Frequently Made Errors in Mechanics: Forces - comments

[haruspex]

haruspex submitted a new PF Insights post

Frequently Made Errors in Mechanics: Forces

Continue reading the Original PF Insights Post.

 

[Greg Bernhardt]

Great first post haruspex! Nice resource!

 

[PeroK]

Point 1, perhaps, needs an illustration. And, maybe, something about two equal and opposite vectors with different lines of action not canceling out to a nett zero force?

In point 2, you could add that a string pulled at both ends (with a force F) is equivalent to a string pulled at one end with a force F and attached to a wall at the other. That seems often to be missed by those who think the tension should be 2F.

 

[rumborak]

Yeah, number 1, in my opinion, makes it more confusing to say the least. I for one think I have a reasonable understanding of what a force is, but I have no idea what a "line of action" is supposed to be in this context.

 

[CWatters]

There are plenty of other common errors. For example the friction force is frequently taken to be μN in situations where that's actually the maximum force before slipping occurs.

 

[haruspex]

There are plenty of other common errors. For example the friction force is frequently taken to be μN in situations where that's actually the maximum force before slipping occurs.

I have separate one on friction in the works. Just wanted to get some feedback on this simple one first. Others to follow... moments etc.

Yeah, number 1, in my opinion, makes it more confusing to say the least. I for one think I have a reasonable understanding of what a force is, but I have no idea what a "line of action" is supposed to be in this context.

I'm unsure how important it is, but I notice that most seem to think of a force as being completely described by its vector. The vector does not tell you the line of action, which as we all know is crucial when it comes to moments. A force really is more like a pair of vectors, but it's never described that way.
I'll expand it, mentioning point of application.

In point 2, you could add that a string pulled at both ends (with a force F) is equivalent to a string pulled at one end with a force F and attached to a wall at the other. That seems often to be missed by those who think the tension should be 2F.

Good idea.

 

[rumborak]

I'm unsure how important it is, but I notice that most seem to think of a force as being completely described by its vector. The vector does not tell you the line of action, which as we all know is crucial when it comes to moments. A force really is more like a pair of vectors, but it's never described that way.

So, I went to college in Europe, and I can say I have never heard of the concept of "line of action", nor, after various Google searches, do I understand the point of it. Force has a vector to it that indicates the magnitude and direction, and obviously there is a point that it applies to.
I looked at http://web.mit.edu/4.441/1_lectures/1_lecture4/1_lecture4.html , and it seems to make a mangle of momentum and other things. Momentum is a separate thing, don't conflate it with force.

 

[haruspex]

So, I went to college in Europe, and I can say I have never heard of the concept of "line of action", nor, after various Google searches, do I understand the point of it. Force has a vector to it that indicates the magnitude and direction, and obviously there is a point that it applies to.
I looked at http://web.mit.edu/4.441/1_lectures/1_lecture4/1_lecture4.html , and it seems to make a mangle of momentum and other things. Momentum is a separate thing, don't conflate it with force.

http://en.wikipedia.org/wiki/Line_of_action states:

"The concept is essential, for instance, for understanding the net effect of multiple forces applied to a body."​

But I would go further. With just one force applied to a body it matters greatly whether its line of action is through the mass centre.
The point of application will obviously tell you the line of action, but of the two it's the line of action that matters.
I'm not conflating momentum with force. Perhaps you mean moments?

 

[rumborak]

Sorry, yeah, I meant moment.

But, please explain this to me. You say "it matters greatly whether its line of action is through the mass centre". So, you have a force vector, applying on the center of the mass. And then you have *another* vector? What does this additional vector refer to?

 

[haruspex]

Sorry, yeah, I meant moment.

But, please explain this to me. You say "it matters greatly whether its line of action is through the mass centre". So, you have a force vector, applying on the center of the mass. And then you have *another* vector? What does this additional vector refer to?

No, I have one force that maybe is not acting through the mass centre. If it is not, it will cause the body to rotate, thereby doing more work on it.

 

[rumborak]

Yes, but that is due to the moment. The force is still just the force, simply acting on a different spot. Don't conflate what it *does* to a body (whose center of mass might be anywhere) with the clean concept of a force.

 

[haruspex]

Yes, but that is due to the moment. The force is still just the force, simply acting on a different spot. Don't conflate what it *does* to a body (whose center of mass might be anywhere) with the clean concept of a force.

You yourself wrote that a force "has a point of application". That is, the point of application is an attribute of the force. When you say "clean concept of a force", you are really referring to the clean concept of a vector. What you call a force, I would call the force vector.

Seems to me we are arguing about semantics. Is a force a disembodied vector, and the application of a force (for want of a better term) the combination of a force and a line of action? Or is a force what we think of in the real world as a force, having attributes of magnitude, direction and line of action?:
http://en.wikipedia.org/wiki/Statics "Force is the action of one body on another."
https://books.google.com.au/books?isbn=812190952X "A force is completely specified by its Vector and its point of application."
http://www.boeingconsult.com/tafe/structures/struct1/forces/forces.htm "a force has magnitude, line of action, direction, and point of application"

If we take the pure vector view, it makes no sense to ask what moment a force has about a point. We must instead ask what moment a particular application of the force has about that point.

 

[rumborak]

I think this is more than semantics. The boeingconsult site says "a force has magnitude, line of action, direction, and point of application".
So, that means, it's
- magnitude and direction => 3-dimensional vector
- line of action => 3-dimensional vector (slope and intercept essentially)
- point of application => 3-dimensional point

A force vector needs 9 scalars to be described? I very much doubt so. In my book, a force is fully described by its 3-dimensional vector of direction, and the 3-dimensional vector of where it is applied.

When I look at things like Lorentz force, I also don't see the "line of action" anywhere.

 

[haruspex]

I think this is more than semantics. The boeingconsult site says "a force has magnitude, line of action, direction, and point of application".
So, that means, it's
- magnitude and direction => 3-dimensional vector
- line of action => 3-dimensional vector (slope and intercept essentially)
- point of application => 3-dimensional point

A force vector needs 9 scalars to be described? I very much doubt so.

The boeingconsult statement is clearly excessive. The line of action can be deduced from point of application and direction. The only question is whether to discard line of action or point of application. All the other references I've found agree with me that it's the line of action that matters.

 

[rumborak]

Maybe this is just my personal Occam's Razor here, but between a point in space, and a line in space, if the point describes it fully, the point should be preferred. For example, what meaning do the infinite other points on that "line of action" have? The line of action extends indefinitely away from the body it applies to; what physical reality does this correspond to?

TLDR, I personally find these additional redundant concepts will wreak more havoc on a student's understanding than the simple, and minimal, "vector + point in space" definition of a force. Especially when the math in physics nowhere mentions any lines, at all.

 

[haruspex]

Maybe this is just my personal Occam's Razor here, but between a point in space, and a line in space, if the point describes it fully, the point should be preferred.

The point requires three coordinates. Since we know the direction, the line of action only requires two.
Is there any problem in the mechanics of rigid bodies where the line of action is inadequate and the point of application needs to be known?

 

[rumborak]

The problem is, while it may make some certain sense in mechanics of rigid bodies, once the student moves on to things like Lorentz force, "line of action" makes no sense at all anymore. A student asking "so, what's the line of action on an electron" will be met with the answer "yeah, forget about that thing here. Force is something different".

BTW, a line may look like it needs only two values, but it also requires a defined x+y offset to a coordinate system. You actually end up with more that way.

 

[haruspex]

The problem is, while it may make some certain sense in mechanics of rigid bodies, once the student moves on to things like Lorentz force, "line of action" makes no sense at all anymore.

Sure it does. The basic definition is for a point particle, so the line of action is clear. In principle, though, it also applies to a larger rigid body. The Lorentz force on the body as a whole will be the net of the forces on the particles, and it will have a line of action.

 

[rumborak]

But either way, I find your "Insight" article to be wrong in the sense that it makes the claim that people are mistaken in not considering the line of action. It is redundant, because the vector+point description uniquely and sufficient describes it. A person using the latter definition is in now way wrong, and in fact is better equipped to use the regular formulas in physics.

Not only that, the term "line of action" produces almost no results on the internet, which means its use will likely be of no help to anybody studying physics.

 

[haruspex]

the vector+point description uniquely and sufficient describes it

So you've shifted your position to "a force is a vector plus a point of application"?

 

[rumborak]

What? I've been saying that the whole time. It is my very point that a force can be described with 2 3-dimensional vectors. You seem to want to add another entity to it, or at the very least consider it "a frequently made error" to not consider that line of action.

 

[robphy]

Probably the biggest error that students make with vectors is
the incorrect thinking that "vectors add like numbers"...
in particular, that magnitude of a sum of vectors is the sum of their magnitudes.

 

[haruspex]

Probably the biggest error that students make with vectors is
the incorrect thinking that "vectors add like numbers"...
in particular, that magnitude of a sum of vectors is the sum of the their magnitudes.

True. If I can find out how to edit the post now that it has been published (anyone know?) I will add something on that.

 

[haruspex]

Probably the biggest error that students make with vectors is
the incorrect thinking that "vectors add like numbers"...
in particular, that magnitude of a sum of vectors is the sum of the their magnitudes.

True. If I can find out how to edit the post now that it has been published (anyone know?) I will add something on that.

What? I've been saying that the whole time. It is my very point that a force can be described with 2 3-dimensional vectors. You seem to want to add another entity to it, or at the very least consider it "a frequently made error" to not consider that line of action.

Then I misunderstood your objection. It seems all we are arguing about is whether a force has magnitude, direction and point of action, or magnitude, direction and line of action. Line of action is enough to define the force, but you find it less confusing to refer to point of action. I'll try to reword it a little.

 

[AlephNumbers]

My favorite insights article so far. I would love to see more articles on common mistakes in other areas of mechanics.

 

[Ben Niehoff]

I have to object to the first item. A "line of action" is insufficient to describe a force except in the special case of a rigid body. In full generality, a force is a vector that is attached to a point, which I guess you can call the "point of application". The point should be thought of as described by some suitable coordinates; not as a "second vector", which is not really the appropriate way to think about it. The "line of action" is merely the line passing through the point of application such that it is collinear with the force vector.

From here it is easy to generalize to fields of force density, as in continuum mechanics.

 

[rumborak]

Lol, I had the same argument the last two pages :D

 

[haruspex]

I have to object to the first item. A "line of action" is insufficient to describe a force except in the special case of a rigid body. In full generality, a force is a vector that is attached to a point, which I guess you can call the "point of application". The point should be thought of as described by some suitable coordinates; not as a "second vector", which is not really the appropriate way to think about it. The "line of action" is merely the line passing through the point of application such that it is collinear with the force vector.

From here it is easy to generalize to fields of force density, as in continuum mechanics.

I can certainly add the rigid body rider (as done already in this thread).
A vector to describe the point of application is perfectly reasonable. It would be an appropriate vector for determining the moment about the origin.

 

[haruspex]

Probably the biggest error that students make with vectors is
the incorrect thinking that "vectors add like numbers"...
in particular, that magnitude of a sum of vectors is the sum of their magnitudes.

Thinking about this some more, it belongs in a separate FME ("Frequently Made Errors") on vectors. Care to write one? If not, I'll get to it eventually. Should be able to link to it from the forces paragraph.

 

[robphy]

Here are other common errors...
1) "the magnitude of the normal force is always mg" (because of a formula they saw).
2) "the magnitude of the static friction force is always $\mu_k N$" (because of a formula they saw)
3) "the centripetal force is an additional force drawn on a free-body diagram"