[freehorse]

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]

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

[justsid]

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.

[Tepix]

I guess Galileo came up with it first:

https://en.wikipedia.org/wiki/Galilean_invariance

[freehorse]

That's a good point. For a stationary observer sitting on the ground it would roughly seem that, in the airplane case, you increase your speed from 100s mph to `100s + ε mph`, while for the home case from 0 mph to ε mph. So that seems like a counterexample to what I described as common kinetic experience.

I think the issue here is that, in order to move, you apply force to the floor of the airplane. Because the airplane has huge mass and your mass and relative speed are minuscule, there is (probably) no perceivable effect on the airplane's motion. So you increase your kinetic energy by the same amount in both cases while expending the same amount of (chemical) energy, but in the airplane case, the kinetic energy of the airplane (just the airplane, without you) decreases (by a miniscule amount compared to its actual kinetic energy, but still).

[PunchyHamster]

you are still moving against reference frame (floor) that is at speed 0.

and also pushing that reference frame down when moving up

[ThoAppelsin]

Scale up the numbers in you example: The effort to move a piece of furniture from 10,000th to 20,000th floor is NOT the same as the effort to move it from the 20,000th to the 3rd. The reduced gravity will help you.

[mistercow]

If you're talking about intuitions, you have no firsthand intuitions about lifting effort decreasing with distance to the Earth. We can intuit about constant gravity, and the math of constant gravity works fine for this description.

And while the real situation at scale is more complicated, the math is going to come out to the same answer, albeit with extra terms muddying everything up.

If someone says that something true can be illustrated intuitively with a thought experiment, "sure, but what if we take that to a scale where our intuitions fail" is a sort of odd place to take the discussion unless you're genuinely curious how the math is going to shake out.

[ThoAppelsin]

I’m not talking about intuitions; I’m talking against them. The intuition about carrying something 1st to 2nd then to 3rd floor is clearly wrong as evidenced by the example I gave; it is less wrong in smaller scales, but it still is wrong.

If the floors were as high as the radius of the Earth, the first one would be three times as hard as the second one. The math doesn’t come out the same. It’s not at all linear, it’s the inverse square; that’s much more than just _extra terms muddying things_.

Calling this relation linear by just looking at the intuitions of tiny humans is akin to hyper-zooming an exponential graph and calling it linear. It is “approximately true” locally, but hey, the same is also true for velocity vs kinetic energy!

[cubic_earth]

Simplifying assumptions are allowed when reasoning about physics. What you are saying is interesting, but I think you might be misapplying it. For small heights differences, the difference in gravitation approaches 0. A ball raised .0002 mm off the ground has twice the potential energy of one raised only .0001 mm. But that is never true for speed. An object moving 0.0002 MPH does have 4x the kinetic energy of an object moving 0.0001 MPH.

So yeah, I am zooming in on an exponential and calling it linear, but that doesn't work for speed. And doubling of velocity gives 4x the energy regardless of how tiny the step.

[mistercow]

But the intuition based on the constant gravity assumption correctly illustrates the point, and adding in the more complicated picture of non-constant gravity creates new terms that exactly cancel out to give the same answer. Why would you talk against intuitions that work correctly?

And to be clear, building intuitions that fail at certain scales is still a useful and important thing to do. But you haven't shown a scale where these intuitions fail. That's not insightful, it's just throwing smoke bombs for no reason.

[gpm]

On earth, it just about is... you haven't scaled up enough. Low earth orbit doesn't have much less gravity, it's just that there's no air resistance so you can move fast enough sideways so that you don't run into the earth. Hence orbit and not just floating.

But more to the point the kinetic energy here is being turned into gravitational potential energy. If you move to a place with a weaker gradient in gravitational potential of course the same amount of kinetic energy moves you farther up.

[nkrisc]

What intuitive understanding do you have of moving furniture up 10,000 floors? None.