Circular Motion - Newton's Second Law: Bead on a Rotating Hoop

[jbriggs444]

How do you know that a given force is applied or resultant? If not looking at where does it come from, single interaction or multiple interactions? How is this applied to inertial forces (zero interactions)?

It is a resultant if it is just something you got by adding up a bunch of other forces.

It is an applied force if it is either an interaction force or a fictitious force resulting from your choice of non-inertial coordinates.

If there is only one force then the distinction becomes pretty much irrelevant. For instance a satellite orbitting a primary under the force of gravity. The resultant "centripetal force" and the applied "gravitational force" are pretty much one and the same thing.

 

[nasu]

How do you know that the forces you add are not resultants too? Is the weight of a macroscopic body applied or resultant? You can think of it as the force between the body and the Earth or as the resultant of all individual attractions between the molecules in the two objects or other parts you can divide the two objects into. What about friction? Which kind is it? Is the contact force between two solids applied or resultant? I don't see how this concept can be useful or/and well defined.
And for the inertial forces, what if you have several components, like Coriolis term, centrifugal term, for example. Is the total inertial force applied or resultant? What about the centrifugal term when the Coriolis term is not zero? It is a component or is applied?
Or you mean that the same force can be applied or resultant, depending on the context? Then, yes it is clear but I just don't see much usefulness. Have you seen this distinction made in textbooks?

 

[jbriggs444]

Or you mean that the same force can be applied or resultant, depending on the context? Then, yes it is clear

Thank you. Then we are in agreement.

but I just don't see much usefulness.

It was useful in this thread. If you write down both individual forces and the resultant which is their sum on the same free body diagram then you risk double-dipping.

Have you seen this distinction made in textbooks?

I've seen the term "resultant" used, yes. I'd not paid enough attention to worry about digging up a word to refer to forces that are added together to produce resultants. "Applied" is not an unreasonable adjective for the notion.

 

[Chestermiller]

How do you know that a given force is applied or resultant? If not looking at where does it come from, single interaction or multiple interactions? How is this applied to inertial forces (zero interactions)?

As reckoned by an observer in an accelerating frame of reference, all masses behave as if they are acted upon by a (fictitious) body force equal to -ma.

 

[haruspex]

How do you know that the forces you add are not resultants too?

They often are, but when you draw an FBD you have to decide which are the forces acting on it. E.g. for gravity, it is usual to consider it a single force acting on the mass centre, though in reality it acts on each atom, or gluon perhaps, separately. Having determined these "applied" forces, a summation of some of them can be considered a resultant, and the resultant of all is the net force.
The error in post #1, and I have witnessed this several times, is to think that the centripetal force is an applied force and write $(\Sigma \{F_r\})+F_{centripetal}=0$, where the $\{F_r\}$ are the radial components of the (actual) applied force; the correct equation, of course, being $\Sigma \{F_r\}=F_{centripetal}$.
In the non inertial frame, we have instead $(\Sigma \{F_r\})+F_{centrifugal}=0$, so the centrifugal force behaves like an applied force.

 

[nasu]

I understand the error in the OP and I agree with your explanation. It is a common misconception in introductory physics to consider centripetal force as some special force in itself. But any force, either a single force or a resultant can be centripetal. It does not have to be a resultant.
Even thought now I am not sure if the centripetal force that acts on a planet orbiting the star would qualify as applied or resultant. And the same for any other macroscopic force.

And I just don't see how calling it "applied force" make any sense. Especially when the label is "applied" to inertial forces or components of inertial forces which are not applied by anything.
It seems to be more misleading then useful.
@haruspex

 

[nasu]

If you look up "applied force" there are other definitions which seem to mean something else than a force that is not a resultant. True, these seem to be used in high school physics.
Accoding to this https://www.physicsclassroom.com/class/newtlaws/Lesson-2/Types-of-Forces tension or spring force are not applied forces. Neither gravity or electromagnetic force.
And according to this https://www.sciencefacts.net/applied-force.html the tangential component of the weight of a body on an inclined plane is the applied force.
This is why I don't feel that terms undefine, vaguely defined or unconsistently defined are useful, especially when we try to correct confusions or misconceptions. And if you define it simply as force that is not a resultant, there are hardly any of them in macroscopic physics, if you apply the definition consistently.

 

[haruspex]

any force, either a single force or a resultant can be centripetal. It does not have to be a resultant.

The centripetal force is that component of the net force which is normal to the velocity. True, there may be only one force, and it may happen to be normal to the velocity, but I do not see how that special case constitutes an objection to the generalised version.

I just don't see how calling it "applied force" make any sense.

We do need a term to refer to those forces that add up to produce the net force. Can you suggest a better one?

 

[AzimD]

I got the question correct and also understand the topic better now! Thank you! @PeroK @haruspex @Chestermiller @jbriggs444 @nasu and anyone else I may have missed!

 

[nasu]

The centripetal force is that component of the net force which is normal to the velocity. True, there may be only one force, and it may happen to be normal to the velocity, but I do not see how that special case constitutes an objection to the generalised version.

We do need a term to refer to those forces that add up to produce the net force. Can you suggest a better one?

Why not just "forces"? The interaction between two objects is what we describe quantitatively by a force. If there is no interaction, then we have a special case and we need a special name, like "virtual force" or "inertial force" or whatever. This show that it is not really the same thing as the "force" as described above (result of interaction) but we like to use it as if it were. But why do we need a special name to name the same thing which was already defined simply as "force"? And if we have the result of more than on interaction, we call it "net force", which is the result of the superposition of individual interactions, each one described by a "force" (which we have already defined).

But of course, if a name (or in general, a world), is used quite frequently, any discussion is useles. The use makes the rule. I suppose you did not make up the term yourself. Is there any reference of a textbook where they use "applied force" with this meaning?