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Thread: Quantifying Energy

  1. #1 Quantifying Energy 
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    Recently I have been takeing the spacial partial inntegration of force formulas to end up with equivelent energy formulas. I have come up with a snag though, static friction. I haven't been able to find a way around the fact that static friction occurs when you're not moving and therefore any spacial integration I do with static friction will in the end just give me a value of 0 J. There has to be a way around this but I need thelp comeing up with that.
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    Quote Originally Posted by Topalk View Post
    Recently I have been takeing the spacial partial inntegration of force formulas to end up with equivelent energy formulas. I have come up with a snag though, static friction. I haven't been able to find a way around the fact that static friction occurs when you're not moving and therefore any spacial integration I do with static friction will in the end just give me a value of 0 J. There has to be a way around this but I need thelp comeing up with that.
    What in the world are you doing? And what do you mean by "spacial partial integration of force" ?

    You can relate work to a line integral of a force field, but that is not some "partial integration", whatever that is.

    Static friction does no work. So there is no energy involved.
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    Quote Originally Posted by DrRocket View Post
    What in the world are you doing? And what do you mean by "spacial partial integration of force" ?

    You can relate work to a line integral of a force field, but that is not some "partial integration", whatever that is.

    Static friction does no work. So there is no energy involved.
    What about the amount of energy to overcome static friction?
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    Quote Originally Posted by Topalk View Post
    What about the amount of energy to overcome static friction?
    Work = Force X distance

    If there is 0 distance, there is 0 work.

    Unless you have some model for static friction in mind that is different from the standard Coulomb model, there is no work done in overcoming static friction.
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  5. #5  
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    Sorry to be a Wiki-pusher, but maybe this may help (?).
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    I think that DrRocket means that until static friction is overcome, and there is movement, there is no Work being done. Force is being applied, but until it moves, there is zero distance.
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    Quote Originally Posted by AlexG View Post
    I think that DrRocket means that until static friction is overcome, and there is movement, there is no Work being done. Force is being applied, but until it moves, there is zero distance.
    I don't see why work is the issue here. Isn't it trivial that no work is done until static fraction is overcome and kinetic friction initiates? Bringing up Topalk's question...

    What about the amount of energy to overcome static friction?
    It seems rather a matter of how much force is needed to overcome static friction in the first place. After a quick search, I thought the static friction section of the Wiki article addressed the issue.

    Maybe the question's terminology has caused some confusion.
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    Quote Originally Posted by epidecus View Post
    I don't see why work is the issue here. Isn't it trivial that no work is done until static fraction is overcome and kinetic friction initiates? Bringing up Topalk's question...



    It seems rather a matter of how much force is needed to overcome static friction in the first place. After a quick search, I thought the static friction section of the Wiki article addressed the issue.

    Maybe the question's terminology has caused some confusion.
    Until force is applied over a non-zero distance, there is no work done, hence no energy expended.

    The question, and the OP, concern energy (aka work). There is a force necessary to overcome static resistance, but that is irrelevant to the question of energy.
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    Quote Originally Posted by DrRocket View Post
    Until force is applied over a non-zero distance, there is no work done, hence no energy expended.

    The question, and the OP, concern energy (aka work). There is a force necessary to overcome static resistance, but that is irrelevant to the question of energy.
    Point taken. I suspected this (albeit without confidence), hence me mentioning terminology. I usually hear phrases like "how much energy is required..." in chemistry class, which seems to be a different sense of the term (not sure about mechanical physics). Despite a misstep in word usage, it's understandable where he's coming from. Sorry for the misunderstanding.
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    Quote Originally Posted by epidecus View Post
    Point taken. I suspected this (albeit without confidence), hence me mentioning terminology. I usually hear phrases like "how much energy is required..." in chemistry class, which seems to be a different sense of the term (not sure about mechanical physics). Despite a misstep in word usage, it's understandable where he's coming from. Sorry for the misunderstanding.
    The term "energy" as used in chemistry is the same as in physics or engineering. Work is force applied over distance, and the result of work can be any of several forms of energy, all of which (in the classical setting) are either kinetic energy or electromagnetic in nature. For instance, if you apply a force to a massive body, over a distance d, then the work done is F x d which results in a like amount of kinetic energy, so .

    This can be made a bit more general through the use of line integrals, but only in the sense that one can change the magnitude and direction of the applied force, and thereby derive somewhat more general principles. The basic concept is unchanged.

    One also has chemical energy (which is basically electromagnetic in nature), thermal energy (which is the kinetic energy of molecules), etc. Conservation of energy is an important principle of physics, as is conservation of momentum. It is very important to make a distinction between an applied force and the energy associated with that force, which to be non-zero requires that the force act over a non-zero distance. In the case of static friction, what happens is that the applied force is reacted by an opposing frictional force of like magnitude so that the net force applied to the object is zero. Neither force is acting over any non-zero distance, and no work is done.

    Friction is not particularly well understood at a fundamental level. There are approximate models, as with Coulomb friction. But no one can derive the approximate models from first principles.
    Feynman once attempted to study friction and develop a fundamental theory, but he failed.

    At some point you may also encounter variational mechanics, the Lagrangian and Hamiltonian formulations of mechanics. They can be shown to be equivalent to the usual Newtonian mechanics (F=ma), but while one can set up ordinary Newtonian problems with a frictional force, the variational formulations do not lend themselves to such problems, because the frictional forces do not arise from a potential, and therefore are not conservative (i.e. a frictional force acting over a closed path does not result in zero-energy expenditure). Frictional forces are "dissipative" (the energy goes into thermal energy somewhere) and that makes them somewhat more difficult to handle in theoretical settings. One is therefore forces to rely on approximate models which are fine for engineering applications, but not so good in purely theoretical considerations.
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