RES.8-005 | Fall 2012 | Undergraduate

Vibrations and Waves Problem Solving

Instructor Insights

Coming Full Circle in Problem Solving

In this section, Wit Busza shares his insights about the importance of hands-on lab experiences in physics.  

A common problem I see is that often undergraduate students have the preconceived idea that problem solving is the same thing as memorizing equations. At the high school level, students remember formulae for solving a finite number of problems, such a falling ball, a ball on an inclined plane, a current going through a resistor, etc. They might obtain good grades by memorizing the answers, but it’s very rare that a student can get much further simply by memorizing formulae.

"It is only laws of nature that will tell us what will and will not happen—it’s not the computer programs that solve equations that give us this information."
—Wit Busza

Even at the university level, I think students do not have enough opportunities to come full circle in problem solving—that is, to implement experiments to test the accuracy of the predictions they derive from their equations. When I was a student, I studied at London University. As an undergraduate, for two years, I had nine hours of laboratory a week. Now, we probably overdid it, but lab experiences seem more impactful than computer simulations. I am not sure if a student looking at a simulation is amazed that mathematics can be used to predict nature. I think simulations make it seem like it’s all mathematics, like there is no nature. With simulations, I don’t think students, as a rule, put together the two parts of physics problem solving. I think this is the price one pays for the technology that’s available today. Fortunately, the current Technology-Enhanced Active Learning (TEAL) format of Physics I and II at MIT is offering undergraduate students more opportunities to engage in hands-on physics labs.

This is important, because I don’t think the average MIT freshman even considers the possibility that if they do the experiment in the problem set, the outcome could be completely different from what they initially expect. For example, suppose I have a chimney, a big chimney. And suppose it gets pushed, and suddenly it flies up, rather than falling to the ground. I don’t think the student even considers that that could happen. Or suppose I put a cup full of water in the oven, left it there for some time, and ice came out. You’d say that would be crazy! But, at the level of subatomic physics, analogous phenomena occur. Or, consider this example that I experienced myself: In my yard, there was a tree, which was about 3 inches in diameter. I cut it with a chainsaw. Because it wasn’t a very big tree, I wasn’t very careful. What do you think happened after I cut the tree? You would probably say something like, “I think it would fall to one side or the other.” That’s the natural inclination. But that’s not what happened. I almost hurt myself, because the tree doesn’t do that; it actually kicks back, which follows from the laws of conservation of angular momentum. It is only the laws of nature that will tell us what will happen in reality in our world and what will not happen. The mathematics simply describe the operation of the laws of nature.

Course Info

As Taught In
Fall 2012
Learning Resource Types
Lecture Videos
Problem Sets
Instructor Insights