How can dynamic equilibrium be best explained to students?

[Farmer Astronaut]

This concept, though intuitive to some, appears to be counterintuitive for 20-80% of smart-to-brilliant students I teach.
How can the idea of an object having non-zero speed while (balanced) forces act on that object, be conveyed without resorting to just a shuffling of physics terms to give a correct but unhelpful reply? In dealing with novice physics students, this can prove baffling for them. I seek a fresh restatement to inspire students to confront their misconceptions about physics and replace them with clearly true and better ones. I humbly ask for your help.

 

[Evo]

Welcome Farmer, as you can see you have asked your question in "Member Introductions Only - No questions". Questions belong in the proper forums where they can be answered.

I have asked to have your post moved to where it can be best answered,

 

[berkeman]

This concept, though intuitive to some, appears to be counterintuitive for 20-80% of smart-to-brilliant students I teach.
How can the idea of an object having non-zero speed while (balanced) forces act on that object, be conveyed without resorting to just a shuffling of physics terms to give a correct but unhelpful reply? In dealing with novice physics students, this can prove baffling for them. I seek a fresh restatement to inspire students to confront their misconceptions about physics and replace them with clearly true and better ones. I humbly ask for your help.

Have you taught your students about fundamental tools like Free Body Diagrams (FBDs) yet? If so, this concept should be pretty obvious and intuitive to them, IMO.

 

[Andy Resnick]

This concept, though intuitive to some, appears to be counterintuitive for 20-80% of smart-to-brilliant students I teach.
How can the idea of an object having non-zero speed while (balanced) forces act on that object, be conveyed without resorting to just a shuffling of physics terms to give a correct but unhelpful reply? In dealing with novice physics students, this can prove baffling for them. I seek a fresh restatement to inspire students to confront their misconceptions about physics and replace them with clearly true and better ones. I humbly ask for your help.

First, I'd lose the phrase 'dynamic equilibrium', as it is internally inconsistent. "Steady state" is better.

Now, how to teach that the sum of forces = 0 is not the same as forces 'disappearing': one related problem to be confronted is the incorrect connection between force and velocity: we often say "forces cause things to move" even though it's not correct: forces cause motion to change.

There are a few demos you could try: one could be an Atwood machine. One block has equal and opposite forces acting on it (gravity and tension), but you can put the block into constant velocity motion and it will continue to move with constant velocity.

 

[brainpushups]

I too find it interesting how students have difficulty with this concept. Not understanding 'dynamic equilibrium' really amounts to not understanding the words in the statement of Newton's first law (and, arguably, the second law too). Last year I told students who, since middle school, could recite Newton's first law that they likely don't actually understand what the words mean and that they would likely get one out of two conceptual questions incorrect even after reviewing Newton's laws. We spend some time talking about the first law which I phrase as: "in the absence of a net force a particle moves with constant velocity." We talk about what the words mean and I then gave two conceptual exercises for them to think about on their own.

One was a question about why you need to pedal your bicycle on flat ground to maintain a constant speed. Every student responded that a force was required to balance friction and air drag - evidence that they understand net forces can result in constant velocity.

The next question was about whether a net force was required to move a book along a table at constant speed. About 90% of the students answered that a net force WAS required because without a push the book would come to rest - evidence of a clear misunderstanding about net forces. Most were surprised that I was right - even after warning them, they missed a conceptual question about something which seems so 'obvious.' A nice illustration of how 'common sense' notions about motion are distinctly Aristotelian.

My qualitative impression is that students did understand the concept much better AFTER having this discussion than in previous years when I didn't ask these two questions back to back.

 

[Andy Resnick]

One was a question about why you need to pedal your bicycle on flat ground to maintain a constant speed. Every student responded that a force was required to balance friction and air drag - evidence that they understand net forces can result in constant velocity.

The next question was about whether a net force was required to move a book along a table at constant speed. About 90% of the students answered that a net force WAS required because without a push the book would come to rest - evidence of a clear misunderstanding about net forces.

Can you please explain this more? I would think that those 90% of students answered correctly, since you already allowed for the existence of friction.

 

[brainpushups]

Can you please explain this more? I would think that those 90% of students answered correctly, since you already allowed for the existence of friction.

Sure. Let me type the actual question. Let me know if you think it is unclear and I can modify it:

"Imagine sliding a book across a table at constant velocity. If the book is initially at rest, is a net force required to get the book to move from rest to the desired velocity? Once the book is moving with constant velocity is a net force required to maintain its motion?"

 

[vela]

Can you please explain this more? I would think that those 90% of students answered correctly, since you already allowed for the existence of friction.

He asked about the net force on the object, not an applied force to counteract the effects of friction.

 

[Andy Resnick]

Sure. Let me type the actual question. Let me know if you think it is unclear and I can modify it:

"Imagine sliding a book across a table at constant velocity. If the book is initially at rest, is a net force required to get the book to move from rest to the desired velocity? Once the book is moving with constant velocity is a net force required to maintain its motion?"

That helps clarify the issue, thanks.

I would change some wording, tho- the phrase 'is a net force required to get the book to move from rest to the desired velocity?' draws a connection between force and velocity. Perhaps the phrase ''is a net force required to accelerate the book from rest to the desired velocity?" would be better. Using the word 'move' reinforces a pre-Newtonian viewpoint.

Similarly, the phrase 'is a net force required to maintain its motion?' seems to connect force and velocity, because it is necessary to apply a force opposing friction in order to maintain constant velocity. Here is a good opportunity to distinguish between 'opposing forces that sum to zero' and 'no force'- you are careful to say *net* force, which is good.

How much time do you spend developing the idea of 'net', 'resultant', 'total' force? In my experience, it's easy for students to grasp the idea of 'net velocity', but really hard to grasp the idea of 'net acceleration'... not sure why.

 

[Chestermiller]

Here is another idea. If the object is moving at constant velocity, ask them what they would observe if they were moving along with the object at the same velocity as the object. From this 2nd inertial frame of reference, they should observe the object to be stationary, and the forces on it to be in balance.

 

[brainpushups]

I would change some wording, tho- the phrase 'is a net force required to get the book to move from rest to the desired velocity?' draws a connection between force and velocity. Perhaps the phrase ''is a net force required to accelerate the book from rest to the desired velocity?" would be better. Using the word 'move' reinforces a pre-Newtonian viewpoint.

I see your point. I was actually deliberately avoiding the word acceleration, the thought being that they should understand the concept that changing velocity (represented here by 'from rest to...') is what force is required for. I thought using the word 'acceleration' was too leading. Regardless, this is the part of the question they got correct.

Similarly, the phrase 'is a net force required to maintain its motion?' seems to connect force and velocity, because it is necessary to apply a force opposing friction in order to maintain constant velocity. Here is a good opportunity to distinguish between 'opposing forces that sum to zero' and 'no force'- you are careful to say *net* force, which is good.

Yes, the connection of force to maintaining motion is deliberate. I spend some time discussing Aristotle's ideas with students. We talk about how his ideas were incorrect and get into some specifics about why as we lead up to Newton. It's interesting that, even when time is spent on the specifics, the students still misunderstand what the first law is really saying. I think the problem is both conceptual and linguistic. Novice students are not used to thinking about force the way it is defined in classical mechanics. This year I'm actually planning on having students do casual observations of motion in the style of Aristotle and provide arguments that either support or refute his claims. If all goes well the debate will be on them and I will have little input. Only later when we discuss Galileo, Descartes, and Newton will we revisit the idea of force and changing motion - this time armed with the notion that careful measurement is what determines scientific truth, not casual observation.

How much time do you spend developing the idea of 'net', 'resultant', 'total' force? In my experience, it's easy for students to grasp the idea of 'net velocity', but really hard to grasp the idea of 'net acceleration'... not sure why.

I agree. Acceleration is, in general, hard for students to understand. I have ramped up my conceptual questions in this area in addition to more quantitative concepts like the connection between graphs of position, velocity, and acceleration. I describe scenarios and then ask students to sketch either the position, velocity, or acceleration vs. time graphs for various situations involving uniform acceleration only (and changes between different uniform accelerations). I have noticed an improvement in student understanding of the concepts since I've devoted more time to it in the past year or two.

 

[aaronrodg]

You can explain it easily with the help of this video
The digging example is good in this video...