PHY138Y - Mechanics - Class 7 - Mon. Oct. 4, 2004


"Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago.”

John Maynard Keynes (1963)


Second Pre-Class Quiz

The Pre-Class Quiz due last Wednesday was completed by 1001 students. This is almost the entire class, so the access problems some of you experienced seem to have been mostly resolved.

The average on the quiz was 93%. This is reasonable, but we hope that as you get used to these quizzes it will go even higher!

Reminder: all Pre-Class Quizzes only test the sections of the textbook for the coming week that are listed in the Curriculum for the course. Sections that are not listed in the Curriculum are not discussed in class, and their content is not tested either on Pre-Class Quizzes or the Tests and Final Exam for the course.

MP Problem Sets

MasteringPhysics has been used for a few years by dozens and dozens of Universities. Both students and profs have very positive things to say about the software, and a study by Ohio State with one of their big 1st Year courses indicates that it is twice as effective as traditional written problem sets in learning Physics.

Sadly, as use of the software has expanded to more and more Universities, various problems in scaling up their servers and software have been encountered. These include:

We are in contact with the vendor, who promises that these difficulties will be resolved.

I can see statistics on how you collectively are doing on the assignments, including the percentage getting the problem correct, the number of wrong answers, the number of hints you used, and how long the question and the overall assignment took the class. I can also see the same numbers for all students from other Universities who have used the software over the past few years: these involve tens of thousands of students.

Here are the percent correct and average time to complete the questions for the first assignment, due on Sept. 24. For PHY138 this is for 1025 students, essentially the entire class.

First MP Problem Set Statistics
Question PHY138 Others Comment
Dimensions of Physical Quantities
99% correct
5 minutes
97% correct
6 minutes
Geometric vs Componentwise Vector Addition
94% correct
22 minutes
91% correct
18 minutes
Running Vectors
98% correct
3 minutes
96% correct
3 minutes
Tossing Balls Off a Cliff
100% correct
5 minutes
100% correct
4 minutes
Overcoming a Head Start
90% correct
9 minutes
84% correct
10 minutes
An Object Accelerating on a Ramp
100% correct
6 minutes
98% correct
5 minutes
Total Time to Complete
50 minutes
46 minutes

Here are the same numbers for the second MP Problem Set, due last Friday. This is for 1015 students.

Second MP Problem Set Statistics
Question PHY138 Others Comment
A Mass on a Turntable
97% correct
2 minutes
98% correct
2 minutes
Pulling Two Blocks
100% correct
3 minutes
99% correct
3 minutes
See Note 1 below
Conceptual Questions on Newton's Laws
91% correct
19 minutes
89% correct
14 minutes
Hanging Chandelier
77% correct
9 minutes
80% correct
9 minutes
See Note 2 below
Pulley Tutorial
96% correct
14 minutes
96% correct
10 minutes
Applying Newton's Second Law
91% correct
26 minutes
88% correct
23 minutes
Total Time to Complete
73 minutes
60 minutes
See Note 3 below

Note 1: This problem accepts this form of the correct answer:

T - m_2 * g * sin(theta)

But it will not accept the equally correct negative of this:

m_2 * g * sin(theta) - T

This is a defect in the software which we have reported.

Note 2: One form of the correct answer is:

mg/( sin(theta_1) + sin(theta_2) * cos(theta_1)/ cos(theta_2))

However, at least early on Thursday afternoon September 30 the program would not accept it, and in fact couldn't even parse this answer. Later that afternoon it started accepting this answer as correct. Not only is this difficulty reported, but I have been strongly complaining to the vendor about this.

Note 3: This was a little too long. The problems discussed in the above 2 notes may be partly responsible. In addition, we know that their servers had some stability problems last week: sometimes a question would not be displayed, sometimes it would only be partly displayed, sometimes we got the dreaded "Page not found" error message. I'm complaining strongly to the vendor about this too.

What do we do?

I think we should be optimistic about MasteringPhysics solving their difficulties, and give the software another couple of weeks. Then we will re-evaluate.

If these difficulties are resolved, it seems clear that your marks on MP Problem Sets will end up close to 100%, as they should. We will try even harder to insure that they take you no more than one hour to complete, preferrably a bit less. And, finally, we believe that if it functions acceptably the software really will help you learn some Physics.


Nature (and/or the way our minds think about nature) measures angles in radians, not degrees. So does MasteringPhysics. Thus:

sin(90 + theta)

is probably not going to be interpreted as you wish.

sin(pi/2 + theta)

is probably what you meant.

Also, only just over half of you (565 students) have done the Introduction to MasteringPhysics non-credit assignment. There you will learn about this and much more useful information on how to use this software. If you have not done so, I strongly recommend you do this assignment. It should take you about 20 minutes.

Labs Begin

The laboratory begins on the day after Thanksgiving. The first laboratory is for section P0201, which meets Tuesday, October 12 at 2PM in MP125/126.

The P0101 lab section begins the same day at 6PM; for students in this section, the next laboratory will be on Monday, October 25 at 2PM.

Check the lab's web page at to determine:

  1. Your lab section and group
  2. Your first experiment

Drop-In Centre Starting

Starting the Tuesday after the Thanksgiving break, the Drop-In Centre will begin at 10 AM. This is a place where you may go to discussion any question you have about Physics. It is staffed by Teaching Assistants from all the first year courses.

The Drop-In Centre is located in McLennan, MP200. This room is on the "cat walk" on the 2nd floor, directly over the main lobby for the building.

You may see the timetable for when the Centre is open at:

Next Representative Assembly

The next Representative Assembly will be with the Representatives for Friday's tutorials. It will meet on Friday, October 8, from 12 noon to 1 PM in MP713. This room is on the 7th floor of the tower.

Written Homework #4

Note that because the University is closed on Monday, October 11, this homework is due in the Drop Box for your tutorial group by 5PM on Tuesday, October 11. It is in pdf format.

In-Class Questions

We asked a question about a man stepping off a wooden box in a totally sealed metal box sitting on a scale.

For Part A, about half the class answered 2) It is less than before he stepped off the box. and about 40% answered 3) It is the same as before he stepped off the box. In-class discussion did not change these numbers significantly, so I explained that the right answer is 2. Then for Part B, about 80% of the class correctly answered 1) It increases and then returns to the reading before he stepped off the box.

We also asked a question about a ball shot off the top of Mount Everest. About half the class correctly answered 2) approximately g


Scalar or Dot Product

We used a Flash animation in our discussion of the scalar or dot product of 2 vectors.

About Integrals

We know that most of you did not cover integration in Grade 12. We also know that MAT135, which most of you are taking, will not get to this topic until January. So, you will not be asked to know how to do the mathematics of integration until then. Meanwhile, however, there is a common circumstance in which we want to find the area under some curve. We will use the language of mathematics to describe how to do this.

The technique is to take the sum or the areas of a number n of rectangles which are under the curve, and realise that as n goes to infinity this sum goes to the actual area under the curve. This limit is the same as saying the width of the rectangles x goes to zero.

In §6.4 of the text, we are finding the area under a plot of the force F versus displacement x using this infinite sum of infinitesimal rectangles.

Symbolically, we write this sum as shown to the right.
Of course, eventually we get tired of writing out all of this, so introduce a shorthand notation:

So, the integral sign only means an infinite sum, and its shape is a stylised S for sum.

I have written a Flash animation illustrating this. For our purposes we only need the first "scene" of the animation.

You may recall that in Figure 2.1 (c) of the text, the distance was found by calculating the area under a plot of v versus t. We can use our new language to say the the distance is the integral of the instantaneous speed over the time.

Robert Hooke

Robert Hooke was working on the same problem as Newton at the same time: what is the relationship between forces, masses, accelerations and gravity. They were bitter rivals. Here is a fragment of a statement by Newton about Hooke:

“This carriage towards me is very strange & undeserved, so that I cannot forbeare in stating that point of justice to tell you further … he should rather have excused himself by reason of his inability. For tis plain by his words he knew not how to go about it.”

Newton won the competition, and today we tend to only remember Hooke for his discovery about the relation between the force a spring exerts on an object and how much the spring is stretched. If you are interested, you can learn more about this remarkable man at

Here is a Flash animation illustrating his "law" about springs.

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