studiot

Since you didn't answer my question about the acceleration and deceleration before I will ask it again (hint hint) What can you say about the two triangles? Now can you write (and post here) 1) an equation connecting the information given (distance) and your graph? 2) an equation connecting the times on your graph and the information given? So what can you say about Ta and Td ?

You have enough information to solve this. I suggest you draw a velocity-time graph. The distance is the area under the graph. What can you tell me about the acceleration periods and deceleration periods?

No Mike, it's actually a game called the epsilon-delta game. You offer the size of your smallest step from one number to the next and I will find a number that fits between them, no matter how small you make that step.

Game or not I would (respectfully) suggest that yield point is not a good indicator of damage resistance. Two alternatives you might like to look up are 'engineering resilience' and 'fracture toughness'. As regards to hardness, this only makes sense for solids. Many elements are not solid, and some do not I think form solids.

If you find ajb's response too technical, try Chad Orzel's How to teach Quantum Physics to your Dog This book is nearer Brian Greene's level, although Chad is actually a quantum physicist.

Looks like The Italian Job to me.

I'm not sure what you are trying to say but it doesn't sound right. Area of a matrix?

It should not be forgotton that the centre refers to the cente of the system, not any particular paticipating particle.

I see you are still talking at cross purposes. Here is a formula from the same linke dWiki article that clearly includes speed However the article also says there are several definitions of the 'coefficient of rolling resistance' It is also about vehicles and states that it includes driving mechanism losses. I understood we were talking about hard bowling balls, with no motive power. My sources suggest that the losses I refer to (they called them hysteresis losses) are less than 1% for metals, but may be up to 90% for elastomers, which is what I said earlier.

The issue of sign seems to have caught several people out so here is the griff. We define PE as swansont has with a negative sign so that as objects approach each other (their separation decreases), the energy change is positive. We want this because this energy change is a measure of the work done. So in the diagram if an object X moves closer to a mass M from position A where the PE is -10 units to a position B where the PE is -20 units the change of PE would be PA - PB = -10 - (-20) = +10 If we used a positive convention then we would have PA - PB = +10 - (+20) = -10 The PE v Separation curve looks like the bottom graph with 0 at infinite separation and (- infinity) at zero separation.

Well a coset is a subspace plus an additional element(s) The kernel is a subspace but not necessarily the whole solution So whole solution is the kernel plus ..... Does this help?

There are additional considerations. Firstly , as I commented in post#8, a body the whole of which is rolling, has only one source of resistance, namely the contact between the body and the bearing surface. Whereas a machine that has parts which move against each other during rolling has additional sources of dissipation. Secondly the faster the motion the greater the rate of strain in the contact zone and therefore the greater the rate of doing dissipative work, as I noted in post#14. However real machines are designed to minimise this effect, and your tables will reflect this so it can be ignored in normal circumstances. Of course a body moving faster also has more kinetic energy to loose in the first place so there is also some offset there.

I very much doubt the professor said exactly that. The flanges take pretty well all the bending moment, but that is not the only load/stress acting. To keep it simple I will ignore torsion and state that the other stress acting is vertical shear. This is taken pretty well completely by the web. So much so that the beam has to be designed to resist the inevitable tendency to buckling that this vertical shear introduces. You will see 'web stiffeners' welded into beams under particular load for just this reason

I don't quite understand what you mean? Why should ag = bg if a and b are different points of S? What does the condition (group axiom) that every member of G has an inverse imply about a and b and the equality of ag and bg? I find it helps to discuss such statements in relation to a particular example, did you have one in mind?

Do you really believe this figure or is it just empty words? What does it mean? Can I say that because we have only breathed one trillionth of the atmosphere there is any reason to believe the rest is not breathable? Or that if I have only swum in .0001% of the sea I have any reason to believe I would not be able to swim in most of the rest of it? Or that because I have only sampled 5% the rest is not made primarily of water? We know some from direct observation We infer more We test our infererences and refine our knowledge from the test results But we should not give credence to non scientific headline pseudofacts. ophiolite sums it up well

Posted at 10.32, offline at 10.33 ? Commercial computer environments are often air conditioned. Hard drives are not static sensitive, it is other computer components that you would need the paraphanalia for. Just observe sensible safety precautions like don't plug and unplug things live unless specifically designed that way.

Good evening doG

I have tried to offer a simple analysis and explanation. If you want the definitive text it is to be found in the Cambridge University book Contact Mechanics by K L Johnson. He decomposes the motion of contacting surfaces into three parts Sliding, Rolling and Spin This introduces both linear forces and moments acting upon the bodies and contact area. It should also be noted that, although the velocity of the contact point in rolling is zero, the acceleration is non zero so Newton's laws require a force to be acting.

If you think about it there must be a weak dependence upon speed. Deformation is a dissipative action, the energy is not recovered into the motion it is lost as heat. So the greater the rate of deformation the greater the heat loss, and one of the functions of the oil is cooling. Engineers ensure however, that this loss is very very small compared to the energy of motion. I repeat, however, that you need to distinguish between the rolling resistance of bowling balls (as asked by the OP) and vehicles, which is vastly more complicated.

Why should it depend upon speed? Rolling resistance of balls is due to the very slight deformation of the contact surfaces. This, in turn, is due to the force pressing the two together. This force is independent of velocity. This is why very high strength steel is used for ball bearings. It leads to minimal contact deformation. You should further note that ball bearings usually run in an oil environment that offers significantly greater viscous drag than air, without ill effect. Why do you think we use oil not air?

Well I think everyone here is talking about different situations. The Original Post . There is no mention of an axle or other connection, it is implied that the whole object is rolling eg a round or constant rolling profile object, like a bowling ball. If a wheel plus axle and drive is intended than there is a whole raft of aditional sources of retarding friction. Secondly I think the OP was not considering objects such as wheels because the rolling resistance of a tyred wheel is affected by tyre pressure, profile, flexibility and many other complicated factors. Energy is lost flexing any flexible wheel.

I don't really catch where this thread is leading but a couple of comments. The mortar in brickwork does not stick the bricks together. It is there to hold the bricks apart. Masonry in general is a compression based system. Many promising very strong fibres are also very slippery. It is all very well creating a strong fibre but a problem if you can't transfer the load into or out of it. Steel reinforcement in concrete copes with this by the use of hooks and other shapes. This option is not available to ropelike fibres. This problem has beset many existing uses of carbon fibres. Creep is another issue with many materials, particularly glasslike structures, plastic and semiplastic materials.

I am beginning to understand your difficulty. A harmonic oscillator has a constant total energy and partitions this between kinetic and potential energy. The potential energy is a minumum at the mean point and the kinetic energy a maximum. At all points the total energy may be expressed as a function of velocity v; frequency [math]\nu [/math]; displacement from mean position,x ; amplitude a; force constant f in an equation given by [math]E = \frac{1}{2}m{\nu ^2} + \frac{1}{2}f{x^2}[/math] Where the first term is kinetic and the second term potential energy. Note that the potential energy is positive , whether x is away from the centre or towards it since the second potential energy term depends upon x squared. The constant f does not change with direction. So when you come to substitute [math]V = \frac{1}{2}f{x^2}[/math] into the Schrodinger equation There is no question of positive or negative signs, it is always positive. You get to the Hermite solution by introducing a new variable s = x/a and allowing the simple constant of integration to become a function of s. Have you seen this derivation?

What you are proposing is tantamount to proposing that each quantum level is 'fuzzy' ie occupies a spread of energy values equal to the peak to peak variation. What evidence do you have for this?

You are posting in the relativity forum but attempting to impose Newtonian mechanics. Apply the correct formula and you will see for yourself why the question is meaningless as posed.