blood flow

Equilibrium: Thermal

• Temperature, Internal Energy • Work (finally!) and conservation of energy• 19th century context : Rumford, Joule,

Carnot• Entropy and free energy• Microscopic picture

Second semester

• More conventional, but still includes unconventional topics, like electrochemistry, and action potential in neuron

• Continues to draw heavily on the story line of physics: Young, Galvani, Volta, Oersted, Joule, Maxwell, Hertz, Planck, Einstein…

• Continues to emphasize continuum objects (like that most useful of concepts, energy current density, in W/m , i.e., brightness, loudness, “hotness”, etc., with frequent reference to sense perceptions.)

2

Student views

• “more coordination between physics, chemistry, and biology classes would be helpful, so that the information presented in each complements what’s taught in the others.”

• “I felt that dimensional analysis is the most useful thing that I learned in physics”

• “when we come across a concept that occurs in biology, such as enzymes (today), we should first discuss as a class how we know them in a biological sense AND THEN move on to …

Physics & BiologyPhysics & BiologyMaking the ConnectionsMaking the Connections

By By Dana AlessiDana Alessi

Spring Semester 2007Spring Semester 2007

PhysicsPhysics as the Foundationas the Foundation

““Many key advances in the Many key advances in the biological sciences have been biological sciences have been

made possible by physics-based made possible by physics-based techniques. The future of techniques. The future of biomedicine depends on biomedicine depends on

collaboration between the two collaboration between the two fields.”fields.”

- Valerie JamiesonValerie Jamieson, , Physics WorldPhysics World, September , September 19991999

http://physicsweb.org/articles/world/12/9/8http://physicsweb.org/articles/world/12/9/8

A Few Connecting ThemesA Few Connecting Themes• Energy & HeatEnergy & Heat

– Metabolism, ATP, brown fat, hibernation, homeostasis.Metabolism, ATP, brown fat, hibernation, homeostasis.• ProportionsProportions

– AnatomyAnatomy• Fluids, Poisseuille & Bernoulli, Viscosity, OsmolarityFluids, Poisseuille & Bernoulli, Viscosity, Osmolarity

– Transport in plants, circulatory system, osmolarity in homeostasis (kidney Transport in plants, circulatory system, osmolarity in homeostasis (kidney function), turgor pressure in plants.function), turgor pressure in plants.

• OpticsOptics– Optometry, microscopes.Optometry, microscopes.

• Electrical CurrentsElectrical Currents– Nervous system, cell membrane transport, electrochemical gradients.Nervous system, cell membrane transport, electrochemical gradients.

• Oxidation & ReductionOxidation & Reduction– Electron transport chain in aerobic respiration (animals & plants!), Electron transport chain in aerobic respiration (animals & plants!),

photosynthesis.photosynthesis.• WavesWaves

– Hearing & sight.Hearing & sight.– Why we have evolved to hear/see what we do & compare to other species.Why we have evolved to hear/see what we do & compare to other species.– Photons X-rays, cancer, bilirubin, vitamin D, melatonin.Photons X-rays, cancer, bilirubin, vitamin D, melatonin.

• RadioactivityRadioactivity– Dosage, biological effects, sensitivity of nucleic acids.Dosage, biological effects, sensitivity of nucleic acids.

• Young’s ModulusYoung’s Modulus– Biomechanics, properties of different muscles & tissues in different species & Biomechanics, properties of different muscles & tissues in different species &

their uses (structure & function!).their uses (structure & function!).

See section 8.17 “The Human Circulatory System” & section 8.18 “A Fractal Model of Circulation” (pages 290-301) of Physics in Proportion, Vol. I, Mark A. Peterson

http://library.thinkquest.org/05aug/01883/introtocircman.gifhttp://www.biologycorner.com/resources/aortic_arch.jpg

http://www.discoveryfund.org/images/Eye_Anatomy-Anat.jpg

“Fish eyes are essentially spherical, unlike ours. Discuss the problem of the focal length of the fish eye, following the discussion in 3.9, not forgetting that, of course, fish eyes must work in water. How can we be sure that there is some essential structure inside the fish eye which is not part of the model in that Section? What could it be?”

-Peterson, Physics in Proportion, Vol. I, p.115

See section 3.13.2 “The Microscope” & section 3.13.3 “Two lenses together” of Physics in Proportion, Vol. I, Mark A. Peterson (pages 93-96).

http://www.ivyhall.district96.k12.il.us/4th/KKhp/Microbes/ProtistGraphics/microscopes/micros2.JPG

See chapter 16, “Bioelectricity, Electrochemistry” on page 485 & corresponding problems on page 514

Physics in Proportion, Vol. II, Mark A. Peterson

http://imagecache2.allposters.com/images/pic/JAG/03-PS121-4~Nervous-System-Posters.jpg

Electrical Charge & Potential

http://www2.montana.edu/cftr/images/IonChannel2.gif

http://www.columbia.edu/cu/biology/courses/c2005/handouts/etccomplexes.jpg

http://www.mie.utoronto.ca/labs/lcdlab/biopic/fig/35.07.jpg

http://www.midamericahearing.com/images/Ear%20Anatomy.GIFhttp://www.ucihs.uci.edu/hesp/images2/waveform.jpg

“In the last century it was noticed by nurses in France that newborns with a temporary jaundice condition, leading to a buildup of waste product called bilirubin in their blood, did better if their cribs were placed near an open window. Somehow sunlight accomplished something that artificial lighting in the room did not. This was later realized to be the photodissociation of bilirubin. Why would the two different light sources make a difference?”

-Problem 19.3 on page 603 of Physics in Proportion, Vol. II, Mark A. Peterson

http://www.onlinetelemedicine.com/html/product/sam_images/X-Ray.jpg

How much of this works?

• Labs do get across the idea of VARIABLES that are functionally RELATED. For weak students, this is a big step, and maybe the most successful aspect of the course.

• Students are surprisingly tolerant of the use of history.

• Some students report more active thinking about their own perceptions of the world in physical terms, the kind of thing the course asks them to do again and again in problems.

What is class time for?

• I use just-in-time teaching. Students do a few short problems on a web page, I see their responses before class, and we go over them.

• I gradually realized that I didn’t have to lecture or derive things. Students were reading! We use class time for problems, group work, discussion.

To repeat!

• Physics starts with Archimedes and Galileo

• Its subject is proportionalities in Nature

• One of its main goals and uses is common-sense estimation, using known proportionalities, dimensional analysis, and a few important data, including natural constants