PHY138 - Mechanics - Class 4 - Wednesday, September 20, 2006


“One of the biggest problems is how to state the problem. It's an old saying that the minute you can state a problem correctly you understand 90 percent of the problem.”

-- John A. Wheeler (physicist)

Today's Class

The syllabus as given in the Mechanics home page has slipped a bit. I will try to get it back "on track" over the next couple of classes. Today we finished Chapters 2 and 3.

In-Class Questions

We asked some questions in class. A pdf version is available via the button to the right; as usual it will appear in a separate window.
For the first question about the Runner and the Bird, initially about 55% of you got the right answer. The histogram to the right shows the distribution

After discussing it amongst yourselves, almost 90% of you got the right answer. The distribution is shown to the right.

One of the lessons from this question is that if one tries to Solve the problem before thinking about it one can end up with a terrible mess involving an infinite series. However thinking about the problem and trying to Guess the answer can make it clear that (B) is the correct answer without needing to do any mathematics at all. This is one reason why the Guess step is part of the "official" Problem Solving strategy we discussed last class.

For the question about a direct measurement of the instantaneous velocity, the class was split. I discussed why I believe that such a measurement is not possible.

Note: the "clicker" software gives me the histogram just as shown to the right. For the two previous histograms, I labelled the axes by hand. I will probably not continue doing this. For all such histograms the vertical ticks are every 20% of the respondents, and the horizontal ticks are the letters A, B, C, D and E respectively.

The final question about throwing two balls had the result shown to the right. If you are among the 30% who missed this question, I urge you to find out why answer (C) is correct.

Stop To Think 2.2

We discussed how the "correct" answer to the text's Stop To Think 2.2 on page 49 is misleading. The answer (c) has two discontinuous breaks in the graph of speed versus time. This is not correct: classical Physics assumes that the world is continous.

Putting the same thing is more mathematical language, classical Physics assumes the the speed as a function of time must be differentiable for all values of the time.

Either way, the "breaks" in the plot should be drawn more smoothly. I have brought this to the author's attention, and he intends to correct this for the next edition of the book.

All Flash All The Time

Here are links to the Flash animations we used in class today:

Visualisations similar to Figure 2.29 of the text Theory of Intelligent Falling
Introducing the integral sign. We only used the first "scene" of this animation. Theory of Intelligent Falling
Flash animation of adding two vectors. Theory of Intelligent Falling
Flash animation of adding three vectors. Theory of Intelligent Falling
Flash animation of subtracting two vectors. Theory of Intelligent Falling
Flash animation of vector addition by adding components. Theory of Intelligent Falling
Flash animation about unit vectors. Theory of Intelligent Falling

About Integrals

I stressed this in class, but it is perhaps worth stressing it again:

We will be using integrals as part of our language in describing the world. You will not need to know the mathematics of integration until MAT135 gets to this topic in mid-January.

Other Class Materials

Here is a pdf of the PowerPoint we used on the side screens today.
Here is a pdf of today's Journal.

Suggested Problems

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