studiot

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.

I am trying to get bon to think about the mechanics of the situation since his approach is fundamentally wrong (and also far too complicated, making life difficult for himself).

Hopefully you understood that. You may have noted that I did not try to calculate the force of impact. Doing that brings in some difficult mathematics. Happily it doesn't matter what the value is - It is the fact the that action and react are equal and opposite that counts. Is light made of a stream of particles (we now call them photons) or is it some form wave motion? This question has been puzzling scientists for nearly 500 years and is still not fully answered since the answer appears to be much more complicated and involve some very deep physics and mathematics. The short answer is yes photons behave exactly as I've descibed above. This was Newton's original explanation for light (although he called them corpuscles). He also showed how a stream of corpuscles could account for the other activity of light - That of refraction. However someone called Young proposed a rival theory that also accounts for both these. It was the wave theory. Both theories correctly predict the size of angles in reflection and refraction. However the the corpusculer theory requires that light speeds up when it enters a denser medium, such as water or glass whilst the wave theory required that light slowed down. No one at the time was able to measure the speed of light so the argument raged. In the early eighteen hundreds Foucalt did measure the speed and showed that light slows down so everybody thought Ahh - light is a wave. But at the end of the nineteen hundreds the photelectric effect was discovered. This cannot be a wave phenomenon. Combined with the explanation for spectroscopic lines the quantum theory was born whereby light has characteristics of both particles and waves. In the middle of the twentieth century further, more bizare effects were discovered that we call quantum entanglement, so the story is ongoing.

Thank you, that is as I read it. However bon has not included the force pulling on the roll of paper in his diagram, so cannot hope to achieve a solution. This is homework help, and I believe this is set work, so I cannot do the problem for him, only prompt for direction.

I'm gald you have been studying resolution of vectors. You should be able to follow this explanation. With reference to the sketches. Let us say we have a single particle moving at steady velocity V towards a wall at angle alpha. It hits the wall and bounces off at angle beta as shown in fig1. What you are asking is why does beta = alpha. In fig2 I have resolved V into two components Vy at right angles to the wall and Vx, parallel to it. V is obviously the vector sum of Vy and Vx In fig3 I consider the instant of impact. Now the velocity parallel to the wall, Vx is unaffected by the impact. The particle continues travelling to the right at the same velocity. That is Vx after the impact is the same as Vx before the impact. However in fig3 we also see that the particle is brought to a complete stop at the instant of impact in the y direction. That is At impact Vy = 0 momentarily. If you have learned about momentum we say that all the momentum in the y direction becomes the force generated by the particle colliding with the wall. If you know Newton's laws you can write this more mathematically, if not it doesn't matter, just accept that this is what generates the force of the particle hitting the wall. I have called this force Fy in fig4. Now one of Newton's law says that action (the impact) by a force of one object on another is always returned by a reaction force from the suffering body (the wall) which is equal in magnitude and opposite in direction to the action. So the wall exerts a force -Fy on the particle This must accelerate the particle to -Vy since it took +Fy to stop the particle from +Vy I have shown this in fig5 So the particle now moves off the wall (ie it reflects) with a velocity V' whose components are Vx and -Vy at angle beta. Can you see that this angle must be the same as angle alpha, since the components have the same magnitude, but only differ in direction?

What tensile force? And, like I already asked you, why did you not show it on your diagram?

So why not show it on your diagram? I am helping you, but you are totally off track with your analysis. If you are to pull sheets off the roll what must happen? That what must the roll do?

I don't see that the tension in the string or weight of the roll has any real relevance to the forces of unrolling. And you haven't shown any pull force on the paper.

Maybe it's the weather, but I'm sorry, I have looked at you diagram three times and I still don't know what is what. Please try to explain in no more than 5 lines what exactly makes up your system or systems. For instance what is a suspended sort What are the circles on your diagram? What is mg the weight of? You have already done a lot of calculation so don't do any more until we understand your setup.

Hello ajinkya, you might be suprised what most people would understand. Much maths is only a posh way of stating what people know anyway. Do you understand resolution of forces, velocities, distances etc into components? By this I mean, do you understand where I would end up if I walked paces west then 100 paces north, relative to my starting point? You answer will determine how I phrase my explanation of your question about the mechanism of reflection.

What I was getting at is that all the curves or graphs I mentioned look the same. The constants are merely scaling values to make the data fit. Of course some phenomena fit different mathematical curves, but the principal is the same. I am suggesting that these fundamental constant can be viewed 'fitting parameters'.

All I can think of is that mathematics uses numbers and doesn't care what those numbers stand for, the mathematics is the same. That is many quite different and unrelated phenomenon follw the same mathematical relationships. So the temperature difference between a cooling object and its surroundings The voltage on a capacitor discharging to earth My bank balance after payday All follow the same the same mathematical relationship. That is the graph of each of these things, plotted against time, is the same. It is the physical units that are different and quite irreconcilable, like your functions of the organs of the body. You would no more take the temperature of my bank balance than you would the voltage.. Is this what you are asking about?

Analytic continuation does not only apply to complex analysis. It is a very useful method that we rely on in numerical methods, differential geometry, real analysis, fourier analysis and and really anywhere that we want to include points on the the domain boundary in our analysis.

I'm sorry I don't see what the question is. What do geodetic potentials have to do with geometric constants? And do you really mean pi radians or steradians (solid angle)?