Physics textbook recommendation for young gifted child

[Muu9]

They've gone through calculus (Essential Calculus by Stewart) but haven't had a formal physics class yet (but a lot of pop-physics reading). I recommended Thinking Physics followed by Conceptual Physics by Hewitt, followed by a meaty calc-based book like Krane or YF, but I wonder if an easy calculus-based book like Knight would be more appropriate instead of conceptual physics. What do you think?

 

[berkeman]

I recommended Thinking Physics

Good choice!

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?

 

[malawi_glenn]

Remember to DO physics as well. Try to make experiments and observations at home, make hypoethesis and predictions, anlaysis of data etc.

 

[malawi_glenn]

part 2: I have taught many "gifted" youngsters in physics and in math. And in my experience, these are the ones in general who are struggling the hardest with the scientific method, experiments, data analysis, how to make hypothesis, preductions, error analysis, and so on.

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...

 

[Demystifier]

part 2: I have taught many "gifted" youngsters in physics and in math. And in my experience, these are the ones in general who are struggling the hardest with the scientific method, experiments, data analysis, how to make hypothesis, preductions, error analysis, and so on.

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...

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

 

[malawi_glenn]

That's why most talented physicists end up as string theorists.

"physics is just applied math" is a common saying among these kids.

 

[vela]

They've gone through calculus (Essential Calculus by Stewart) but haven't had a formal physics class yet (but a lot of pop-physics reading). I recommended Thinking Physics followed by Conceptual Physics by Hewitt, followed by a meaty calc-based book like Krane or YF, but I wonder if an easy calculus-based book like Knight would be more appropriate instead of conceptual physics. What do you think?

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.

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.

 

[MidgetDwarf]

not sure if this is a good recommendation for a kid. but someone on this forum recommend me Shankar's books on fundamental physics to brush up on my physics. I found the first volume well explained (on Chapter 7), intuitive, and rather funny. My version, the expanded edition has problems at the end of book. Maybe buying the schaum's problem book or any other run of the mill physics book for problems, can be an ideal first exposure.

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.

 

[malawi_glenn]

@MidgetDwarf it was me :)

 

[gmax137]

Remember to DO physics as well. Try to make experiments and observations at home, make hypoethesis and predictions, anlaysis of data etc.

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.

 

[Muu9]

I feel like answering, "carry this 40 pound bag of Sakrete up a flight of stairs and then ask me again.

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?

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.

 

[gmax137]

Yeah, I was just thinking about this wrinkle in my example. A possibly instructive wrinkle for a high schooler, no so much for an eight year old.

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

 

[PeroK]

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.

In other words, none of us knows whether this child even exists.

 

[jtbell]

The child is 8 years old, by the way.

So, they're in third grade or thereabouts.

They've gone through calculus (Essential Calculus by Stewart)

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?

 

[MidgetDwarf]

@MidgetDwarf it was me :)

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.

 

[malawi_glenn]

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

 

[Frabjous]

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

The kid’s gifted and can pick it up quickly if they already haven’t.

 

[robphy]

Try a “Physics First” textbook.
One by Tom Hsu looks interesting.

 

[symbolipoint]

"physics is just applied math" is a common saying among these kids.

It makes one wonder if students should be reminded, the physicist must look for the Mathematics which describes the Physics.

 

[PeterDonis]

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?

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.

 

[Merlin3189]

Sounds to me as if they need to do some biology in order to understand physics here. IMO the reason you need to do work to carry the <heavy object> horizontally, is not so much to accelerate it horizontally to slow walking speed, nor to overcome friction (where?), rather the biological fact that walking involves a sort of bouncing motion and despite some elasticity in your body, energy is converted to heat on each up down cycle of lifting your mass and that of the <HO>. Muscles use fuel and produce heat both in contracting against a load and in extending under a load. (If anyone has heard of regenerative muscle operation - I'm quite out of touch these days - I'd love to hear about it.)

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.

 

[Mark44]

"yes, but why is Work = Force times Distance?"

Not exactly. Work is the dot product of the force and displacement vectors, something that @PeterDonis alludes to in the following quote. If the force and displacement vectors are othogonal, the work done is zero.

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.

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.

 

[Mark44]

In other words, none of us knows whether this child even exists.

Excellent point.

 

[Merlin3189]

Re. comment about "Why is work force times distance?"

Not exactly. Work is the dot product of the force and displacement vectors, ...

Doesn't that just mean the question needs to be phrased better, as "Why is work the dot product of 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!)

 

[PeterDonis]

That's good, but doesn't seem to me to answer the question as to why work is force times distance

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]

I wondered if that was the real answer. It does seem to be the answer to many questions here.

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=F.s If they can't frame the question correctly, maybe they need something more than the correct answer - more like an elucidation of the concept of mechanical work and how it comes to be so defined.
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.)

 

[PeroK]

I wondered if that was the real answer. It does seem to be the answer to many questions here.

A discussion on the history of kinetic energy is included 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:$$d(KE) = \vec F \cdot d\vec r$$

 

[Mark44]

But for me, it dodges the issue. Why did we adopt this definition? Why not include speed, or mass in the equation?

To be clear, "this definition" is $W = \vec F \cdot \vec{ds}$.

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 v, as it also must be done to slow it down at the end of the journey.
Let's assume that the sled moves on a frictionless surface for the sake of simplicity. Then once the sled reaches v, the sled will continue to move with no effort (force) required from us, regardless of the mass of the load or the speed.
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.

 

[vela]

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"?

From Newton's second law, it's straightforward to show that
$$\frac 12 mv_{\rm f}^2 - \frac 12 mv_{\rm i}^2 = \int_{\rm i}^{\rm f} \vec F_{\rm net} \cdot d\vec r.$$ 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.

What about all the situations where you work your ass off and achieve nothing?

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.

 

[PeterDonis]

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.

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.