In this TEDxWarwick talk, Cambridge University physicist David MacKay uses some back-of-the-envelope calculations to discus how Britain’s energy needs might be met without the use of fossil fuels.
Many of the calculations done in physics are horrendously complicated, not because they are intended to frighten children and small pets but simply because they have to be in order to get the job done. Not all calculations have to be like that to be useful. So-called back-of-the-envelope calculations, though very simple, can be useful for getting a reasonable idea of the scope of a problem or for finding a starting point. In the video, MacKay gives some examples of how to do this for a subject that is of tremendous importance to millions of people, most of whom have no interest in mathematics or physics.
Because alternative energy sources are such a hot topic, I hope to use his examples as a discussion point with some of my students. Sometimes they are baffled when a textbook question asks them to estimate a physical quantity. After becoming accustomed to solving problems that expect specific answers to be found using specific methods, they usually feel helpless when confronted with a question that appears to have insufficient information for them to work with and no exact answer to discover.
As a bonus, the video demonstrates the use of a log-log graph. I do not understand why students are not normally introduced to logarithmic scales shortly after learning a bit about logarithms.