# PHY138Y - Mechanics - Class 11 - Wednesday Oct. 15, 2003

## Introduction

In Class 10 we discussed how the "Laws" of Physics are really just abstractions of the characteristics of various physical phenomena. Here is a statement of that idea, applied to the Law of Refraction (Snell's Law), by Ernst Mach in 1883:

“In nature there is no law of refraction, only different cases of refraction. The law of refraction is a concise compendious rule, devised by us for the mental reconstruction of a fact, and only for its reconstruction in part, that is, on its geometrical side.”

## Problem Set #6

This Problem Set is due Monday, October 27th by 5PM in the Drop Boxes.

 Since the problem set is due on the day before the test, I have selected Problems from the textbook for which full solutions are available in your Study Guide. Be disciplined, and do not look at the solutions before solving the problem. Looking at solutions to problems you have not attempted to solve will teach you nothing. Also, I strongly recommend that you do this Problem Set well in advance of the due date.

After attempting to solve the problems, you should compare your work to the solutions in the Study Guide.

### Supplemental Problem

In Problem Set #5 you investigated conservation of energy for six different simulated air track collisions, using the Flash animation at:
http://www.upscale.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/AirTrack/AirTrack.html

Verify that the horizontal component of the total momentum of the two carts is conserved for all six different collisions

## Announcements

### Future Classes

We have three more classes in which we will be discussing new Physics content: today, and next week Monday and Wednesday. In these classes we will finish our discussion of Chapter 7 - Potential Energy, and will then talk about Chapter 8 - Momentum and Collisions and Chapter 10 - Rotational Motion.

The class on Monday, October 27 will be a review for the test.

The class on Wednesday, October 29 will be a discussion of Error Analysis. This is a topic intended to help your understanding of the experimental aspect of PHY138, i.e. the laboratory.

The second section of the theoretical aspect of PHY138, dealing with the topic of Waves, will begin on Monday, November 3. The lecturer for this section will be Dr. Vatche Deyirmenjian.

### Wednesday Representative Assembly

The Representative Assembly for Wednesday's tutorials meets this week. Friday, October 17, 12 noon to 1 PM in MP713.

## Today's Class

We finished our introduction of potential energy.

We talked about §7.6 - Potential Energy for Gravitational and Electric Forces. In using the result of the gravitational potential energy to simply write down the electric potential energy, I stressed the similarity of the force laws except for the differences in symbols, such a -G and k. Thus, we simply changed the symbols in the gravitational equation to get the result for the electrical interaction.

We followed the textbook fairly closely for §7.7 - Energy Diagrams and Stability of Equilibrium.

We then began Chapter 8 - Momentum and Collisions by discussing §8.1 - Linear Momentum and Its Conservation. I stressed that the vector momentum is just what we were earlier calling inertia. Newton called the momentum the "quantity of motion" and in his statement of the second law he said that the force is proportional to the rate of change of the quantity of motion. In this correct view, then, F = ma is just a special case of constant mass.

The text derived that the total momentum of an isolated system is conserved for when the system contains 2 objects that are possibly interacting. We generalised to a system of 3 objects. You can then see how to generalise it to arbitrary numbers of objects.

 You may access the "Journal" from today's class by clicking on the button to the right. Separate window, 217k.