5 ms·

> We know intuitively that a ball atop a 20ft ladder has twice the potential energy of a ball atop a 10ft ladder. What makes this intuitive? The foundation of

> We know intuitively that a ball atop a 20ft ladder has twice the potential energy of a ball atop a 10ft ladder. What makes this intuitive? The foundation of the asker’s question is that it seems intuitive that kinetic energy would increase linearly with speed, but that turns out to be wrong.

hunter2_ 4mo ago
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.
- SilasX 4mo ago
  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!
  - hibernator149 4mo ago
    All intuitions are wrong, but some are usefull. You have to do the experiment, discover the formula, and then adapt your intuitions accordingly.
    - SilasX 4mo ago
      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?
  - exe34 4mo ago
    At some point you just have to shut up and calculate.
  - Gibbon1 4mo ago
    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.
  - drabbiticus 4mo ago
    > 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 4mo ago
      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 4mo ago
        > 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.
- Someone 4mo ago
  > 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”
  - GroksBarnacles 4mo ago
    Friction. Work isn't just about height.
    - thfuran 4mo ago
      Holding that block stationary at arms length then. 0 work.
      - dotancohen 4mo ago
        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.
        thfuran 4mo ago
        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.
- TeMPOraL 4mo ago
  "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.
  - anon84873628 4mo ago
    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.
throwawaytea 4mo ago
Because things like energy are relative. So if you label the ground 0, and go up 10 feet, you get x energy. Going up another exact same x from your 10 foot ladder spot you could now call 0 again, would mean you gain x energy again. Since they're both the same height, and you gained the same energy, you could infer double the height has double energy.
- pishpash 4mo ago
  Not really. Potential energy in a gravitational well obviously has absolute coordinates.
- nlawalker 4mo ago
  What if you label standing still as 0 mph and start moving 10 mph, gaining x energy, then call that zero and start moving 10 mph from there? It's just as intuitive to say that you would gain x energy in that case, but you don't.
  - hunter2_ 4mo ago
    When you're already going 10 mph and you're about to add another 10 mph, you can only "call that zero" (i.e., go from 0 mph to 10 mph again) if your point of reference (i.e., the ground) also begins moving with you at that point. Since the ground is stationary, you're definitely about to increase from 10 mph to 20 mph relative to the ground, not from 0 mph to 10 mph, and that's harder to do. But if you're on a treadmill that was stationary for the first change, and then suddenly starts moving at 10 mph right before the second change without affecting your speed relative to the ground, then you can "call that zero" and you'll be able to add another 10 mph (ending up at 10 mph relative to the treadmill and 20 mph relative to the ground) with the same ease as the first go.
  - cubic_earth 4mo ago
    I suppose they are both "intuitive", but the example I gave was both intuitive and correct. Probably for anyone who has carried something or themselves up a hill, or climbed a set of stairs can relate to that from firsthand experience. I don't know what the kinetic energy corollary to that would be? "Stand still and I will throw a baseball at you going 15mph, and note how much it hurts. Now I will throw it at you going 30mph. See! It hurts 4x as much" :D
raldi 4mo ago
Because if the one falling 20ft lands on a seesaw, the other side of it will toss two balls each of the same mass 10ft up.
- pishpash 4mo ago
  Then 20ft should not be used in the explanation. They should just have one ball going at 2x speed hit the seesaw and have 4 of those balls go up at 1x speed.
  - regularfry 4mo ago
    That ends up begging the question, because the next step is "how high do you have to drop it from so that it's travelling twice as fast?" and you're immediately going round in circles.
    - pishpash 4mo ago
      Nothing of the sort. The seesaw can be in space far from gravitational influences. Potential energy is extraneous in this explanation.
gorgoiler 4mo ago
Because physical movement is intuitively transitive. Going from A to B then B to C is the same as going from A to C. The journey from Y to Z might feel more tiring than the journey from A to B, but only if you do them all in one day :)
- WithinReason 4mo ago
  So why isn't increasing your velocity from A to B then B to C the same as A to C? Isn't that intuitively transitive too?
  - PunchyHamster 4mo ago
    it is if your reference point is A in both cases.
- Joker_vD 4mo ago
  > Going from A to B then B to C is the same as going from A to C. Not really, no. Not all forces are conservative.
aaron695 4mo ago
[dead]
freehorse 4mo ago
The effort to move a piece of furniture from 1st to 2nd floor is the same as the effort to move it from the 2nd to the 3rd. We have good intuition for this by our experience, which derives a linear relationship. The effort to move a piece of furniture up two floors is double the effort of moving it up one floor (ie you have to put the same effort twice, assuming enough rest). I would not say we have the same intuition for kinetics. Increasing walking/running from 0 to 5 km/h doesn’t feel the same as than moving from 5 to 10, which does not feel the same as moving from 10 to 15. I don’t think we have an experience of linear relationship between running speed and effort, or other types of speed/energy types of relationships.
- trinari 4mo ago
  Can someone help me understand the following? Getting up from a seat als walking a couple steps feels that same at home and in a flying airplane (or does it?). But the base speed is 0 in the former and several hundred mph in the latter case
  - Tepix 4mo ago
    I guess Galileo came up with it first: https://en.wikipedia.org/wiki/Galilean_invariance https://en.wikipedia.org/wiki/Galilean_invariance
  - justsid 4mo ago
    When you get up from a seat and walk a few steps you are already doing that on something that is hurtling down space. We don’t notice that our planet moves a lot, because we can’t really see the movement in our reference frame. If you were on a plane without any windows, no turbulence and no sound cues from the engine, you wouldn’t know when getting up from your plane seat that you are in a moving object either. Acceleration is a real force that we can feel. But once moving at a constant speed, physics dictates that it’s all the same. That’s also why you can throw a tennis ball up on a plane and not have it fly backwards immediately smacking into the person behind you. In the reference frame of you and the aircraft, you are not moving at all and neither is the plane. In the reference frame of the ground you and the plane are moving.
njstraub608 4mo ago
Feels like what OP meant to say is, “you could rightly assume that a ball…” instead. Seems like a fair starting point if you’re just doubling things because if the height difference. I really liked cubic’s explanation overall.
- cubic_earth 4mo ago
  That indeed would have been better. Much too late for that edit now. But the subsequent debate over the intuitive claim is fun.
NoMoreNicksLeft 4mo ago
> What makes this intuitive? 20 million years of evolution hard-wiring it into our primate brains on a genetic level, from every thrown rock and fall from a tree. That's what made it intuitive. But not everyone gets the same batch of genes, I guess..,

hunter2_ 4mo ago

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.

SilasX 4mo ago
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!
- hibernator149 4mo ago
  All intuitions are wrong, but some are usefull. You have to do the experiment, discover the formula, and then adapt your intuitions accordingly.
  - SilasX 4mo ago
    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?
- exe34 4mo ago
  At some point you just have to shut up and calculate.
- Gibbon1 4mo ago
  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.
- drabbiticus 4mo ago
  > 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 4mo ago
    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 4mo ago
      > 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.
Someone 4mo ago
> 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”
- GroksBarnacles 4mo ago
  Friction. Work isn't just about height.
  - thfuran 4mo ago
    Holding that block stationary at arms length then. 0 work.
    - dotancohen 4mo ago
      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.
      - thfuran 4mo ago
        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.
TeMPOraL 4mo ago
"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.
- anon84873628 4mo ago
  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.

throwawaytea 4mo ago

Because things like energy are relative. So if you label the ground 0, and go up 10 feet, you get x energy. Going up another exact same x from your 10 foot ladder spot you could now call 0 again, would mean you gain x energy again. Since they're both the same height, and you gained the same energy, you could infer double the height has double energy.

pishpash 4mo ago
Not really. Potential energy in a gravitational well obviously has absolute coordinates.
nlawalker 4mo ago
What if you label standing still as 0 mph and start moving 10 mph, gaining x energy, then call that zero and start moving 10 mph from there? It's just as intuitive to say that you would gain x energy in that case, but you don't.
- hunter2_ 4mo ago
  When you're already going 10 mph and you're about to add another 10 mph, you can only "call that zero" (i.e., go from 0 mph to 10 mph again) if your point of reference (i.e., the ground) also begins moving with you at that point. Since the ground is stationary, you're definitely about to increase from 10 mph to 20 mph relative to the ground, not from 0 mph to 10 mph, and that's harder to do. But if you're on a treadmill that was stationary for the first change, and then suddenly starts moving at 10 mph right before the second change without affecting your speed relative to the ground, then you can "call that zero" and you'll be able to add another 10 mph (ending up at 10 mph relative to the treadmill and 20 mph relative to the ground) with the same ease as the first go.
- cubic_earth 4mo ago
  I suppose they are both "intuitive", but the example I gave was both intuitive and correct. Probably for anyone who has carried something or themselves up a hill, or climbed a set of stairs can relate to that from firsthand experience. I don't know what the kinetic energy corollary to that would be? "Stand still and I will throw a baseball at you going 15mph, and note how much it hurts. Now I will throw it at you going 30mph. See! It hurts 4x as much" :D

raldi 4mo ago

Because if the one falling 20ft lands on a seesaw, the other side of it will toss two balls each of the same mass 10ft up.

pishpash 4mo ago
Then 20ft should not be used in the explanation. They should just have one ball going at 2x speed hit the seesaw and have 4 of those balls go up at 1x speed.
- regularfry 4mo ago
  That ends up begging the question, because the next step is "how high do you have to drop it from so that it's travelling twice as fast?" and you're immediately going round in circles.
  - pishpash 4mo ago
    Nothing of the sort. The seesaw can be in space far from gravitational influences. Potential energy is extraneous in this explanation.

gorgoiler 4mo ago

Because physical movement is intuitively transitive. Going from A to B then B to C is the same as going from A to C. The journey from Y to Z might feel more tiring than the journey from A to B, but only if you do them all in one day :)

WithinReason 4mo ago
So why isn't increasing your velocity from A to B then B to C the same as A to C? Isn't that intuitively transitive too?
- PunchyHamster 4mo ago
  it is if your reference point is A in both cases.
Joker_vD 4mo ago
> Going from A to B then B to C is the same as going from A to C. Not really, no. Not all forces are conservative.

aaron695 4mo ago

[dead]

freehorse 4mo ago

The effort to move a piece of furniture from 1st to 2nd floor is the same as the effort to move it from the 2nd to the 3rd. We have good intuition for this by our experience, which derives a linear relationship. The effort to move a piece of furniture up two floors is double the effort of moving it up one floor (ie you have to put the same effort twice, assuming enough rest). I would not say we have the same intuition for kinetics. Increasing walking/running from 0 to 5 km/h doesn’t feel the same as than moving from 5 to 10, which does not feel the same as moving from 10 to 15. I don’t think we have an experience of linear relationship between running speed and effort, or other types of speed/energy types of relationships.

trinari 4mo ago
Can someone help me understand the following? Getting up from a seat als walking a couple steps feels that same at home and in a flying airplane (or does it?). But the base speed is 0 in the former and several hundred mph in the latter case
- Tepix 4mo ago
  I guess Galileo came up with it first: https://en.wikipedia.org/wiki/Galilean_invariance https://en.wikipedia.org/wiki/Galilean_invariance
- justsid 4mo ago
  When you get up from a seat and walk a few steps you are already doing that on something that is hurtling down space. We don’t notice that our planet moves a lot, because we can’t really see the movement in our reference frame. If you were on a plane without any windows, no turbulence and no sound cues from the engine, you wouldn’t know when getting up from your plane seat that you are in a moving object either. Acceleration is a real force that we can feel. But once moving at a constant speed, physics dictates that it’s all the same. That’s also why you can throw a tennis ball up on a plane and not have it fly backwards immediately smacking into the person behind you. In the reference frame of you and the aircraft, you are not moving at all and neither is the plane. In the reference frame of the ground you and the plane are moving.

njstraub608 4mo ago

Feels like what OP meant to say is, “you could rightly assume that a ball…” instead. Seems like a fair starting point if you’re just doubling things because if the height difference. I really liked cubic’s explanation overall.

cubic_earth 4mo ago
That indeed would have been better. Much too late for that edit now. But the subsequent debate over the intuitive claim is fun.

NoMoreNicksLeft 4mo ago

> What makes this intuitive? 20 million years of evolution hard-wiring it into our primate brains on a genetic level, from every thrown rock and fall from a tree. That's what made it intuitive. But not everyone gets the same batch of genes, I guess..,