# Confusion about terminology related to tension force and Newton's third law

Consider a car pulling a trailer with a tight string between the two objects. The car is moving at constant velocity. If we consider the car as a separate system from the trailer, we can state, based on Newton's third law, that the car pulls on the string, and the string pulls on the car with an equal force in the opposite direction. The force equals the tension on the string.

If we consider the string to be massless, the same tension force will pull on the trailer, and the string/trailer will form another force pair in accordance with Newton's third law.

Now let us consider the car and trailer as just one system. The tension force now becomes an internal force. In one of my textbooks, the following statement is then made for this scenario:

"The Tension force $$T$$, which acts on the trailer, has a reaction force $$T'$$ which acts (via the massless string) on the car. Both of these forces act between internal parts of the system when we choose the car and the trailer to represent just one system: they are internal forces. All internal forces occur as action-reaction pairs. According to Newton's Third Law, the forces in such an action-reaction pair are equal. As such, the net sum of the internal forces is zero".

I find this statement slightly confusing, in particular the first sentence. I have always assumed that when dealing specifically with contact forces, Newton's Third Law is valid for the two objects which are actually in contact. It therefore makes sense to me that when the forces between car/string and the forces between string/trailer are considered, Newton's Third Law applies. However, from the statement above, it seems to me that now the entire string is completely igonred as a phyhsical object, and it is now claimed that it is between the car and the trailer that Newton's Third Law applies. Even though, technically, these two objects are not directly in contact. Is this because, as we now consider the car and the trailer as just one system, we can simply ignore the massless string as a physical object, and, in a way, almost "pretend" that the car and the trailer are in direct contact?

If someone can clarify this for me, then I will greatly appreciate it!

• Your are right, they are not action reaction pairs. It is an abuse of language, only useful because the cord is massless and you then can imagine it as providing a mechanism for long distance interactions. More confusing than helpful. Commented Aug 27, 2023 at 4:39
• @Pato Galmarini: Thank you so much for your answer. Good to hear that my criticism of the textbook language is valid! Commented Aug 27, 2023 at 7:48

Because the string is massless the net external force on it must be zero and so the magnitude of the external force $$F_{1\rm T}$$ ( force on molecule 1 due to trailer) must be the same as the magnitude of the external force $$F_{3\rm C}$$ and they must be opposite in direction.
That being said then all the forces shown in the diagram are often called "tension" and the string just having the external forces labelled $$T$$.