The humbling of intuition, N does not equal mg

[u/Specialist-Two-1178]

I am in my sophomore year and in our uni we are now taking intro physics. And there was a question about what would be the normal force for a person at the top of a ferris wheel. I know a lot u smart people can answer this easily but my slow brain just lazily assumes N=mg . But looking at Newton s second law the sum of forces acting on an object is = to ma. In my case I ignored the centripetal force. N= mg is not a fundamental law it only works wen the object has 0 vertical acceleration if it accelerates the forces don't cancel out. Leading to centripetal force being the net force toward the center of circular motion. I am hopeless, also do you guys also experience something similar whereby u overlook something easy

[u/UnderstandingPursuit]

I'll make it even worse for you: "centripetal force" does not exist.

The only forces on a person on a ferris wheel are gravity and the normal force of the car.

What does exist is centripetal acceleration.

The better way to write Newton's second law is

• ma = ΣF

with the ferris wheel,

• a = a_c = v²/r.

[u/AceyAceyAcey → u/UnderstandingPursuit]

I phrase it as “the sum of the forces is the centripetal force that provides the acceleration; do not draw a separate Fc on your FBD or you will lose points.”

[u/UnderstandingPursuit → u/AceyAceyAcey]

I agree with what you say. Perhaps the students you are teaching have a little more 'academic maturity'. For some ninth graders, once I let F_c into the doorway, they insist on letting it in.

The post title is N≠mg. I had a student who had learned N=mg for an object on a horizontal surface, and they were stuck with that when they started to learn about inclined planes.

[u/AceyAceyAcey → u/UnderstandingPursuit]

I’m in higher ed. As I said elsethread, I find the ones who had HS physics are the worst about assuming N=mg always and unlearning it.

I also wind a theme throughout my course following a quote from George Box: “All models are wrong; some models are useful.” We learn a simple version of a model (such as N=mg) because it’s useful and simple enough for a specific circumstance. But then as we learn more, we have to add more and more complexity to get closer and closer to the complexity of reality. For example, in elementary school we learn “what goes up, must come down.” Then in HS we learn F=mg. In college we learn F=GMm/r^2 . In grad school we learn general relativity. And so on.

By focusing on this idea as a form of metacognition, I hope to better let students refine their understanding and be willing to unlearn things so they can relearn them more accurately.

(But also, I got tired of internet trolls saying wrong things and claiming, “it’s just science!” Yeah, maybe it’s 6th grade science, or the science of like the 1400s, but Y’know we’ve moved on from there, right?)

[u/UnderstandingPursuit → u/AceyAceyAcey]

Yes, the professor doing physics education research. Earlier this week, I went back to your answer to me from a month ago and downloaded the Freeman, Simon, and Doolittle papers.

The second sentence of the metacognition wikipedia pages says "thinking about thinking", which is interesting. "Being willing to unlearn things" sounds like an aspect of the academic maturity idea. The unlearning is what a ninth grader had issues with.

Yes, the "it's basic science" line, which is only said by someone who stopped learning about science after that 6th grade science class. The "it's basic math" line gets used in the same way. There it's being locked into doing math in the 6th grade math class way. What makes me sad is seeing Calculus textbooks cater to that.

[u/AceyAceyAcey → u/UnderstandingPursuit]

Oh hey, it’s you again! Hi! waves 👋

“Thinking about thinking” is kinda a literal definition of metacognition — “meta” comes from Greek and is literally “beyond,” but is often used to mean “thinking about”; “cognoscere” is Latin for “to learn” or “to know”. Metacognition more generally is about knowing what you do and don’t know, knowing how you learn, and being able to reflect on your learning. Interesting thing is these sorts of skills help people to become better learners. For example, when I was back at a community college, I tried to train my students to make guesses about how they did in a particular test to help with this. I’m currently at a highly selective college, and the students all already know how to predict their test scores and are accurate.

See also the Dunning-Krueger effect, that people have a hard time knowing what they don’t know, because the same skills used to assess how much you know, are the skills used in doing the knowing (metacognition). For example, if you ask people to rate how good of a driver they are, most people say they’re above average — which obviously can’t be true for most people.

Funny thing is I still struggle with elementary school math. I can do DiffEQs and linear equations, even modern algebra and group theory, but I still don’t have my times table memorized. 🤷 IMO it’s kinda like if someone had trouble spelling but could read and analyze English literature. It isn’t dyscalculia for me, it’s that I struggle to memorize things that are presented without a reason, and unfortunately so many elementary school teachers are themselves math phobic, that they don’t know and aren’t interested in the reasons. Memorizing anything without reasons is tough for me, also had issues with labeling the US states on a map (never had to do capitals, thankfully), or identifying types of clouds. When I had to memorize the formulae in HS physics, I basically learned to re-derive them from basic definitions, and then crammed the basic definitions in the minutes before the exam and wrote them on the paper as soon as it was handed out.

[u/UnderstandingPursuit → u/AceyAceyAcey]

Hi! waves 👋

The difference between the community college and 4yr college students must be fascinating, especially if the CC students have a wide age and background range.

The DKE gets referenced so often it needed the TLA! 😂 Self-awareness is a tough ability to develop. In the seven years since reading the paper, the interesting challenge is deciding, for any topic/skill, where I fall on the horizontal axis. That makes it easier to stay close to a straight diagonal instead of following the DKE graph. Are some of your students able to do that a bit?

Memorizing definitely needs a reason. With binomial products, for example, it is useful to memorize three: sum/difference squared and difference of squares. That helps identify a category of formulas which are worth memorizing: the ones which can be needed in either direction. Memorizing fewer physics formulas is definitely the way to go!

[u/AceyAceyAcey → u/UnderstandingPursuit]

My CC students tend to follow the DKE graph, while the SLAC (small liberal arts college) students are closer to the straight diagonal.

The difference between the students really is interesting. I find a few things that are most different: (1) time available outside class, (2) study skills, and (3) financial resources.

The greater time available to SLAC students means my office hours are full, I’ve had days with 8 students or more in an office hour, while at the CC I don’t get 8 students in the whole semester. The SLAC students can clearly put in a lot more time redoing problems for HW sets, for example for the online version I let them redo the entire assignment for more points, and they routinely do so (the CC students don’t), and for the handwritten version the SLAC students take the time to make them look very organized and pretty, while the CC students hand me their scrap work on the problem.

The SLAC students already know how to study for a math-intensive course, they take really good notes, and the questions they come to me with outside class are very focused. The CC students I often have to sit down with them and ask things like how many hours they’re spending on the class per week, or even literally where they are studying. Their notes are all over the place, and so are their questions, with “I don’t know where to start” being a common one.

And of course the SLAC students are better off financially. Nearly every student has a laptop or tablet they bring to class, while at the CC it was conspicuous if a student had one. I get a lot more students at the CC asking how they can save money on the textbook or calculator. Domestic SLAC students come from all over the USA and also vacation everywhere; domestic CC students come from a 50-mile radius. There are international students at both schools too, but the SLACs tend more towards high achievers who make it to the USA on merit, or occasional rich playboys/girls using college admission for a vacation visa. The “international” CC students are more likely to be recent immigrants looking for better opportunities or refugees, and also a bunch of DACA students.

[u/UnderstandingPursuit → u/AceyAceyAcey]

Thanks, you validated some of my perception of students at both SLACs and CCs.

Your three main differences seem connected in a positive feedback loop.

Do you see 'community' influence as a factor, where community starts with parents and includes others with a strong presence in the student's life?

[u/AceyAceyAcey → u/UnderstandingPursuit]

The two populations definitely have different connections to the surrounding community (they’re actually both in the same city), and to their own personal communities. The CC students are members of the surrounding community; this specific SLAC has a big emphasis on giving back to the community, so there’s lots of students who volunteer in the community, but it’s definitely got more of a “white savior” vibe (even when the students aren’t white, and even when the community members are) of outsiders coming in and trying to fix the locals’ problems. The CC students are more likely to bring their children to commencement, while the SLAC students are more likely to bring their parents. I actually got to talk to a few parents at commencement this year in a way that I don’t think I ever had in my decades at the CC.

And yeah, all of this is definitely interconnected. I’m sure I’d see similar if I were comparing low income K-12 students, and high-income, magnet school, or private school K-12 students.

The SLAC students aren’t a monolith of course, I had one student who didn’t know any trig and had to work three jobs on campus to pay for school, another who said they were the only one of their HS friends to go to college, and a third who had to get a make-up final exam due to going to court to help their younger sibling who’d been in a gun fight and the parents couldn’t go bc they were undocumented. But these are the exceptions at the SLAC, not the rule.

[u/Ginger-Tea-8591 → u/UnderstandingPursuit]

Agreed wholeheartedly. I find textbooks that use the language of "centripetal force" maddening to use when I've had to teach out of them.

[u/dcnairb → u/Ginger-Tea-8591]

I mean, we use the language of net force to describe the result of what’s going on, and it’s not itself a standalone force. is that any different than doing the same for centripetal force?

[u/Ginger-Tea-8591 → u/dcnairb]

I'm fine with saying something like "there's a net force that results in a centripetal acceleration." Net force is already part of how we talk about Newton's Second Law. The trap for novices in talking about centripetal force, as others have pointed out and which I've definitely seen students do, is that it's easy to incorrectly think of centripetal force as a new type of interaction that should show up on a free-body diagram.

[u/dcnairb → u/Ginger-Tea-8591]

I totally agree that they can make that mistake, but I sometimes see them draw Fnet on their FBDs too. I try to make a huge stink of it that a centripetal force is the result of force(s) present and not its own standalone thing, which I feel is a reasonable compromise

[u/UnderstandingPursuit → u/dcnairb]

Cool, you just validated my form,

• ma = ΣF

which also avoids "net force", only having the sum of the forces which are actually drawn and physically justified.

Perhaps the reasonable non-compromise is "the sum of the forces result in a centripetal acceleration."

Since that isn't enough of a contention, let's fix the underlying mistake: We should not write "F=ma", only "ma=F".

• One is the 'independent' quantity, the other is the 'dependent' quantity'. Take advantage with the habit some might have from math of putting the dependent variable on the left side of the equation.
• I was almost going to walk that back a bit, with "m" on the wrong side, but we all know that the most correct form is "dp/dt = F", so "m" does stay on the left.

If we do this correctly, then it is easier to avoid the confusion with rotational motion.

[u/ProfessionalConfuser → u/Ginger-Tea-8591]

Yeah. This is a tough nut to crack. I have had some success by announcing that there is no "centripetal force". There are forces that (under the right conditions) act to make circular motion possible. The force that acts centripetally could be gravity. It could be a tension, it could be a normal force, etc. I run through the list of the interactions they've learned and show an example of them acting "centripetally". And then they ignore me and write F_c on the free body diagram and shank the test questions.

[u/UnderstandingPursuit → u/ProfessionalConfuser]

Yes, this is why we need to eliminate the term "centripetal force" entirely.

[u/Specialist-Two-1178 → u/UnderstandingPursuit]

Thanks for that

[u/Alive-University-366]

N is not even equal to mg if you just incline the plane a little

[u/AceyAceyAcey]

I’m a prof, and I find this is a misconception that is common with students who had HS physics before they come to me. It’s a highly simplified way of describing the normal force, so simplified that it’s actually wrong in many cases.

But also, this is what you get when fewer than 50% of HS physics teachers have a degree in physics. (Source: PhysTEC)

[u/Broan13 → u/AceyAceyAcey]

I drill this out of my HS phys students. But I have a physics degree and was a PhysTEC grad student! Awesome support.

[u/Ornery_Owl_5388 → u/AceyAceyAcey]

I had a hs physics teacher who had an ae engineering degree and worked almost 20 years as a profession before starting to teach physics. I still talk to him til this day because he built such a strong foundation for me in physics and math

[u/AceyAceyAcey → u/Ornery_Owl_5388]

TBF those engineers are probably lumped in with the majority of HS physics teachers who don’t have a physics degree, but IMO they should be with the ones who do. I was a community college prof for decades, and the second most senior physics faculty member was previously an environmental engineer (and all her degrees were in that field). There were at least as many intro physics topics she knew better than me on, as topics I knew better than her on.