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Muu9

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In summary: Hewitt will help. It's not like we limit ourselves to one source when we're learning about a new topic.I think this is very important. Including the "observations." We see questions: "yes, but why is Work = Force times Distance?" I feel like answering, "carry this 40 pound bag of Sakrete up a flight of stairs and then ask me again." If you can't tie physics to observations, it's just squiggles on paper.I feel like answering, "carry this 40 pound bag of Sakrete up a flight of stairs and then ask me again.

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Muu9

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berkeman

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Good choice!Muu9 said:I recommended Thinking Physics

Can you say how young they are? And are there any schools nearby with Math or Physics clubs that might allow the child to sit in a few times to see if they like it?

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malawi_glenn

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malawi_glenn

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I remember two years ago, I had a gifted student who seriously asked me, why I needed to do experiments in class when I had derived the formulas during a lesson the previous week...

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That's why the most talented physicists end up as string theorists.malawi_glenn said:

I remember two years ago, I had a gifted student who seriously asked me, why I needed to do experiments in class when I had derived the formulas during a lesson the previous week...

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malawi_glenn

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"physics is just applied math" is a common saying among these kids.Demystifier said:That's why most talented physicists end up as string theorists.

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vela

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Knight sounds like a good choice. The last time I asked, my students had good things to say about the book. That said, we don't really know what the reading comprehension level of the child is. If they struggle with reading, I'd think many textbooks might be too dense for them.Muu9 said:

If cost is not an issue, using two or more books at the same time could work as well. If the kid isn't getting some concept from reading YF, maybe the simpler explanation in Hewitt will help. It's not like we limit ourselves to one source when we're learning about a new topic.

An applied/empirical approach would be good too. A lot of my students have trouble connecting the mathematics to the real world, so I'd encourage anything to start building those connections.

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MidgetDwarf

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I have a BS in mathematics, and was a few classes short (4) for a BS in physics. May or may not suite your purpose, but it is worth a look.

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malawi_glenn

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@MidgetDwarf it was me :)

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gmax137

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I think this is very important. Including the "observations." We see questions: "yes, butmalawi_glenn said:

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Muu9

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If the flight of stairs is 10 feet tall, can I carry it across 10 feet instead? After all, the work would be the same wouldn't it? And if you say the direction of the force in relation to the distance matters and so walking with the bag actually requires no work, then why is it more tiring than walking without the bag?gmax137 said:I feel like answering, "carry this 40 pound bag of Sakrete up a flight of stairs and then ask me again.

The child is 8 years old, by the way. Right now they're focused on getting a rocketry certification. I don't know them personally, I just communicated with their parent in an online forum.

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gmax137

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Still I think observation is important, even for the young ones.

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In other words, none of us knows whether this child even exists.Muu9 said:The child is 8 years old, by the way. Right now they're focused on getting a rocketry certification. I don't know them personally, I just communicated with their parent in an online forum.

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jtbell

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So, they're in third grade or thereabouts.Muu9 said:The child is 8 years old, by the way.

I would just let them do whatever they express an interest in doing, at this point. Does that include going through a "real" physics textbook?Muu9 said:They've gone through calculus (Essential Calculus by Stewart)

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MidgetDwarf

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Not sure if you wanted this information public lol.malawi_glenn said:@MidgetDwarf it was me :)

Now need to look up what's used for intro EM course labs, in particular, labs dealing with circuits, resistors, capacitors. Since I did the calculations and the other members set up the equipment lol.

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malawi_glenn

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MidgetDwarf said:Not sure if you wanted this information public lol.

Now need to look up what's used for intro EM course labs, in particular, labs dealing with circuits, resistors, capacitors. Since I did the calculations and the other members set up the equipment lol.

If you knew Swedish, I could give you my book written in Swedish and my lab instructions :D

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Frabjous

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The kid’s gifted and can pick it up quickly if they already haven’t.malawi_glenn said:If you knew Swedish, I could give you my book written in Swedish and my lab instructions :D

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Try a “Physics First” textbook.

One by Tom Hsu looks interesting.

One by Tom Hsu looks interesting.

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symbolipoint

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It makes one wonder if students should be reminded, the physicist must look for the Mathematics which describes the Physics.malawi_glenn said:"physics is just applied math" is a common saying among these kids.

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PeterDonis

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No, it wouldn't. To first order, zero work is required to move an object horizontally, because you don't need to exert any force. Because the real world is messy, you do have a correction due to friction, which means you need to exert some force to overcome friction to get the object moving, and then some force to stop it again. But, particularly if the surface is smooth or if you're smart and use something like a wheeled cart, you can reduce the force required, and therefore the work expended, to something very small, much, much smaller than the unavoidable work required to lift the object 10 feet against gravity.Muu9 said:If the flight of stairs is 10 feet tall, can I carry it across 10 feet instead? After all, the work would be the same wouldn't it?

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Merlin3189

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To the general issue, I'd definitely go for giving anyone interested in science plenty of practical experiences. At 8 yo even if very clever, I'd have thought there's a lot to be learned in children's playgrounds, using bikes, scooters and skates, playing with balls, catapults, bows and arrows, ropes, water, burning stuff and no doubt lots of things not coming to mind. IMO intuition is internalised experiences and the more you have, the better. Maybe now that physics has moved away from classical stuff to mathematical, non-intuitive understanding, perhaps experience could actually be a handicap? But I guess most people still go through most of the classical stuff to get to the level where they're taught the Truth.

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Mark44

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Not exactly. Work is thegmax137 said:"yes, butis Work = Force times Distance?"why

And as @Merlin3189 points out, if we're carrying the sack of concrete mix by walking, our steps are a sequence of up-and-down motions, so there is work performed in lifting and lowering the load.PeterDonis said:No, it wouldn't. To first order, zero work is required to move an object horizontally, because you don't need to exert any force. Because the real world is messy, you do have a correction due to friction, which means you need to exert some force to overcome friction to get the object moving, and then some force to stop it again.

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Mark44

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Excellent point.PeroK said:In other words, none of us knows whether this child even exists.

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Merlin3189

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Doesn't that just mean the question needs to be phrased better, as "Why is work the dot product of force and displacement vectors?"Mark44 said:Not exactly. Work is thedot productof the force and displacement vectors, ...

Gmax137 seems to be speaking about other people on the forum asking that question and that experiments might help them understand.

For me, the dot product framing is just offering a neat mathematical way of expressing the relationship concisely and precisely. That's good, but doesn't seem to me to answer the question as to why work is force times distance (or however it should be carefully expressed.)

I honestly don't know the answer to that one, but I'd go for a nice 'arm-waving' thing so despised by the cognoscenti here. (You'll be relieved that I just deleted my attempt, as unnecessary to this thread!)

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PeterDonis

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Work = force times distance is a definition. There is no "why". We adopt this definition because it works: because the theories of physics we obtain when we use this definition (and many others that go along with it) makes accurate predictions.Merlin3189 said:That's good, but doesn't seem to me to answer the question as to why work is force times distance

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Merlin3189

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But for me, it dodges the issue. Why did we adopt this definition? Why not include speed, or mass in the equation? What is it that F.s does that "works"? What about all the situations where you work your ass off and achieve nothing? Surely our decision to invent a concept of work and define it as F.s (before vector maths was invented?) was based on some experiences?

The point I failed to make in my post is, when someone asks such a question, there is something they don't understand, but want to. (I may be wrong: some people just want the correct answer to put in their HW or exam, or an equation they can put into their calculator, but I think most who make the effort to come to PF, want to increase their understanding.) Dot product helps those who know about vectors*, to do the maths, and may add to their understanding. I suspect those might have asked in the first place why W=

I said that mainly to support Gmax137's suggestion to do practical work, gain real experiences and get stimulated to consider concepts like work.

* I believe I learnt about mechanical work and the mechanical equivalent of heat, at least a year (I think 2) before I encountered vector multiplication and dot products. If vectors were mentioned at the time, they were just arrows or quantities with magnitude and direction - no maths beyond add, subtract and multiply by a scalar. Mechanical work was definitely force times distance, as was torque, which was not a cross product (and probably not even a vector, since it was always about axes in a single direction, so fully defined by a scalar.)

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A discussion on the history of kinetic energy is included here:Merlin3189 said:I wondered if that was the real answer. It does seem to be the answer to many questions here.

https://en.wikipedia.org/wiki/Kinetic_energy

One of the key observations is that if total momentum and total kinetic energy (defined as ##\frac 1 2 m v^2##) of a system of particles is conserved in one inertial reference frame, then they are conserved in them all. And, the difference in total kinetic energy of a system of particles is frame-invariant. That makes kinetic energy a useful concept. The factor of ##\frac 1 2## is included because kinematically, for constant acceleration, we have:

$$mv^2 - mu^2 = 2mas = 2Fs$$That equation can then be generalised to:$$d(KE) = \vec F \cdot d\vec r$$

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Mark44

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To be clear, "this definition" is ##W = \vec F \cdot \vec{ds}##.Merlin3189 said:But for me, it dodges the issue. Why did we adopt this definition? Why not include speed, or mass in the equation?

Consider a block of steel sitting on a sled that will be moved across a frozen lake. Work needs to be done to the sled and its load to accelerate the combination up to a certain speed

Let's assume that the sled moves on a frictionless surface for the sake of simplicity. Then once the sled reaches

In the real world there aren't frictionless surfaces, so we'll need to apply some force (do some work) to keep the sled moving.

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vela

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From Newton's second law, it's straightforward to show thatMerlin3189 said:But for me, it dodges the issue. Why did we adopt this definition? Why not include speed, or mass in the equation? What is it that F.s does that "works"?

$$\frac 12 mv_{\rm f}^2 - \frac 12 mv_{\rm i}^2 = \int_{\rm i}^{\rm f} \vec F_{\rm net} \cdot d\vec r.$$ Once we had this relationship and it proved to be useful, it made sense to give these quantities names. The righthand side seems to coincide, at least partially, with our intuitive notion of work, so that's probably where the name came from.

We need to recognize that the work done by our bodies and the work done on an object aren't necessarily the same because of the way our muscles work. I think this is similar to how Galileo deduced the law of inertia by abstracting away the complications due to friction, air resistance, etc. Once we take our complicated selves out of the situation and focus on the object and the forces acting on it regardless of their causes, the definition of work suggested by the math makes sense.Merlin3189 said:What about all the situations where you work your ass off and achieve nothing?

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PeterDonis

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We do work, but the work is not done on the sled. All of the energy we expend as work in this way gets dissipated as heat. None of it goes into increasing the energy of the sled.Mark44 said:In the real world there aren't frictionless surfaces, so we'll need to apply some force (do some work) to keep the sled moving.

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Merlin3189

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I was probably wrong to branch by commenting on someone's response to GMax's obiter dictum remark about work.

I think his point was not that he (or I) wanted an explanation of why work is <what you said in nice Latex>, rather that this is the sort of question that arises for curious people, and "tie physics to observations" might be a useful thing to do. I just wanted to support his view, because I'm such a person for whom squiggles on paper mean little unless I can relate them to practical experiences.

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berkeman

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So I think our best advice should be:PeroK said:In other words, none of us knows whether this child even exists.

"Have the child read this PF thread, and then do an Amazon search with "Look Inside" to find books that they like. If they are bright enough that's the best strategy for multiple reasons.

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pointlessgomboc

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Personally, I find young and freedman a great textbook for beginners to calculus, whereas if you have a strong foundation in calculus you can try morin; there are 2 books published by David Morin I believe, the easier one is referred to as 'baby morin' usually, which mainly covers classical mechanics, whereas the more advanced one goes into deeper topics is often referred to as 'daddy morin', either one is great for people who want to do more practice questions on physics, but disclaimer: they are not meant as textbooks, but rather almost pure practices booklets with detailed explained solutions, so I would recommend using it with a textbook like young and freedman for reference.Muu9 said:

Additionally, there are lots of awesome physics courses available online, and the ones I would recommend are those on the MIT opencourseware website, such as courses 8.01 (Classical mechanics), 8.02 (Electricity and magnetism), and 8.03 (Vibrations and waves), and if you want, 18.01 for single variable calculus to a relatively deep level. Hopefully this is of help :)

MITOCW website: https://ocw.mit.edu/

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"The Cartoon Guide to Physics" by Larry Gonick and Art Huffman is often recommended. It presents fundamental physics concepts in a fun and engaging way, making it accessible for younger readers.

"Physics for Kids: 49 Easy Experiments with Acoustics" by Robert W. Wood is a great choice. It includes simple and safe experiments that help children understand basic physics principles through hands-on activities.

"Conceptual Physics" by Paul G. Hewitt is an excellent option. It covers more advanced topics while emphasizing conceptual understanding over mathematical complexity, making it suitable for young learners with a strong grasp of the basics.

"Khan Academy" offers a comprehensive online physics course with interactive exercises and videos. It is a great supplement to traditional textbooks and allows children to learn at their own pace.

Look for textbooks that are specifically designed for younger audiences, with clear explanations, engaging visuals, and minimal technical jargon. Reading reviews and seeking recommendations from educators can also help ensure the material is suitable for your child's age and skill level.

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