These are excellent ideas. Thank you Momentum, energy, and angular moment are all conserved but you would not guess that from the chapter headings. (The text is better). I should fix that, so people do not suspect that I am not discussing conservation laws. I have done symbolic manipulation homework for freshman E&M, using Mathematica, where there were some natural problems. E.g. We have a cube of 12 resistors. We put 1 volt between opposite corners. (picture labelling R1 through R12). Resistor Rn is an n ohm resistor, so no two resistors have the same resistance. What is the current though the voltage source?

I might try computer late in the course for coupled masses. It's a good idea. I am a bit concerned about overloading the students. You haven't seen the labs yet.

On a different note, I do not copy the past when this appears to be a bad idea. As discussed in the project updates, consider

Newton's Third Law

I have made it a point to think about what is being said, as opposed to paraphrasing what has been said before. As an example, a discussion of Newton's Third Law of Motion: And now we reach the \emph{Third Law}. My statement of the Third Law is quite different from the one you will of encountered elsewhere. It does have exactly the same content. However, the point of having the Third Law is to get across a certain amount of information, not to repeat the not very good English translation from centuries ago of Newton's original book, which was, of course, written entirely in Latin in the form of a plane geometry text. The Third Law tells us that: All forces come in action-reaction pairs. If we call the two forces of an action-reaction pair $\vec{F}_{1}$ and $\vec{F}_{2}$, their properties are as follows. 1) The forces of an action-reaction pair are always on two different bodies. Two forces on the same body are never an action-reaction pair. 2) The forces in an action-reaction pair are equal in magnitude, so that $F_{1} = F_{2}$. The forces in an action-reaction pair point in opposite directions, so that $\mathbf{\hat{F_{1}}} = -\mathbf{\hat{F_{2}}}$. As a result, $\vec{F}_{1} = - \vec{F}_{2}$. 3) The forces in an action-reaction pair have the same physical basis. What do I mean "physical basis? The answer will become clearer after further discussion. 4) The action and reaction forces are simultaneous. By 'simultaneous' I mean that it is incorrect to say which force is the action force and which force is the reaction force. The two forces always come as a pair. However, if we call one of the two forces the "action force", then the other of the two forces is the "reaction force", but it does not matter which of the two forces we call the action force. As a modest qualification, if one studies for example intermolecular forces there are also \emph{three-body forces} in which three objects put a force on each other that cannot be split into a trio of pair forces. Three-body forces are actually quite important in dealing with properties of, for example, liquids. Trios of noble gas molecules form triangular clusters that are not held together by the short-ranged pair van der Waals force. For this course we will stay with two-body forces. That's quite enough. Some critics of Newton propose that Newton's laws are actually content-free. That is, the way we know that there is a force is that there is a response, an acceleration or other forces, and therefore the Second Law is a definition, not a scientific law. We could imagine how this claim could be true. People have put into orbit around the earth thousands of earth satellites. If the force between each earth satellite and our planet was different from the force on each of the other satellites, so that corresponding to each earth satellite there was a different law of gravity determining its orbit, the laws of gravity would be little more useful than a list of the positions of and velocities of each orbit at different times. That's not what happens. Instead, there is one law of gravity, with all satellites being subject to the same law of gravity. There is one gravitational force that rules them all and in their orbits binds them. By introducing the correct forces, we take a huge numerical description of planetary orbits, and reduce it to a few equations and a small number of constants. That's a strong argument that forces are real, and that we more or less know what they are. The reality, a third of a millennium after Newton did his work, is that a very small number of forces and a few other bits and pieces describe a huge number of natural phenomena.