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Oh ok, I see the edited message now. This is the problem which had me start this topic. By the way, I'm realizing just now that I was not very precise in my OP. The problem is n° 62 in chapter 24 (page 767 in my version of Cutnell and Johnson's "Physics, 9th edition"). This is what I initialy...

Sorry I keep confusing the angles... Kuruman says that \theta (i.e. the position of the analyzer) is fixed, and the polarizer is rotated. But rotating the polarizer does change the angle between the analyzer and the polarizer, whatever we may call that. Also it changes the angle between the...

Wait, now I cannot rotate it all the way? So what you're saying is that I rotate between some angle and some other angle, which do not necessarily correspond to the absolute maximum and absolute minimum of the intensity? I choose a value for \theta look at the intensity, then change \theta by...

No, I do not agree. Or better, as I mentioned, I think that the problem does not make sense this way. If I can rotate the polarizer relative to the analyzer, I can get to the point where their axes are crossed. Nothing gets to the photocell in that situation, because whatever emerges from the...

Hi kuruman, not sure I follow now. My interpretation of the problem is that the angle \theta between the analyzer and the polarizer is fixed, and the angle \phi between the polarizer and the incident polarized light varies. This gives your second formula for the intensity at the photocell, which...

Hi kuruman, thanks for your reply. It seems to me that, as far as the maths is concerned, we are saying the same thing. You wrote the general form for the intensity reaching the photocell, while I wrote its maximum (\cos(\phi)=1) and minimum (\cos(\phi)=0) value, which are directly involved in...

Hi Steve4Physics thank you for your reply, and for your praise of my English :smile: Sometimes I worry I am not understanding something obvious because of the "language barrier". I thought that "polarizer" might mean the whole "polarized + analyzer" system, but I was not sure. After all, I think...

Hi scottdave, thanks for your help. I have found an article in the American Journal of Physics that should cast some light on the subject. I have not had the time to read it seriously, but straight from the abstract it challenges the claim that the particles come to rest at (or close to) the...

This is problem 62 in Cutnell & Johnson's Physics (9th edition): Suppose that the light falling on the polarizer in the figure is partially polarized (average intensity \bar S_P) and partially upolarized (average intensity \bar S_U). The total incident intensity is \bar S_P+ \bar S_U and the...

hi scottdave, your reply is very short, so I'm not sure I get what you mean to tell me. Are you suggesting that the bright areas are bright because the pressure is changing a lot with time? Thus, being antinodes, the bright areas would indeed be the places where pressure reaches its maximum...

So the video I'm referring to is the second in this webpage. Around time stamp 3:55 mr Wolfgang, the demonstrator, says that the little balls settle down at the high-pressure areas, which are signaled by the bright bands in the Schlieren image. We understand this by noticing that the area near...

Thank you for your answer. I have a really little knowledge of magnetism in ferromagnetic materials, but your explanation is more or less what I figured from tech99 reply. I tried to put my understanding into words, but couldn't explain myself well. I thought that as well, but then I read that...

Hi, i think I've got my answer, which is along the lines of what gmax137 suggested. A friend suggested that W. Fendt's is actually a very simplified version of a real dynamo, and that one could use more than one armature. I made some diagrams. This is what happens with W. Fendt "single...

Oh, I think I sort of see what you mean. I did not think of the role of the iron core. I'm not exactly sure I know what you mean by "steady component", though. My knowledge of this field is extremely limited. Can I understand it like this? Since the current changes in time but flows always in...

So, if I get it right, the basic argument goes like this: AC was preferred to DC because its voltage can be stepped up by a transformer. This limits losses while the current is transported from the production plant to the final user. The voltage is subsequently stepped down when delivered to the...

Thanks for your help. I usually find a translation, when it exists, often using the method you suggest. The point here is the lack of a translation, though. As I mention in the O.P., since in this case I could not find one, I suspected that there wasn't any. Your examples above sort of...

Of course, that's why I've asked in the first place. Thanks

I suspected that English might not have/need those definition, but I was not sure. For instance, I believe you have definitions for similar concepts in the context of linear systems (consistent, inconsistent, dependent). I see what you mean. My only worry is that the notes I'm looking at refer...

Hi fresh_42, thanks for the tip. I usually try that. Or better, I look for definitions in English and match them to the Italian ones. The method you suggest won't always work. Wikipedia pages in different languages may have pretty different structures. Often they are not simple translations of...

Hi, I am looking at some lecture notes in Italian, and I'm wondering about the correct English translation for some terms. I am afraid that in some cases the "literal" translation would sound weird. I looked online but I still have some doubts. In some cases I was not able to find a satisfactory...

What you are describing is an algorithm for determining the unknown vector. As you say, when the vectors are unknown, sometimes there is no way of drawing them in their actual direction for sure. I agree that in these cases the cleanest way to go is to draw them in the same direction as the...

I think the point is kind of subtle, and has to do with the definition of cartesian components. I think that, rigorously, components are scalars. Sometimes these are represented as vectors along the relevant axis. If the sign of the cartesian component is known, there is no real problem with...

Yes, I think I understand what you mean. I was just referring to the fact that the vector I initially draw before writing and solving the equations might have the wrong direction. After solving the equations I might have to draw a new figure where the direction of the unknown vector is the...

I was afraid of that. So one has to start by guessing the direction of the friction. The equations will contain the cartesian component of the friction rather than its (positive) magnitude. If this component turns out to be positive, the initial guess on the direction was correct. Otherwise, the...

The figure illustrates the situation. The radii of the larger and smaller discs are 2R and R, respectively. Their masses are M and 2M, respectively (the largst disc has the smallest mass). Also, m=5/4 M, where m is the mass of the suspended object. The pulley is "massless" (negligible moment...

Do you mean something like this? If there is no friction between the table (and if we assume a chalked cue, to avoid the normal force from the table), the only relevant force is the one applied horizontally by the stick. One can set ##\tau = F(h-r) = I \alpha## and ##F = m a##. One can then...

yes, I can imagine that... And if it is not chalked one should consider the reaction of the plane. I guess I'm trying to find a set of reasonable assumptions that make the problems like the one in the OP not too messy. These problems are like Find the optimal height such that the ball rolls...

Ok so if I get it right: the chalked tip of the stick exerts an additional vertical force which makes the reaction from the ball horizontal or almost horizontal (the additional force would be tangential, but anyway this means it has a vertical component and a horizontal one. The former ends up...

Yes, even while asking that question I was not very convinced that the ball would jump upwards. I was just trying to understand what to make of the reaction of the table.

ok yes, of course. I was focusing only the impulsive friction related to the the impulsive normal reaction from the table. Is there any other effect I did not consider? Are you suggesting that the ball tends to jump upwards because there is no force balancing the impulsive reaction from the table?

Ok, yes... I get it. The part of the friction that is proportional to the ball weight can be safely ignored. However, the large horizontal impulsive force generates a large reaction force from the table, which in turn generates a large frictional impulse. This still does not contribute to the...

Hi, thanks for your help. not really... I am considering an axis of rotation on the table. The correct lever arm for the force is ##h##, right? The approach of thread 1 confuses me a little. I guess it's hard for me to imagine a horizontal force acting on the ball for a finite amount of...

Summary:: I'd like to check my understanding of standard problems where a billiard ball resting on a plane is hit horizontally at some height above its center So the situation is that a ball of mass ##m## and radius ##r## is at rest on a horizontal surface. There is friction between the ball...

No worries. I would like to have time to brush on that formalism. So my book starts with the (in my opinion) handwaving and confusing introductory part, then gives the postulates of SR, discussing (a simplified version of) the de Sitter argument in support of the invariance of c. The explicit...

So I'm still not clear on how "Newtonian mechanics works just fine with Maxwell’s electrodynamics.". This sounds more like "Newtonian mechanics was expected to work just fine with something more intricate than Maxwell's equations, but this turned out not to be the case in the end". I never had...

Whoa. This is way too advanced. The level of the textbook is basically the same as "Physics" by Cutnell and Johnson. The authors added a paragraph on Lorentz boost, but not with this formalism. Most of the students are already struggling with what's in the book. I do realize that my calculation...

Thanks for the paper, I'll look into it. As I mention, the textbook is aimed at high school students. The material is basically the same as in chapter 28 of Cutnell and Johnson's "Physics" but with a few additions. Though not very advanced, my calculations would fly over most of the students'...

Not sure I understand. Are you saying that assuming the existence of aether one could make sense of the disagreement in the "two proton example"? Does that mean that the different acceleration in the two frames of reference can be explained by the fact that (at least) one of them is moving wrt...

Hi, sorry, it's just unlikely anyone here is familiar with that book. It is an Italian high school textbook, mostly adapted from Physics 9th edition by Cutnell and Johnson. A lot of the material there is the same as in the original book. However, the Italian authors added a sort of introductory...

Before introducing Special Relativity, a textbook highlights the inconsistency of Maxwell's Electrodynamics and Newtonian Mechanics through the standard discussion about the velocity of light in different frames of reference. A further inconsistency discussed. In some inertial frame of...

Yes, I understand this. Only, we cannot lower the topmost point alone, so the "lowering" (and the loss of contact) would start below that point. Of course we can argue that the "jumping point" is arbitrarily close to the topmost point. I was just trying to imagine a reasonably simple smooth...

ok... the dirtbike jumps before the top... That is also my intuition. But I think the hills are not shaped for avoiding that effect. I am wondering whether it's (theoretically) possible to build a hill where the motorbike would lose contact at the topmost point only, like the skier in the...

Ok so, the "other scenario" was a hill shape on which the contact force is absent. Actually, I should have thought of that! So if the central part of the hill is a parabolic arc, then there is a critical velocity for the skier at the inflection point connecting such arc with the concave part...

first of all, thanks for your time and help. Ok, in a way the subtext of the original problem is "just focus on the very top of the hill, without bothering about what might happen elsewhere". The fact that I'm not able to picture in my mind the shape of the hill such that nothing actually...

I'm actually not very clear on what is meant here by "crest of the hill". I interpreted that as "the uppermost portion of the hill", not just its very top. That is, I assumed that the (section of the) top of the hill can be described as a circular arc, which is what the figure suggests. In that...

This is problem 49 in chapter 6 of "Physics - 9th edition". A similar question was asked here several years ago (although with a different height). The figure is below. I added point A and angle \theta . The solution is pretty easy. For the purpose of my discussion I'm assuming that the height...

Uhm... I see. I tried representing what you're suggesting in a sketch. Since the dimensions for the coefficients should be ##\rm W m^{-2} K^{-1}## , I guess that the three relevant equations are $$ \left\{ \begin{array}{l} P = C_{\rm i} A (T_h-T_1) \\ P = k \frac{A}{\tau} (T_1-T_2) \\ P =...

Hi haruspex, thanks for your reply, and Merry Christmas. I'm not sure I understand your suggestion, though. You're saying that I should assume that ##T_h## is the temperature "at the flame" and it decreases through the hot air inside the balloon, so that it reaches ##T_1<T_h## at the internal...

Me again. I am still not clear about the convective heat transfer coefficients, which in the original problem are dimensionless numbers. I think one could work out an upper limit for the thermal conductivity coefficient of the balloon "skin". I'm going to introduce an efficiency coefficient...

The problem gives these data external (cold) air temperature: ##T_c = 20^\circ{\rm C}## internal (hot) air temperature: ##T_h = 80^\circ{\rm C}## lantern volume ##V=0.2 {\rm m^3}## lantern surface ##A=2.0 {\rm m^2}## lantern mass ##m_{\rm L}=30 {\rm g}## external convective heat transfer...