Class Notes for Fall, 2000

Week of Aug 23 Sep 6 Oct 2 Nov 6 Phy 205 page
Aug 28 Sep 11 Oct 9 Nov 13
Sep 18 Oct 16 Nov 20 Notes for Fall, 1999
Sep 25 Oct 23 Nov 27
Oct 30

Phy 205, Week 10

23 Oct Review of the relationship between forces and potential energies:

Fx = - dU/ dx.

This leads to a conservation form of the work-kinetic energy theorem:

m v2/2 + U( x ) = E = constant.

I spent some time interpreting this and showing how you can use this to get a qualitative understanding of the motion of a mass subject to such a force. One example was the motion of the atoms in an H Cl molecule. If the molecule is disturbed, the atoms can vibrate about their equilibrium position. If they are disturbed enough, the molecule can be broken apart (dissociation).

Another example, one that we will be able to do quantitatively, involves a mass hanging on a spring. The potential energies come from gravity and from the force by the spring.

Branching over to another subject, work and energy in three dimensions. Tipler tries to make too large a leap, from one dimension constant force to three dimensions non-constant force. I prefer to separate the issues. One dimensional non-constant force is what I have spent the last couple of days on. Now, examine three dimensional constant force.

To do this, i went back to the same sort of analysis that led me to the work-energy result in the first place. I manipulated the basic (constant) force equation and its results into the relation

F · Dr = F · ( r - r0 ) = m v2/ 2 - m v02/ 2.

This is where the dot product appears.

25 Oct A brief recapitulation of the basics of kinetic and potential energies, restating the meaning of the dot product and its interpretation.

Various forms that energy can come in: kinetic, potential, heat, light, sound, chemical, mass, ...
Some of these are really variations on the same idea, for example heat in a gas is just the random motion of molecules, so it is just a form of kinetic energy. It is however convenient to treat it as if it is different.

The example of a cart going through a toy roller-coaster. Show the demo, and then work out what is needed so that the cart will go all the way over the top without falling off the tracks. I used both conservation of energy and F=ma.

Power. Its definition as dW/dt and then a discussion of the various units that it (and energy) come in.

27 Oct Power of just living: metabolism. This depends on the individual, but an average value is somewhere around 2000 kcal per day. The kcal, kilocalorie, is the dietician's Calorie. To compare this metabolic power to something else, I have to convert it to a standard set of units, the Watt = Joule per second.
2000 kcal
day
x 1 day
86400 sec
x 4200 Joule
1 kcal
= 100 Watts
Demo: bring out a bicycle rigged to generate electrical power to run some light bulbs. How difficult is it to double your power output? For comparison, Florida Power and Light charges somewhere aroung 5 or 10 cents per kilowatt-hour. This is 3,600,000 Joules.

Collisions. Look at inelastic collisions again, but this time examine the results for the energy loss. After solving for the final velocity, compute DK = Kafter - Kbefore.

Look at various special cases to see if the result makes sense, and also to learn what it's trying to tell us.


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