Understanding Newton's Laws: The Confusion Between II and III Revealed

[vco]

I am not a teacher, but I have made an interesting observation regarding classical mechanics education.

It is surprisingly common that even students at academic level do not seem to fully understand Newton's third law (action and reaction) and confuse it with Newton's second law (equilibrium/motion), apparently due to the algebraic similarity when the net force is zero. An example of this is mistaking gravitational force and supporting force as an action-reaction pair.

I believe a possible contributing factor to this confusion might be poorly chosen terminology in the English language.

The force acting on a body is referred to as the "action" and the equal but opposite force acting on the other body is referred to as the "reaction". However, especially in engineering, the known forces on a body are referred to as "applied forces" or simply "loading" and the unknown forces on the same body (forces at the supports) are referred to as “reaction forces”. The semantics imply that the applied forces and the reaction forces are action-reaction pairs, which is of course untrue.

In my native language (Finnish), the action-reaction pair is referred to as “force and counter-force”, and therefore the terminological confusion does not arise.

What do you think, is the English terminology confusing?

 

[DoItForYourself]

Indeed, this is an interesting observation.

Perhaps, another name for the forces at the supports would be a good idea.

 

[vco]

Perhaps, another name for the forces at the supports would be a good idea.

That would be the obvious solution. However, the problem is that the terminology is quite well-established in the scientific community. It would not be easy to get people to start using a new expression for the forces at the supports that does not contain the word “reaction”.

 

[PeroK]

I am not a teacher, but I have made an interesting observation regarding classical mechanics education.

It is surprisingly common that even students at academic level do not seem to fully understand Newton's third law (action and reaction) and confuse it with Newton's second law (equilibrium/motion), apparently due to the algebraic similarity when the net force is zero. An example of this is mistaking gravitational force and supporting force as an action-reaction pair.

I believe a possible contributing factor to this confusion might be poorly chosen terminology in the English language.

Langauge may be a contributing factor - especially as "action" and "reaction" are slightly obscure terms for force.

But, I think the concept itself is not that intuitive. We can all push things without being aware of the reaction force. One person can push another to the ground without themself also falling over!

Also, I think it is easy to imagine a central body that pulls all other bodies towards it without itself being pulled. It was a real insight of Newton that a one-way force of this nature is not possible. Again, someone standing on the Earth can pull a vehicle towards them without moving, so there's not a solid intuitive basis for Newton III.

 

[DoItForYourself]

I agree that many people cannot initially understand Newton III because it is not intuitive.

However, I think that someone who has a deep understanding of Newton III (even if it is not intuitive), will not be confused because they know that the forces of the pair action - reaction cannot be applied in the same object. For example, when calculating torques in a seesaw, they cannot consider the reaction force of the support equal to the weight of the seesaw, because they are both applied to the seesaw.

Finally, if I was asked to change the reaction force term with another one, I would use a term with an additional word (for example reaction-support force), in order to maintain the older term.

 

[robphy]

When I teach Newton's Third Law, I avoid the use of "action" and "reaction" altogether... because of the misuse of those words and because it's not very useful in that form.
I prefer "the force on A due to B" is equal to "minus the force on B due to A": $\vec F_{\scriptsize\mbox{on A, due to B}}= - \vec F_{\scriptsize \mbox{on B, due to A}}$. So, there is an indication that these are not forces on the same object (as they would be in applying Newton's Second Law).
In addition, I emphasize the force-pair forces must be of the same type [e.g. both gravitational or both normal, but not one gravitational and the other normal].

There are some books (like Moore's Six Ideas That Shaped Physics and Chabay&Sherwood's Matter & Interactions) that emphasize "momentum transfer" as the essence of the Third Law.

 

[physbits]

I am a high school teacher and yes, this is a very common problem.

Similar to the above, I tell my students that
(1) Third law force pairs mean two forces of the same type, (ie both gravitational, or both magnetic, or both contact, whatever) acting between two objects
(2) Second law force pairs act on the same object and may be of different types.

At least at HS level this seems to help

 

[robphy]

I am a high school teacher and yes, this is a very common problem.

Similar to the above, I tell my students that
(1) Third law force pairs mean two forces of the same type, (ie both gravitational, or both magnetic, or both contact, whatever) acting between two objects
(2) Second law force pairs act on the same object and may be of different types.

At least at HS level this seems to help

Just some comments on phrasing...

I avoid using the word "between"...
I prefer to say the "force on A due to B" and the "force on B due to A"
because when I ask for these forces to be drawn, I get (or hope to get),
for the first vector, a force vector drawn with tail at A (or head at A).
For the second vector, I get a force vector drawn with tail at B (or head at B).
When the word "between" gets used,
I occasionally get a force vector drawn at the midpoint "between" the two objects,
which means nothing physically, even though they have drawn "a force between two objects"

While there are "third law force pairs", there aren't always "Second Law Force Pairs".
Maybe in some situations, there are two forces on an object that balance each other.
But in general, the balancing forces don't come in pairs.

 

[physbits]

Just some comments on phrasing...

I avoid using the word "between"...
I prefer to say the "force on A due to B" and the "force on B due to A"
because when I ask for these forces to be drawn, I get (or hope to get),
for the first vector, a force vector drawn with tail at A (or head at A).
For the second vector, I get a force vector drawn with tail at B (or head at B).
When the word "between" gets used,
I occasionally get a force vector drawn at the midpoint "between" the two objects,
which means nothing physically, even though they have drawn "a force between two objects"

While there are "third law force pairs", there aren't always "Second Law Force Pairs".
Maybe in some situations, there are two forces on an object that balance each other.
But in general, the balancing forces don't come in pairs.

In real life, the forces don't always come in pairs; however, when students are asked to differentiate between 2nd and 3rd law forces they almost always do - at least in they curricula I have taught.
The 'between' is simply a quick phrase to help them remember and distinguish the two ideas. I don't recall ever seeing the midpoint vector you refer to. Students tend to know how to draw the forces but simply struggle with spotting and distinguishing between the different types of ''force pairs',

 

[Mister T]

In my native language (Finnish), the action-reaction pair is referred to as “force and counter-force”, and therefore the terminological confusion does not arise.

No, but there's another misconception that it shares. Students think that the action somehow precedes, or is at least the cause of, reaction. Likewise a force would seem to precede or be the cause of a counter-force. Students need to appreciate that there is no way to discern which is the force and which is the counter-force. The situation is entirely symmetrical with respect to the two forces. Moreover, the counter-force doesn't counter the force in the sense that the two don't sum to a net force of zero.

I think the problem with teaching and learning Law III is that when it's taught to students they aren't required to identify Third Law pairs of forces in situations involving the interaction of two objects. Most of the time is spent focusing on one object at a time, finding the net force on it, and studying how it moves. We don't really give our students the chance they deserve to learn it!