# PHY138Y - Mechanics - Class 10 - Monday October 17, 2005

## Introduction

" Science is facts; just as houses are made of stones, so is science made of facts; but a pile of stones is not a house and a collection of facts is not necessarily science."

-- Poincaré

## Test #1

The test is Tuesday, November 1, from 6:00 to 7:30 PM. Reminder: if you have a demonstrable conflict you must see Dr. Savaria in MP129E by Monday October 24.

### Format & Aids

There will be a multiple-choice section and a single long-answer question with multiple parts. I will announce more details about the test when we have met and finalised it.

The test is closed book. You may bring to the test:

• A non-programmable calculator without text storage capabilities
• A single 8.5 by 11 inch sheet of paper on which you have written anything that you wish.

You must bring your student card to the test.

### What Is Examinable?

All sections of the text and the Supplementary Material that are listed in the Syllabus for this quarter of PHY138 are "fair game" for the test. In general, we are more interested in testing your understanding of the concepts and how to apply them then in your ability to take some formulae and using them to "plug and chug" to a solution.

We have had In-Class Questions, MP Problem Sets, and a Written Homework assignment. You can expect to see some questions on the test that are at least similar to them.

I'm not sure if I have ever met an "average" student, but in the context of the final mark in PHY138 such an average student will receive a mark of 70. This is the marking standard used by U of T. The marking standard also says that about 15% or so of the students in a large class like PHY138 end up getting marks of 80 or better.

The final mark in the course has many components.

15% of the mark is from the various assignments:

• MP Problem Sets (6%). The software is designed so that almost all students end up with the correct answer, and in fact if a lot of students do not finally get the answer the designers view it as a flaw in the program. Thus the marks on these problem sets are very high.
• Pre-Class Quizzes (3%). These too are designed so that the marks are very high if you have read the textbook.
• Written Homework (6%). Since these are a group effort we expect the marks to also be very high.

So, we expect an average student to get about 13 marks out of 15 for these.

20% of the final mark in the course is from the laboratory. An average student will get about 70% in the laboratory, or 14 marks out of 20.

The Tests and the Final Exam count for 65% of the final mark in the course. In order for an average student to end up with a final mark in the course of 70, this student's score on the tests and Final Exam must be 43 out of 65.

The table summarises:

Performance By an Average Student
What Mark Out Of
Pre-Class Quizzes, MP Problem Sets, Written Homework
13
15
Laboratory
14
20
Tests and Final Exam
43
65
Final Mark
70
100

But, for the Tests and Final Exam 43/65 is just 66%. Thus the average student should end up with an average of about 66% on these.

Since only the best 3 out of 4 Tests are counted towards the final mark in the course, to end up with a total of 43 out of 65 requires that the average of each individual test is less than 66%.

We know that virtually all PHY138 students got very high marks in High School Physics, and are used to getting almost all of the questions correct on tests and exams. Thus it can be a bit of a shock when you confront your first University-level test.

If it is any consolation, you may wish to know that Test Theory says that the test that is most fair to you has an overall average of 50%, although we intend for this test to have a higher average than this. Nonetheless, a "hard" test really is the most fair one. You can learn more about this in a little document I wrote a few years ago; it is on the web here.

### What If We Screw Up?

More often than we would like, we set a test and are very surprised by how the class performed on it: sometimes it is much too easy and sometimes it is much too hard. So although we will try very hard to get a class average on the test to be a bit below 65% we (not you) may fail.

• If the average is higher than 66%:
• We will congratulate the class for knowing more than we thought.
• We will live with the marks and will not adjust them.
• If the average is lower than 60% or so:
• We will adjust the marks.

### Finally ...

If you are not doing as well on the test as you anticipated, don't panic. Chances are that you are doing better than you think. Staying calm and confident increases your ability to do as well as possible.

## Representative Assembly

 On Friday October 14 we met with Representatives from the tutorial groups to discuss issues of communication and organisation in PHY138. The link to the right summarises that discussion.

## Announcements

• MP Problem Set Chapts 10 - 11 released. It is due by 5 PM on Friday October 21.
• The Reference Frames subsection of §10.6 Elastic Collisions is deleted from the syllabus.
• The Mechanics home page the the Syllabus pdf have been updated.

## Today's Class

We began Chapter 10, but particularly because of the technical problems in Con Hall, did not finish it. We essentially got through §10.3. We will continue this next class.

## §10.1

The text has a lovely introduction to the concept of energy as a "natural money." The origins of this treatment go back to at least Richard Feynman, who was a master teacher and also won a Nobel Prize in physics.

 I recently wrote a little document with much in common with both Knight and Feynman's approach. If you are interested, it is available via the link to the right.

## Demonstration & Flash Animations

 We did a demonstration in class. A Flash animation of the the demonstration is available. We asked the class to predict that results of the demonstration before we did it. The overwhemling majority of the class chose answer 3: the balls finish at the same time

In-class discussion did not change this very much. We then did a demonstration that showed the the correct answer is that given in the above Flash animation: ball B which goes down the curved track finishes first.

 Some people find that thinking about the problem in terms of skiers instead of balls on a track is helpful. A Flash animation of this case is also available.

## The Gravitational Field

In class I introduced the concept of a field. Since this is not in the textbook here I will review that discussion.

 In Newton's original description of gravitation, the Earth exerts a force w on a mass m as a long-range action-at-a-distance interaction. However, it is possible to break the description of this interaction into 2 parts:
1. The Earth creates a gravitational field Eg at all regions of space around it.
2. If a mass m is placed at some point in space, the gravitational field exerts a force on the mass.

If, as usual, we choose the y axis to point upwards, then near the surface of the Earth we can say the gravitational field is:

Then the force exerted on a mass is the mass times the field:

This approach to forces will be used heavily in the 3rd Quarter of PHY138.

But we can begin to see the value of a field description now. We have been talking about the gravitational potential energy, and have also been discussing how the overall energy of an isolated system is conserved. But exactly what is the gravitational potential energy? It turns out that it is just as real as the other forms of energy, and is stored in the gravitational field.