Linear approximation and school mechanics

Extract

Oxbridge Tripos examination questions originating from the turn of the century have had a marked effect on the teaching of mechanics both at School and at University. These questions, reproduced in the standard textbooks of the day, were the stable diet of the undergraduate population over so many years and set the pattern for a style of question in which the student applies mechanical principles by rote without ever questioning the validity or relevance of those principles. An unfortunate consequence of this state of affairs is that mechanics has been largely overlooked as a vehicle for the teaching of mathematical modelling. There have been moves recently to make questions more “relevant” and it is not unknown to see illustrations of “real” boats, shotputters etc. However, the student is still expected to answer the question “mechanically”, if the reader will excuse the pun, without any discussion of the modelling process. How refreshing it is, even with first year undergraduates, to look at the problem of a tin can being knocked off a wall by a bullet and, instead of asking the students to apply two conservation laws in order to determine the speed with which the can hits the ground, to ask under what assumptions the two conservation laws would appropriately model the physical situation? It is quite staggering how the lecture theatre erupts with ideas, suggestions and interest.