Suppose you are teaching an introductory-physics course. You ask your students to consider a box on a rough, level surface that remains at rest while a horizontal 30 N force is applied to it (see figure 1a). Your students seem to recognize that because the box is at rest, the frictional force must be equal in magnitude to the applied force. Using that realization, they correctly deduce that neither the mass of the box nor the coefficient of static friction is relevant for determining the magnitude of the frictional force.
As an instructor, you might be tempted to celebrate that little instructional victory. But then you ask your students a follow-up question about two identical boxes on surfaces with differing roughnesses, as shown in figure 1b. Both boxes remain at rest when pulled by horizontal forces of equal magnitude. You notice that many students seem to abandon the...
