That is just wrong. Equilibrium is not the same as stability. A perfectly balanced wheel gives us equilibrium with zero stability. If we add a weight to the bottom, we get equilibrium with positive stability. If we add a weight to the top instead, we have equilibrium with negative stability. If we add a weight to the side, at the 9:00 position, we no longer have equilibrium.
Also this is bad pedagogy. It violates the principle that learning proceeds from the known to the unknown. A student who doesn’t know what equilibrium means cannot be assumed to know what stability means. Evidently, even the author doesn’t know what stability means.
This is bad pedagogy. It puts too much emphasis on terminology and not enough on ideas. Are we defining mass in terms of inertia? What then is the meaning of inertia?
If you are going to assume the students know what inertia is, why not just go all the way and assume they know what mass is?
Books that take a more scientific approach stick to using the scientific term, mass, and don’t even mention inertia.
Four hundred years ago and more, a fast-moving ship sailing over calm seas was quite sufficient to demonstrate relativity, i.e. invariance with respect to uniform motion. Not every person had this experience, but more than a few did. The significance of this was explicitly pointed out in 1632 (reference 3 or reference 4).
It is a cheap shot to say that it was “said” to be done ... when in fact it was not done. We are supposed to be scientists, not smart-aleck lawyers.
There is no valid scientific or pedagogical reason to bring up this bogus story.
This is a big deal because it undercuts the credibility of many other statements throughout the book. For example, in section 19.1 we learn that «According to Huygens, you can replace the crest of any wave by series of equally-spaced wave sources....» OK, let’s stipulate that Huygens said that; the question then remains, was what he said true, or was it as bogus as what was said about the leaning tower of Pisa?
Very few airplanes fly «normally» – or at all – at a speed of 80 km/h. That’s 43 knots.
Furthermore, even setting aside that detail, this question is broken at a deeper conceptual level. The question is underspecified several times over. The pilot’s response to the perturbation is unspecified, the type of speed is unspecified (airspeed versus groundspeed), and even the definition of “forward” is unspecified (heading versus velocity). In aircraft – unlike cars – there is not a one-to-one relationship between heading and direction of motion.
- One way to analyze the situation would be to assume that the pilot encounters a crosswind and does not correct for it, allowing the airplane to be blown off course. In this case the groundspeed goes up.
- Another approach would be to assume that we have a direct crosswind, directly across the route of flight, and the pilot applies a suitable crosswind correction, so that the airplane remains on course. In this case the groundspeed goes down.
- Thirdly, in the real-world, if a copilot or an air traffic controller asks about “the” speed, the pilot will say “the” speed is unchanged. That’s because unless otherwise specified, speed means airspeed ... and the airspeed is unaffected by the crosswind. There is a good physics-based reason for this. Galilean relativity is a fundamental principle of physics, and is of immense direct significance to pilots. Sometimes you care about groundspeed and sometimes you don’t ... but you always care about airspeed.
- By the way, what’s the point of quantifying the original 80 km/h speed, but not quantifying the crosswind?
More importantly, it is a bad practice to use fake data and try to pass it off as real-world data. This is considered scientific misconduct.
OK, I’ll bite. Please tell me, why do forces always occur in pairs? I cannot imagine how a student is supposed to answer this question. I cannot imagine what purpose is served by asking such a question.
Galileo emphasized that the laws of physics must say what happens. The laws may or may not say how it happens ... and they rarely if ever say why it happens. Recognizing this distinction has been called the epoch, i.e. Day One of modern science. This is what sets physics apart from metaphysics and speculative philosophy.
This is a big deal; asking «why do forces always occur in pairs» sets science back 400 years.
Newton, having gone to school on Galileo, answered a similar question by saying “Hypotheses non fingo.” That is Latin for “I’m not going to pretend to guess”. To say it another way: nobody knows the answer, and nobody ever will, because question is not worth asking. There is alas nothing in this text that trains students to give such a response.
It’s not even 100% guaranteed that the third law is exact. If you express it strictly in terms of particles exerting forces on other particles, there are gross violations, as illustrated by the spinning disk in Feynman volume II figure 17-5; see reference 5.
It is better to reformulate the third law in terms of conservation of momentum (rather than force pairs) – but Hewitt does not do so. This allows us to answer a somewhat different question. Evidence suggests that the non-conservation, if any, must be very small: Kreuzer (1968); Bartlett and van Buren (1986). However, the fact that you can publish any data whatsoever on this topic means that intelligent people are willing to entertain the possibility that the discrepancy is nonzero. They want to see the evidence.
See also item 48. For more about what we mean by words such as “why” and “because”, see reference 6.
In summary, here is how I would respond to such a question. It must be emphasized that this is a response, not an answer, because the question in its original form is not answerable.
- The first rule is, all ill-posed questions must be recognized as such. The general topic of ill-posed questions is discussed in reference 7.
- Try to transmute it into the question that should have been asked.
- A question that begins with «why» should raise lots of red
flags.
- Transmute «why X» to whether X.
- Transmute «why X» to how do we know X and then how sure are we of that.
- Transmute «why X» to how could we have predicted X and then what is the evidence for X.
- In general, always ask in what ways is X consistent (or inconsistent!) with other stuff we know?
- Replace force-pairs by conservation of momentum.
- Rather than assuming strict conservation, assume there is some small violation, and look for evidence that places upper bounds on the magnitude of the violation.
It would be nifty if the book explained how to do all of that, or any of that, but it doesn’t.
First of all, momentum is never “in” mass or “in” speed. And even if it were, it would be proverbially crazy to compare apples and oranges in such a way.
Really? How do you know? If the concept is so central, why was it not developed until roughly 200 years after the so-called laws of motion?
I cannot imagine why anybody would say such a thing, or ask students to learn such a thing.
I don’t think conservation of energy is more central than conservation of momentum. I don’t think energy is more central than space and time. I don’t think energy is more central than arithmetic. I don’t think tunneling is well explained by focusing on energy transfer to the neglect of other considerations. See also item 50.
The whole discussion of what is “most central” is misguided. There is no center as far as I can tell. It’s not like high-school geometry proofs. Feynman said that knowledge is like a grand tapestry. A forgotten fact is like a hole in the tapestry. You should be able to repair the hole in several different ways, by reweaving down from the top, or up from the bottom, or in from the sides. Any important fact can be rederived in numerous ways, because the things we know are interconnected in innumerable ways.
It would be better to write it as “force • distance”, using a dot rather than a cross. You could argue that a student reading the book for the first time would not appreciate the distinction between cross-product and dot-product ... but what about somebody reading the book a second time?
Perhaps the assumption is that nobody will ever give this book a second look.
- For starters, there are other ways of defining power. For
example, it could be defined in terms of energy instead of work.
I hope nobody argues that the distinction between work and energy is beyond the scope of the presentation, because on the facing page of the book there is an example that involves just such distinctions, including thermodynamical notions such as dissipation and temperature.
- Given that the students don’t really understand work, it does no good to define power in terms of work. In particular, in any nontrivial situation, work is a vector in thermodynamic state space ... and it is not the gradient of any potential. The same is true of power. Therefore a lot of the ways you might like to keep track of power are mathematically impossible.
- Even if the work-based definition were the only definition, it would still be problematic, because there are four or five competing definitions of work.
- What’s worse is that oftentimes people define power
one way and use it another.
I get almost twice as many hits from googling “watts of thermal power” than from “watts of mechanical power”.
This sows confusion for no reason. It would have been super-easy to state things more carefully. The rule should be, if you mean energy say “energy” and if you mean kinetic energy say “kinetic energy”. This involves no extra work and no increase in complexity, and results in a significant increase in clarity and correctness.
This pulls the rug out from under the whole discussion of the law of conservation of energy.
Given that the physics energy is conserved, it cannot have any sources or sinks.
Apparently 9.11 is using the word energy to mean something other than the physics energy, presumably some kind of “available energy”. This is one of the homespun meanings of the word energy. Available energy is important, but it is not the same as the physics energy.
Because it is conserved, the physics energy cannot have any sources or sinks. When people talk about a «source of energy», it would usually be more accurate to rephrase it in terms of making energy flow in useful ways. For example, consider the rest-energy tied up in the mass of a large stone. That is an enormous amount of energy, but it usually isn’t considered “available energy” because there is no way to make it flow in useful ways.
I mention this because even if we re-interpret the statement as a claim that the sun drives «practically all» of the energy flows on earth, it’s still an overstatement. There is a nontrivial contribution from radioactivity i.e. nuclear energy. Note that geothermal energy flows can be considered an indirect manifestation of nuclear processes within the earth.
By way of contrast, consider gravitation. We do not normally introduce gravity by reference to the upward «force you feel from the» floor. That is, we do not normally describe a given force in terms of the constraint-force necessary to oppose the given force.
The fact is, the centrifugal field exists in a rotating reference frame and not otherwise ... as correctly explained in section 10.5. That means the discussion of centripetal forces in a rotating frame should be delayed until the relationship between the centripetal and centrifugal forces can be appreciated.
That’s weird. First of all, it not uncommon for an object to go out of equilibrium while its center of mass is still above the area of support. An example is the top-heavy bus discussed in item 18.
(Conversely, for what it’s worth, it is possible, and indeed common, for an object in equilibrium to have its center of mass below the area of support ... not above.)
More importantly, the idea of «area of support» is not helpful for analyzing the rotational equilibrium of a bird, aircraft, or spacecraft in flight. It does not even apply to the nut+wrench situations that are prominently featured in section 11.1.
The idea of «area of support» is a watered-down version of the idea of “line of action” of a force, which is not covered in this book. Furthermore, its relationship to equilibrium depends on the notion of force of constraint, which was hinted at in the «Personal Essay» in section 2.1 but never fleshed out to a usable degree.
The problem is, the statement is just not true. It is certainly not true for a top-heavy bus while cornering.
There is no such thing. It should have said neutral stability or perhaps neutrally-stable equilibrium.
However, the fact is that in the Gulf of Mexico, it is normal to have only one high tide and one low tide per day. This fact is symptomatic of a deeper problem, namely failure to distinguish between (a) the tide-producing stress, and (b) the actual tides that are produced when this stress drives a very complicated response function. See reference 9.
This paints a highly misleading picture of the history. This principle is properly known as Galileo’s principle of relativity. The author must know this, since it was discussed in sections 3.6 and 4.1 of the book.
The problem is, those two statements do not correctly summarize special relativity. The chapter fails to mention the breakdown of simultaneity at a distance. We are left with a caricature of relativity that is so incomplete as to be conceptually incorrect and utterly unusable.
See also item 23.
However, the fact is that those two statements are – at best – matters of opinion. For more than 100 years, the consensus of expert opinion is that a boost (changing the velocity) does not change the length of a ruler, just as a spatial rotation (changing the orientation) does not change the length of the ruler. It may change the projection of the length onto this-or-that coordinate axis, but it does not change the length per se.
It is perfectly possible to teach relativity the modern (post-1908) way, using clocks that mean what they say and rulers that mean what they say; that is, emphasizing proper time, proper length, and invariant mass. See reference 10 and references therein.
See also item 22.
First of all, that is wrong because the rest energy mc2 is not even numerically equal to the total energy; it is just one contribution to the total energy, as we can see from the more-detailed expression E2 − p2c2 = m2c4. We see that E=mc2 only when the momentum p is zero, i.e. only in the rest frame of the particle. By way of counterexample, for a photon m=0 and E=pc. The photon is never at rest so it never has E=mc2.
Secondly, at the conceptual level, even if/when two things are numerically equal, that does not necessarily mean they are «the same thing». Despite the title, this book does not seem to care much about conceptual issues.
That’s untrue several times over.
- For one thing, a real airliner’s flight path will generally differ from the great-circle (geodesic) route for practical reasons. This includes taking advantage of favorable winds, avoiding restricted airspace, making way for conflicting traffic, et cetera.
- Secondly and more importantly, although the earth is curved and the map is flat, this does not even begin to tell you how much the geodesic appears to curve when plotted on the map. Aeronautical charts use conformal projections, so that on the map some geodesics are straight and the rest are so nearly straight that their non-straightness is negligible compared to the non-straightness of the practical route as discussed in the previous item.
As a matter of principle: If you want to talk about some model system in which your idealized aircraft flies along a geodesic, that would be OK in moral terms (although of dubious relevance and practicality). However, you have to say what you are doing and not pretend you are doing something else. It is highly improper to pass off models and idealizations as if they were observations about the real world.
This does not count as misconduct, because it is clearly labeled as a simplified analogy ... but still, it’s wrong physics and bad pedagogy. Better analogies are available, analogies that are simultaneously simpler and far more apt. It turns out that gravitation causes spacetime to be strongly curved in the time direction, and this must be taken into account. Also, the marble does not roll along a geodesic. Methods for constructing simple, highly informative geodesics are available; see reference 11.
See item 23 for more on this.
That’s just not right. There were plenty of people who understood atoms before Einstein. One major turning point was in 1865 when Loschmidt measured the size of the molecules that make up air. On the other side of the coin, for what it’s worth, there were still people who disbelieved the evidence long after the early 1900s.
For one thing, the experimental chemistry and the theoretical atomic physics both indicate that there are 15 lanthanoids, from 57La through 71Lu inclusive. See reference 12.
It’s true that the dynamic pressure ½ρv2 is equal to the kinetic energy per unit volume, and it’s true at the level of dimensional analysis that the overall pressure P has dimensions of energy per unit volume. However, there is more to physics than dimensional analysis. The pressure is simply not numerically equal to the energy per unit volume. Actually, for nonmoving air, the pressure is numerically equal to about 40% of the energy per unit volume.
Bernoulli’s equation can be explained in terms of enthalpy. Enthalpy has the same dimensions as energy, but it’s not the same thing. Also there is no law of conservation of enthalpy, so what the book says is just not true. Not quantitatively, not qualitatively, not conceptually, not at all true.
First of all, the claimed effect is not what actually happens. (There are situations where the Mpemba effect can be observed, but this is not one of them.) In any case, the second part of the statement, i.e. the explanation, is complete hogwash.
In fact, though, the way in which kinetic energy “approaches” zero is wildly different from the way in which temperature “absolute” zero, because of the quantum-mechanical “zero-point motion”. The temperature can get arbitrarily close to zero, but the kinetic energy cannot.
No part of that explanation is correct.
The flow of air through an orifice is never adiabatic. Adiabatic expansion would require doing work against some sort of engine. This should be obvious from the proportionality between energy and temperature for air (or any other polytropic ideal gas).
Also, even if the process were adiabatic, the cooling associated with expansion would simply undo the immediately-prior heating associated with compression.
Alas that’s not what entropy is.
This misconception is plausible and widespread, but it is still a misconception. The fact that it is plausible makes it all the more pernicious.
Still, if you think about it for a moment, you realize that entropy is a property of the macrostate, whereas disorder is a property of the microstate ... so these things could not possibly be equivalent. If we know what microstate the system is in, even if it is a very disorderly-looking microstate, then the system entropy is zero. See reference 14 and references therein.
That’s certainly not true for Čerenkov radiation. It is not true to any significant degree for the pop of a firecracker or the crack of a whip.
That’s certainly not true for light. There is no medium. The idea of a luminiferous ether has been dead for more than 100 years.
That relationship is not even remotely true for waves on the surface of a body of water. The propagation of such waves is highly dispersive. It’s also not true, if look at all closely, for waves on a piano string. For a wide range of practical purposes, the group velocity serves as “the” speed of the wave, and that goes like dω/dk not ω/k.
That’s not true for sound waves in solids.
That’s untrue in principle, and if the voltage is high enough it will be untrue to a quite significant degree. This is an AC circuit, and a dangling person has a nonzero self-capacitance. For a 500,000 volt line, if we model the dangling person as a cylinder 0.15 m in radius with a length of 2 m, I calculate a current of about 8 mA, which is well above the threshold of pain.
| є0 | 8.8542E-12 | F/m | ||
| radius of cylinder | 0.15 | m | ||
| cutoff | 2 | m | ||
| log factor | 2.59 | |||
| length | 2 | m | ||
| capacitance | 4.2955E-11 | F | ||
| freq | 60 | Hz | ||
| impedance | 61752458 | ohm | ||
| voltage | 500000 | V | ||
| current | 0.008097 | A |
For an even more spectacular example of self-capacitance in connection with high-voltage power lines, see http://www.youtube.com/watch?v=rkYq17gTCq8
That evidently assumes that any device that «fails» becomes an open circuit. That is simply not true. It’s not even true for all strings of decorative lights; in many cases the lamps in such strings are engineered to fail short rather than fail open.
This same misconception is repeated elsewhere in the book. It is simply not correct – and not safe – to assume that every failed device is an open circuit.
Again: It is simply not correct – and not safe – to assume that every failed device is an open circuit.
That is misleading several times over. For one thing, in the first sentence it would be better to say “can be made” rather than «are made» since that is by no means the only way of making permanent magnets.
In the second sentence, I generously assume «soft iron» refers to highly pure iron, which is both mechanically soft and magnetically soft, so that the distinction between mechanical softness and magnetic softness does not matter too much. It would be completely unreasonable to expect students to recognize the distinction.
Also in the second sentence, context seems to require that the word «magnetize» must refer to permanent magnetization (as opposed to temporary induced magnetization) ... which means the sentence is entirely false. It is absolutely not easier to create permanent magnetization in soft iron, compared to the alloys that are normally used for permanent magnets.
Alternatively, if you assume that «magnetize» refers to temporarily induced magnetization, the book is wrong for the opposite reason: The silicon steel used in real-world transformers has almost an order of magnitude more permeability than pure mechanically-soft iron ... not to mention the fact that the latter would be wildly impractical in economic terms, and is never used in practice, contrary to what the book says.
Really?
For starters, not all matter is solid. How are we supposed to understand what light does in the presence of a rarefied gas? Or a dense liquid?
Furthermore, the fact is that there are innumerable examples of wavelike interactions between light and matter. Familiar examples include:
- Light interacting with the solid matter in a diffraction grating.
- Similarly, X-ray diffraction within the bulk of a 3D material.
- The anti-reflection coating on a lens.
- The colorful films mentioned in section 31.5.
See also item 8 and reference 6.
That’s not actually true. Chemical reactions involving deuterium proceed at a different rate compared to hydrogen. The same is true to a lesser (but still noticeable) degree for the isotopes of lithium.
At a more fundamental level, if the sentence is going to talk about the number of neutrons, why not define isotope in terms of the number of protons? This makes the sentence simpler and more correct. As emphasized by Strunk & White among others, if you are going to draw a parallel or draw a contrast, use corresponding words for corresponding ideas.
Sorry, the energy argument in the second sentence is not correct. For starters, 236U is lower in energy i.e. more tightly bound than 235U. You should know that fact even without looking it up, because fission is promoted by slow neutrons, and if the neutron were not attracted to the 235U it would never have been absorbed. Alternatively, you could just look it up (reference 15) and find that the binding energies are:
| nucleon | bound state energy | |
| 235U | −1783870±2 keV | |
| 236U | −1790415±2 keV |
More generally, despite what the book says in chapter 9, not everything can be analyzed by focusing on energy transfer to the neglect of other considerations. For more about the actual mechanism of induced fission, see reference 16. See also item 10.