Is the Total Radial Force on a Current-Carrying Hoop Zero?

[etotheipi]

With respect, I believe this reference from a 19 century mathematician should conclude the discussion.

I would say that all meanings are equal, but some meanings are more equal than others...

 

[fresh_42]

Linguistic Treatment

Given that the term net force is used in a certain context. If then appears total force on the stage, it must be something different, as otherwise there wouldn't be a need to switch terms. Magnitude is the only possibility left.

Given that total force appears alone, the question is, what does the adjective indicate? If it is used as a singular, then total has to indicate magnitude since otherwise unspecified force would have done the job, and again there wouldn't be a necessity for the adjective.

Given total forces is used as plural and alone, i.e. without the term net forces, then further context is necessary, since total only indicates that there are several of a kind. How these total contribute to certain directions is completely unclear and an interpretation as sum of magnitudes still possible - and in my opinion more likely than the resultant, which I would not specify as total because its ambiguity. Classical Mechanics Treatment

It is going to be hard to find anything in dynamics because as you have pointed out in this topic we are only ever interested in the vector sum of forces (resultant force).

General Treatment

The word total should be specified in its usage, since it neither automatically implies a summation nor specifies the nature of what should possibly be added, or if it even allows an addition. Look up the specification within the given context. Examples for the need to distinguish meanings can be found here:
https://www.physicsforums.com/threads/total-radial-force-on-a-hoop.991385/#post-6367379Humpty Dumpty Treatment

https://www.physicsforums.com/threads/total-radial-force-on-a-hoop.991385/page-2#post-6367789Total Résumé

Both adjectives are borrowed from common language, i.e. there is no definition available as it is for force. Hence we are forced to consider common English. And as with every context sensitive specification, discussions can go on forever as participants tend to switch between these contexts to refute each other. It is meaning- and senseless to have such a discussion.Net Résumé

Just because we do not allow topics like religion, politics, and philosophy does not mean you should search for substitutes. Authors have the right to use their own definitions as long as they do not collide with commonly known ones. So argue with the authors of textbooks, although I dare to claim that they won't answer.Outlook

Is there any reason not to close this thread?

 

[etotheipi]

Given that the term net force is used in a certain context. If then appears total force on the stage, it must be something different, as otherwise there wouldn't be a need to switch terms. Magnitude is the only possibility left.

I do see your point, but I would disagree. I can find many examples where they are used synonymously even within the same reference. And my comprehension of the terms is that they are analogous.

Is there any reason not to close this thread?

Nope, I think we are done here. I must now leave anyway!

 

[pbuk]

and again, the total force here is the pressure times the projected area, which equals the vertical component of the resultant force

And is this the same as the net force (I think we can assume that the vessel is not accelerating)?

Both 'net' and 'total' to me imply a summation, and that they are interchangeable.

`The usage of total force being synonymous for net force is abundant in the literature, and I would very skeptical of anything said to the contrary.

I like all of those terms, but 'resultant force', 'sum of forces', 'total force', 'net force', all mean the same thing.

 

[etotheipi]

Well it does make clear to say "the total force due to the internal pressure". Yes I would say we could also call it the net force due to the internal pressure. Tomato tomato, the important consideration is that we are performing a surface integral of the vertical components of a vector field over a curved surface (or indeed the surface integral of the vector field itself, with lateral components cancelling - it amounts to the same thing), but in cases like this the calculation can be greatly simplified to a multiplication by a projected area.

The total or net force on the half pipe in the equilibrium case is zero, since the vertical component due to pressure is balanced by the forces due to circumferential stresses in the pipe walls.

And in no point in the analysis is it necessary to ever bring up an integral of the magnitudes of the pressure forces within the pipe. In fact, I think that would be rather confusing, more than helpful. It's certainly not a helpful quantity for analysing the dynamics

 

[pbuk]

There really is no point in continuing; @fresh_42 please please save us from ourselves.

 

[etotheipi]

There really is no point in continuing; @fresh_42 please please save us from ourselves.

I will take this moment to mention that you still have yet to produce a reference in support of your claim