Final answer:
The magnitude of the static friction (fs) is less than or equal to the product of the coefficient of static friction (μs) and the normal force (N) while there is no motion, leading to the correct option being c) (fs < N).
Step-by-step explanation:
When discussing the relationship between the magnitude of the static friction (fs) and the normal force (N) while there is no motion between objects, it is crucial to understand the role of the coefficient of static friction (μs). The coefficient of static friction is a dimensionless value that represents the amount of friction between two surfaces before movement starts. The inequality fs ≤ μs N illustrates that the static friction is less than or equal to the product of the coefficient of static friction and the normal force. This means that the static friction can adapt up to its maximum value, which is determined by the normal force multiplied by the coefficient of static friction, to prevent any motion between the objects.
In simplified terms, when no motion is present between objects, the frictional force will only be as large as necessary to prevent movement, up to a maximum value dictated by the coefficient of static friction and the normal force. Hence, the correct option about static friction in the absence of motion is option c) (fs < N), signifying that the static friction is always less than or equal to the normal force but never greater.