Recently, I have written about the imortance of frequent problem solving for physicsstudents. Thomas Kuhn, the philosopher of science, wrote that:
Students of physics regularly report that they have read through a chapter of their text, understood it perfectly, but nonetheless had difficulty solving the problems at the end of the chapter. Almost invariably their difficulty is in setting up the appropriate equations, in relating the words and examples given in the text to the particular problems they are asked to solve. Ordinarily, also, those difficulties dissolve in the same way. The student discovers a way to see his problem as like a problem he has already encountered.
This post explores this idea, demonstrating the importance of two types of knowledge: subject knowledge and procedural knowledge in learning physics. I have used an example to demonstrate the knowledge involved.
This example is adapted from a lovely physics book: 200 Puzzling Physics Problems (with hints and solutions) by Gnadig, Honyek and Riley (2001). The puzzles (without the hints or solutions) can be found here.
A bottle of water is suspended from a fixed point by a inextensible rope. The bottle is set in motion and the system swings as a pendulum. However, the bottle leaks and the water slowly flows out of the bottom of it. How does the period of the swinging motion change as the water is lost?
There is a lot of knowledge hidden needed to solve this problem: Continue reading