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Comment by hunter2_ | Hacker News Reader

That's a good question, and I suppose the mgh formula isn't a suitable answer, so my answer would be something like: if you lift an object to some height, and then you repeat that action (lifting it from there to twice the height), you've done twice the work, and doing twice the work requires twice the caloric intake.

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"Work" is the weird thing in physics, I'd say is about as opposite to intuitive as you can get when introducing a concept. It's only intuitive when considering lifting an object - say, a bag of groceries. Heavier the bag, higher the lift -> more work. But then you carry that heavy bag a couple kilometers, arrive at home exhausted, only to be told by the physics teacher that you did exactly 0 work. Or in fact negative work, if upon coming home, you put the bag down.

I understand the concept myself somewhat intuitively now, but that intuition is not connected to everyday experience - it's just familiarity with a detached concept of physics!work that just is what it is, but is consistent in being that.

Well, a good physics teacher might note the difference between external work on the gravitational field, versus the internal thermodynamic work of the human body. Which could lead to a quick discussion of how muscles are a dynamic system depending on constant activation of actin & myosin (and therefore consumption of ATP) as opposed to a static elastic system like a piece of metal.

Very intuitive analogy is that running an engine in neutral burns fuel, but doesn't do work to move the car forward.

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!

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

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?

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

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.

> 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.

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?

> 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.

> if you lift an object to some height, and then you repeat that action (lifting it from there to twice the height), you've done twice the work, and doing twice the work requires twice the caloric intake.

You’re introducing two new intuitions, and it’s not intuitively obvious how they are related to each other. Why would work correlate 100% with caloric intake, and caloric intake 100% with kinetic energy?

Certainly, ‘work’ is highly counterintuitive. If I move a concrete block over loose sand on a beach, I’m doing zero work, in the physics definition, so moving it over a kilometer should be as easy as moving it for a millimeter.

Even ignoring the difference between caloric intake and caloric expenditure, it also isn’t intuitive to me that caloric expenditure is independent of the speed at which one lifts an object.

In the end, the answer is “because the math works out that way, and kinetic energy is a useful concept”

Friction. Work isn't just about height.

Holding that block stationary at arms length then. 0 work.

Put that block on a shelf at the same height. 0 work.

The fact that your muscles burn ATP just fighting gravity is a feature of biology, not fundamental to the physics involved.

If you want to read about another similar example, Google for rocket launch gravity losses.

I think you're missing the point. A lot of basic mechanics actually isn't especially intuitive because things like work simply do not map well to everyday experience. I'm not suggesting that work is defined incorrectly or something.

I see what you're saying now, and I agree.

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