A question, but some preliminaries in order to avoid answers involving concepts not yet introduced in the text I'm reading--Den Hartog's Mechanics.
Near the very beginning of his book, Den Hartog tries to articulate the intuitive notion of (i.e., some might say 'defines') 'mechanical contact force' in his introductory comments on statics (page 3):
"If there is any doubt as to whether there is a mechanical contact force between two bodies, we may imagine them to be separated by a small distance and a small mechanical spring to be inserted between them, with the ends of the spring attached to the bodies. If this spring were to be elongated or shortened...there would be a direct contact force."
In relation to springs, he notes that a 'dynamometer", "force meter" or what we might call a 'scale' is used for the practical measurement of force:
"In a spring the elongation (or compression) is definitely related to the force on it so that a spring can be calibrated against..."
He then states (p.4) the first axiom of statics AKA Newtown's third law. He gives about the simplest possible illustration of the axiom: a book at rest on a table, stating
"the push down on the table by a book is equal to the push up on the book by the table."
(a still simpler case, I suppose, would be book resting on earth)
"Thinking about our imaginary experiment of inserting a thin dynamometer spring between the book and the table, the proposition looks to be quite obvious: there is only one force in the spring."
I'm puzzled by this last (bolded) comment. Let me try to be more specific. I've seen this experiment (both in thought and laboratory) described a little differently: In what I recall, two (not one, but two) spring-operated scales are hooked to each other, back-to-back -- i.e., one connected to table, the other connected to the book, and the two scales connected to each other in the middle. In this type of arrangement, one scale measures the push of the book, and the other measures the push of the table, and we find (consistent with the Third Law), that they come out equal.
Each of those two equal forces acts on the connected spring system in opposite directions and everything remains at rest as expected.
It's also clear that you can think of this connected double-spring system as a single spring, essentially no different than Hartog's set up, with the exception that this arrangement has two force measuring pointers, one at each end.
Again, it is really his conclusion that the third law in this case is obvious or makes sense because
"there is only one force in the spring,"
that I find as odd. Is it even a true statement? What I think is true is that the spring measures the force acting on it by the book (from above) and the opposite and equal force of the table (from below) and is therefore at rest. There are two forces (from two different objects) acting on one object (the spring).
Any thoughts appreciated!