We began with a follow-up to a discussion after Monday's class. In class I had written:
A student mentioned that his high-school teacher had written:
The high-school teacher's version has a virtue that mine does not: it has vectors on both the left and right-hand sides of the equation.
Mine has a sort of virtue too, however. A vector of truly zero length has an undefined direction, since any specification of the direction is the same zero length vector.
Thus, I think both of these ways of using mathematics to describe the addition of a vector and its negative are equally valid. Words with similar meanings are called synonyms: an example in English are the words stone and rock. So, the right-hand sides of both of the above equations are synonyms.
We finished our discussion of Chapter 2 with §2.7 - Freely Falling Objects. As part of this we also discussed the topic of model building, which in the text is in §1.11. We also talked about the lab experiment Free Fall; the Guide Sheet for the experiment is at http://faraday.physics.utoronto.ca/IYearLab/Intros/FreeFall/FreeFall.html .
Next we began Chapter 3. Because of the way we discussed Chapter 2 on Monday, we had already covered the material in §3.1 and §3.2.
We showed a Flash animation of a classic demonstration that motions in the horizontal direction are independent of motions in the vertical direction. You may access it with the button to the right. Separate window; 11k. | |||
We then worked through projectile motion, which is discussed in the text in §3.3. One emphasis was on using the seven-step list of Problem Solving which we introduced in Class 2. We also discussed how the 5th step, solving the equations, was "just" mathematics, and showed how software such as Maple or Mathematica could do the maths for us. The links to the right provide access to html versions of the output of the software for solving the trajectory of the object; each will appear in a separate window. For Maple, the user input is in red; for Mathematica it is in bold face. Despite initial appearances, the two solutions are identical and also agree with Eqn. 3.14 of the text. We still have to do the range for the projectile. |
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You may access the "Journal" file that I wrote during class by clicking on the button to the right. Separate window; 160k. |
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summary. |