1

I'm holding a bag with some mass $m$. The force required for not letting it fall is equal to its weight $m \cdot g_L$ (where $g_L$ is the local gravity, assuming Earth this is $\approx 9.8 \; \text{m} \text{s}^{\text{-1}}$).

Now, in order to create and maintain a such force, ATP molecules (in my muscle cells) have to bind to myosin releasing its actin, ADP and some energy from the bond. This energy is then used to contract the muscle cell. Though no energy is putted into the bag (as its potential energy does not increase nor decrease) my muscles must still hydrolyse ATP in order create that energy needed to contract. This energy is in the end released as heat.

Now, my question is: how much energy – or rather power – is needed to maintain my bag in place counteracting gravity? Now human muscles aren't perfect so to avoid any complicated biology I simply want to know how much power it would take, assuming no losses and a perfect system.

DanielSank
  • 24,439
Madde Anerson
  • 797
  • See also the related question http://physics.stackexchange.com/questions/99616/while-holding-an-object-no-work-done-but-costs-energy-in-response-to-a-similar – Kyle Kanos Feb 03 '15 at 16:00
  • 1
    @KyleKanos: I don't think either of those are duplicates. This question specifically asks how much power is used by the processes responsible for a human arm to hold up an object. Neither of the other two questions ask this. The first asks why the power is not zero and the second does not have a clear question at all. – DanielSank Feb 03 '15 at 16:17
  • @DanielSank I can see the distinction that you suggest, but I'm not sure that the answer to the power question is really clear without a very health input from biology, which the core reason that idealized lack of work doesn't jive with "man this is hard!" remains the same. – dmckee --- ex-moderator kitten Feb 03 '15 at 16:59
  • @dmckee: Sure, what you say makes sense. So why is this closed as a duplicate? This seems to happen a lot: people VTC for one reason, and then when I ask about it someone else defends the close for a different reason. The problem of course is that when this happens OP doesn't get the right feedback :) – DanielSank Feb 03 '15 at 17:47
  • @DanielSank I didn't vote to close, but I'm not sure that you understood the full implication I intended to convey. The part of this question (as it stands) that is on-topic for physics without amendment is exactly the part answered in the proposed duplicate. There should be a a way to supply a little more information and re-write this question in terms suitable for Physics SE (the power to hold up ... knowing that the twitch rate is xxx and waste heat per twitch is yyy), but it need to be amended and extended. Nor am I sure that [bio.se] would take it in its current form, either. – dmckee --- ex-moderator kitten Feb 03 '15 at 20:08
  • Madde Anerson, it is not clear to me what you mean by "a perfect system"; the method used by mammalian muscles is lossy be definition, and I know of no common parameterization to work from. (Note that my ignorance is of no bearing as such, but no previous question on a similar topic has such a parameterization in the answers either which may be more telling. Or may not.) – dmckee --- ex-moderator kitten Feb 03 '15 at 20:12
  • @dmckee How is my question in any sense a duplicate of http://physics.stackexchange.com/questions/1984/why-does-holding-something-up-cost-energy-while-no-work-is-being-done? I know that the energy released in the process of hydrolysing ATP converts into heat, which I clearly stated in the question. I also said that, as human muscles use more energy than really needed in order to maintain the force, I asked for the minimal amount of power needed for doing so. – Madde Anerson Feb 04 '15 at 15:58
  • @dmckee As for my definition of a "perfect system", it would release waste heat, but what I asked for was how much power you need – at least – to maintain the force. – Madde Anerson Feb 04 '15 at 15:59
  • @MaddeAnerson The point is that there is no fundamental physical limit other than "no work at all". It depends on the details of the system and you are asking about neither that actual biological system nor the idealized physical system. So do you have a simplified model system for us to use? I still think this question can be made into a good one that is not a duplicate, but it need more specification. – dmckee --- ex-moderator kitten Feb 04 '15 at 17:02
  • @dmckee Are you telling me that creating a force counteracting gravity isn't requiring any energy? – Madde Anerson Feb 04 '15 at 21:51
  • @MaddeAnerson That's what a table does, and it represents what I would describe as a "perfect system". Presumably you intend some idealized muscular system that is not so simple as a table, but how would we recognize it? – dmckee --- ex-moderator kitten Feb 04 '15 at 23:57
  • @dmckee I would argue that the force of a table actually requires work. The force ultimately depends on the pressure of the matter Earth is made of, and that matter is compressed by gravity. Without a upward force, the table wouldn't be able to maintain that force. – Madde Anerson Feb 05 '15 at 00:28
  • @MaddeAnerson, work is essentially a measure of the amount of energy converted from one form to another. On your view, what energy conversion is brought about by the table? – Alfred Centauri Feb 05 '15 at 01:39
  • 2
    As an alternative to what Alfred Centauri said, you could just take the rote definition that is taught in high school physics -- $\Delta W = F \Delta s$ where $\Delta W$ is the work done, $F$ is the force applied and $\Delta s$ is the distance the object moved while the force was applied. For a table in a gravitational field with a bag sitting on it, the bag doesn't move anywhere. So no matter how large $F$ is, $\Delta s$ is zero so $\Delta W$ is zero and no work is done. – tpg2114 Feb 05 '15 at 01:44

0 Answers0