| 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 |
2 Oct Friction and its (approximate) properties. Demonstrate how static friction works, and do in some detail the problem of finding the limiting angle at which a mass can sit on an incline. From this, compute the coefficient of static friction for the given surfaces (aluminum on aluminum).
Demonstration: the Atwood machine, two masses hung over one pulley. Set up the equations of motion for it, though I didn't get to finish them off. Emphasize: This problem has two masses, so you go through F=ma twice.
4 Oct Circular motion. Derive the acceleration of an object moving on a circle at constant speed. I did this by going back to the definition of acceleration and then to the definition of a derivative. The geometry got a little difficult at one point, as there is one useful geometric result that a lot of people didn't remember: The arclength along part of a circle obeys the equation s = rq, when q is measured in radians. [More generally it would be s = krq, where k is one only if you are using radian measure for angles.]
Apply it to swinging a bucket of water overhead. Apply F=ma to to water in the bucket. The only forces on the water are from (1) gravity and (2) bucket.
In order that I don't get wet, the bucket has to apply a force to the water: Fbucket > 0. This gives an inequality for the speed, v > ( g r )1/ 2.
6 Oct Do a homework problem in detail.
Discuss the confusing terms "centripetal force" and "centrifugal force."
The first is just a way to state that some other force
(gravity, a string, whatever) is pointing toward the center of a circle.
It's a pretty useless term.
The second is more important and more confusing. Recall that Newton's first law is really a way to define what in inertial coordinate system is: "if no forces act on an object and its acceleration is zero, then you're in an inertial coordinate system." Newton's second law says that IF you're in an inertial coordinate system, then F = ma.
But what if you aren't in an inertial system. If you are rotating, as the Earth does, then in that system F does not equal ma. But then what replaces it? The answer is that you have to patch up the equation by adding a couple of new terms call "centrifugal" and "Coriolis" forces.
We will not do this. F = ma is quite good enough for now.
The conical pendulum. The only forces acting on the mass swinging around are (1) gravity and (2) the rope. Pick a simple basis and write these forces in this basis. The acceleration is v2/r toward the center of the circle, so that tells me the other side of the equation. Break the vectors apart to get the equations
It's not so easy to measure the speed of the mass, it's much easier to measure its period (the time it takes to go around). Try to solve for that.
are the two equations that let you eliminate the extraneous variables. The result, after some manipulation, is
The next step is to compare this with experiment.
