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If energy is defined as the capacity to do work, and the formula for work is force times displacement, if we place an object on a frictionless surface and apply any amount of force to said object, the object and thus the displacement will approach infinity. We know that any number times infinity is also infinity, so regardless of the force we apply to the object, its energy should also approach infinity.

So, can we conclude that every object has an infinite amount of energy?

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  • $\begingroup$ Do you mean applying a force for a limited finite duration or applying a force forever? $\endgroup$
    – Vincent Thacker
    Commented May 2 at 16:38
  • $\begingroup$ In this post I was talking about applying force for a limited finite duration. But I don't think there's a difference between the two; since our object is on a frictionless surface the object should approach infinity regardless of how much force is applied to it over what period of time based on Newton's First Law of Motion. $\endgroup$
    – ryangosling
    Commented May 2 at 16:41
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    $\begingroup$ 1. There is no speed greater than c. 2. There is no "any amount of force". How do you imagine it? $\endgroup$
    – trula
    Commented May 2 at 16:48
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    $\begingroup$ Does this answer your question? Can infinite work be done? $\endgroup$
    – Dale
    Commented May 2 at 16:58
  • $\begingroup$ Every object now and then has limited amount of total energy which is bounded by condition : $$\sqrt{\frac {E_{tot} } {\gamma m} } \leq c$$. Your problem is that you include not that distance in work calculation - it must be distance over which force is applied, not total covered distance by body. $\endgroup$
    – Agnius Vasiliauskas
    Commented May 2 at 17:03

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Work is the product of force times the displacement that happens while the force is being applied. Hence, if you apply the force for a finite amount of time, the work will be finite.

No object has infinite energy.

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  • $\begingroup$ What if force is being applied to our object over an infinite duration? In that case, would work and energy be infinite? $\endgroup$
    – ryangosling
    Commented May 2 at 17:03
  • $\begingroup$ If you consider the "total work" to be the total work done after an infinite amount of time has passed, then yes it's "infinite" in the sense that the work is growing without bound. But the total work done "up til now" for a given time remains finite, at all times. $\endgroup$
    – AwkwardWhale
    Commented May 2 at 18:35
  • $\begingroup$ In general you should be very wary of trying to draw conclusions from the infinite time limit of models with external forces and no damping. The external forces you're modelling, in the real world actually require an energy reservoir to sustain them, and this is certainly not infinite; i.e. realistic models should only apply the force for a finite length of time $\endgroup$
    – AwkwardWhale
    Commented May 2 at 18:37
  • $\begingroup$ @ryangosling I completely agree with the comments of AwkwardWhale (I'm only making this comment to tag you) $\endgroup$
    – Níckolas Alves
    Commented May 3 at 0:04

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