studiot

I don't know what you mean by simple symmetric processes (or systems). Consider, for instance, the question "What is the kinetic energy of Mars?" Well to know the KE, you have to know the velocity and the mass. But someone on Earth, Jupiter, Alpha Centauri or some nearby black hole would all disagree on the velocity, although they might agree on the mass. So how can you tell if the KE is conserved if you don't even know what it is? I'm sure there are equivalent electrical questions. COE works well when we consider the change of energy from one form to another, which was why I mentioned processes. So you could ask Does COE hold for generating electrical energy from steam? or in the electrical heating of my bedroom? or perhaps can I transfer all the electrical energy from one battery to another?

Well I think COE applies to processes not systems.

Well I'd like to thank you for bringing something I'd never heard of to my attention. There really are some fascinating relationships in number theory.

What is the difference between a mirror and a sheet of paper in terms of what happens to incident light? Look up the term 'specular'.

As stated I find the question meaningless. What do you think the COE applies to and what sort of proof are you looking for?

Consider a situation where there are plenty of free electrons, say in a cathode ray tube. Are they reflective?

That is a perfectly reasonable question to wonder about. You need to distinguish between macroscopic and sub atomic effects. Macroscopic effect are due to the combined efforts of a very large number of particles and any network of forces or bonds joining them. Sub atomic effects are due (usually) to the interaction between a few (sub atomic) particles or even the interaction between one particle and its surroundings. The absorbtion and subsequent emission of photons is a sub atomic effect, called the photo-electric effect. Note that this occurs for a specific wavelength or a number of wavelengths, for example the sodium yellow spectrum lines. It does not occur for a broad range of frequencies as happens in reflection of light. Reflection is a macroscopic effect that is best not thought of in terms of quantum mechanics. Note I did not offer any structure to my reflective wall. This is usual for the physics of macroscopic quantites - we do not enquire into the fine structure. Note, however if you made a mirror of polished sodium, it would remove the yellow light and perhaps re emit it randomly, as you describe. Meanwhile it would reflect the rest of the wavelengths you shone onto it.

The Mathematical Description of Shape and Form Lord and Wilson pub Ellis Horwwod Geometry of Spatial Forms Gasson pub Ellis Horwood Computational Geometry for Design and Manufacture Faux and Pratt pub Ellis Horwood Elementary Linear Algebra Anton and Rorres pub Wiley

Extrapolation means going beyond what you know to guess at what you don't know. This can lead to your guess being wildly wrong, as in the above. The Wave Function is in no sense an extrapolation. Interpolation means bracketing what you don't know between things you do know in the hope that your guess will be closer. It can also be very inaccurate, but it can yield useful, even good results as well.

What more did you want to know? I made it about as simple as possible.

I'm glad to learn that you have solved the problem yourself, this is always the best way. I did observe that this problem has subleties - you need to invoke most of the principles of mechanics to justify the steps in the solution, so I would be interested to see your solution if you would care to post it.

There are too many questions in the original post. As a start I suggest you get hold of the difference between interpolation and extrapolation and why the latter is a more risky method. Both methods are ways of obtaining the value of some function at points you have not measured or do not have tabulated data for and cannot calculate exactly.

Thank you for replying. You haven't got your mechanics quite right. The above is true but the only because it determines the tension in the string, which in turn determines the horizontal reaction from the wall. Nor does it negate what I said since I did say moment about the centre of the roll, not some other point where there are undoubtedly different moments.The trick in mechanics is to take your moments about points where as many forces as possible pass through and therefore have zero moment. This question is actually quite subtle. There are three situations: 1) With the roll just hanging there and no pull on the paper. 2) With the roll hanging and a pull on the side opposite the wall. 3) With the rolll hanging, and a pull on the side by the wall. Since the tension is not necessarily the same in each case that yields 9 equations in 12 unknowns. There is no deformation so we cannot use compatibility Stress is not considered so we cannot use elasticity However we can consider the situation at limiting friction which yields a further 3 equations, bringing the total up to 12 - a happy situation since we now have enough to solve the question. Here is the full set of 12. Note I have replace sin and cos by constants a and b since the geometry does not change so we can more easily see the set of equations is linear and and manipulate them. What remains is a page of further manipulation, first substitution then setting up and manipulating an inequality to achieve the desired result. I will leave that part to bon if (s)he is still interested.

Can you expand on that?

So what do you want to say is true?

You said the frictional force is equal to the pulling force. Applying this to test if the frictional force is equal to the pulling force it must have the same amount and direction. Is this true?

What is your condition for one vector to be equal to another? Now test this against your statement above.

OK you seem good on the formula side but perhaps lacking in experience in translating this into hardware. This is not a criticism the skill should come with practice. A force cannot exert a moment about any point in its line of action. Or The moment of a force about any point in its line of action is zero. So the moment of W about C is zero - It has no moment about C. Because its line of action passes through C. Now look at your first diagrams. You have shown two forces whose line of action pass through the centreline of the roll - the tension in the support string and the weight of the roll. Therefore these forces have zero moment about the centreline of the roll. That is why I said they are irrelevent. That leaves only two forces that can exert a moment about the centre line of the roll. Can you see this and tell me why we need a moment about the centreline of the roll?

That last post is college level stuff. So why can't you tell me what the moment of force W is about point C in my diagram? Hint it is exactly the same as the moment of the weight (mg) of your roll in your diagram about the central axis of the roll.

You have stated that the moment of a force is the force times the distance from the force to some point. This is not true, because it is imcomplete and the missing bits are very important. The moment is the force times the perpendicular distance from the point of application to the line of action of the force. Do you understand what this means, because your responses suggest you do not. Do you have any course notes? I suggest you revise moments or torque or turning effect before proceeding.

So what is the distance from C since since the line of action of W passes through C? In other words, what is the value of r?

So in my sketch of the block on the table, if C is the fixed point and W is the force what is the moment of W about C?

bon, do you understand what a turning moment is?

Oh dear oh dear, You still haven't responded to my question. I have no idea what Fz and Fr or T might be. I am guessing that R is the radius of the roll. Here is a block resting on a table. The weight of the block acts at the C of G of the block and passes through point C as shown. What is the moment of W about C? This is absolutely fundamental to your understanding not only of this problem but mechanics more generally.

Bon, I will try one last time. If you want to make progress, please simply reply to the questions or comments I (or perhaps others) make. That is the point of a forum. I have told you twice that your approach is fundamentally wrong, but you haven't asked me about it. So one last time. What do you know about the moment of a force about a point the force passes through? You may call it the lever rule.