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 3

6 Sep How to make an easy problem into a hard one:
(1) Try to find a formula to plug into.
(2) Do the entire problem in one line.
(3) Never draw a picture.
(4) Vector notation is just being fussy; ignore it.
(5) Paper is very expensive; half a page should be enough for an entire assignment.
(6) Never use words.
(7) Make the work sloppy and unreadable; this endears you to the grader.

Do some homework problems in detail, showing how I think they should be done:
(1) State explicitly what is given
(2) Sketch the problem.
(3) State what is to be found.
(4) THEN, start to work out the problem.

Talk about angles in three dimensions, latitude and longitude on the Earth and its analogs in math and science. The biggest difficulty here is drawing the pictures.

Start on the meaning of velocity, or more specifically, average velocity.

8 Sep The average velocity for something moving along a straight line is the distance (really displacement, positive or negative) moved along the line divided by the time it took to move there. The concrete example is a car moving along a straight road. Take some example distances moved between 12:00 noon and 2:00 p.m. To get the velocity at a particular time such a 1:00 p.m. you can't take such coarse information as a two-hour time interval; you have to take a short time period and measure what the car did in this interval. Perhaps from 1:00 p.m. to 1:01 p.m. (one minute), or to 1:00:01 p.m. (one second), or even less.

Re-state this in mathematical language. Let x( t ) represent the position of the car along the x-axis at time t. This notation means that x is a function of t, not x is multiplied times t! Instead of specific times such as 1:00 and 1:00:01, call these two times t and t + Dt.

The time interval is denoted Dt, so the algebraic representation of what I did above is

The mathematical process in which I took smaller and smaller time intervals is idealized to the word "limit." The instantaneous velocity of an object is then

vx = lim Dt ® 0  x( t + Dt ) - x( t ) Dt = dx dt

This is one of the only two equations in chapter two -- at least the only two worth bothering about.

The performance of a car is often expressed in terms of the amount of time it takes to get from 0 to 60 miles per hour. Five seconds would be pretty good. Ten is o.k. Quantitatively, this is a quotient:

For ten seconds, you get 6 mi/(hr sec).

For comparison, if you drop the car over a cliff, it will accelerate at almost 10 m/sec² because of gravity. If you want to compare this to either of the two numbers just above, you have to do some unit conversion. It beats them both.

Again, convert this into a mathematical notation paralleling the one for velocity. In the same Dt time interval, the velocity changes from v_x( t + Dt ) to v_x( t ). The average acceleration in this time interval is

As before, to get the instantaneous acceleration you have to take shorter time intervals, ideally taking the limit as Dt approaches zero:

ax = lim Dt ® 0  vx( t + Dt ) - vx( t ) Dt = dvx dt

This is the other of the two important equations in chapter two.