" To anyone who reflects on it, it soon becomes clear that F = ma by itself does not provide an algorithm for constructing the mechanics of the world. The equation is more like a common language, in which different useful insights about the mechanics of the world can be expressed. To put it another way, there is a whole culture involved in the interpretation of the symbols.
...when we hold up a weight— we definitely feel we are doing something, even though no mechanical work is performed. Force is an abstraction of this sensory experience of exertion. D'Alembert's substitute, the virtual work done in response to small displacements, is harder to relate to. (Though ironically it is a sort of virtual work, continually made real, that explains our exertions. When we hold a weight steady, individual muscle fibers contract in response to feedback signals they get from spindles; the spindles sense small displacements, which must get compensated before they grow..."
Walter Noll. On the concept of force (April 2007)
" When applied to the rest of classical mechanics, Wilczek’s statement is absurd. For example, engineering students often take a course called “Statics”, which deals with forces in systems having no moving parts at all, and hence accelerations are completely absent. The beginning of a textbook on statics often contains a statement of Newton’s laws, but this functions like a prayer before a business meeting; it is almost totally irrelevant to the substance of the subject. The substance of statics consists in singling out parts of the system under consideration by drawing “free-body diagrams”.
For suﬃciently many of such parts, one writes down two equations: The ﬁrst states that the sum of all the forces acting on the part is zero, and the second that all the torques acting on the part is zero. In this way, one obtains suﬃciently many linear equations to determine the force acting on each structural member of the system. This information is then used to decide whether the system may or may not collapse.
Engineering students often also take a course called “Dynamics”. Its basic structure diﬀers from the course in statics only by including the inertial forces among the forces considered. (I have taught courses on Statics and Dynamics in the late 1950s, and this experience has inﬂuenced my analysis of the foundations of mechanics.) The two basic principles of classical mechanics are these: 1) Balance of forces: The total force acting on a physical system and each of its parts is zero. 2) Balance of torques: The total torque acting on a physical system and each of its parts is zero."