[SilasX]

Okay but that depends on the intuitions the question is trying to justify, which makes it circular. We also know, for example, that the body uses more than twice as much energy to do twice as much work (because of fatigue on the muscles or whatever the right term is here). In fact it takes positive energy just told a weight at a fixed height, doing zero mechanical work! So you’re actually appealing to even weaker intuition than the one the question is trying to ground!

[drabbiticus]

> In fact it takes positive energy just told a weight at a fixed height, doing zero mechanical work!

Stacking a weight on top of a table holds it at a fixed height and requires zero mechanical work.

The failure in intuition here relates to physiology and the mechanism by which muscles work, not physics. Myosin and actin are constantly cycling through bonding and release during muscle contraction, as this is how the shortening action actually occurs. In fact, muscle contraction is particularly unintuitive because people frequently consider ATP the "energy currency", yet the ATP-consuming steps are actually the release/relaxation and preparation for binding, not the pulling action. This is also why the phenomena of rigor mortis upon death occurs.

[SilasX]

I get that involving a human body complicates the analysis. That was the point: that you can’t appeal to it as a simple example to ground the intuition in other case.

Also:

>Stacking a weight on top of a table holds it at a fixed height and requires zero mechanical work.

I was referring to a human holding it. What would have been a better way to keep you from missing that?

[drabbiticus]

> I get that involving a human body complicates the analysis. That was the point: that you can’t appeal to it as a simple example to ground the intuition in other case.

Yeah, fair enough. It's unfortunate that the comment you were responding to involved "caloric intake" suggestive of a biological system when it could just as easily have involved a mechanical pulley. Their intuition would have been stronger phrased as: Within a gravitational field that is approximated as a uniform force field, the amount of energy/work to raise a weight by a fixed distance is independent of the initial position of that weight on a (massless) rope attached to a (frictionless) pulley.

> I was referring to a human holding it. What would have been a better way to keep you from missing that?

Since you are asking, for me, it would helped to have the following inserted text: "In fact it takes positive energy [for biological muscle] just told a weight at a fixed height, doing zero mechanical work!" so that the statement stood on it's own, or else including within your post a more definitive statement to the effect of "intuitions involving the human body complicates the analysis", as you did in this reply. If "that was the point", go ahead and state it.

To be fair, I often have the same problem. It's easy for me to write a lot of text that goes around a statement without actually getting to it.

[hibernator149]

All intuitions are wrong, but some are usefull. You have to do the experiment, discover the formula, and then adapt your intuitions accordingly.

[SilasX]

What point that I made are you responding to? I was disputing someone’s appeal to a specific intuition for being an unhelpful one to use here. So I obviously get the concept of some intuitions being useful. Did you see the comment being responded to?

[Gibbon1]

I think if you define energy as force X distance then integration alone will give you the squared term.

How I got banned from some reddit channel. Flip this around ask if a ball were fired out of a gun up into the air what height would it reach? A ball twice as fast goes up 4 times as high. If energy is force times distance it had 4 times the energy.

[exe34]

At some point you just have to shut up and calculate.