III: A Complaint about a-Level Examination Questions in Applied Mathematics

Extract

According to orthodox teaching texts the tangential component of the reaction between two surfaces in contact is μ times the normal component when slipping is just about to take place. The tangential component cannot exceed this value, so it is asserted, and is equal to this value when slipping is occurring. The coefficient μ is a property of the surfaces in contact and is a constant, independent of the normal component. This may be a basis for some mathematical exercises, but typical texts even go so far as to say that these statements are true within the limits of experimental error (see for instance Quadling and Ramsey, Elementary Mechanics Vol. I, Bell, 1963, p. 58). Yet no experiments on this are normally performed or discussed in schools. One could argue that since the coefficient varies according to the nature of the surfaces it is so particular as to be not worth measuring, but this would equally justify not doing any exercises on the idea.