Why don't ants get brain-addled when they stop so suddenly?

It has almost no inertia. As you note, it has very small mass, and it’s moving very slowly. So if m is small and v is small, m*v is going to be really really small.

[QUOTE=Lemur866]
It has almost no inertia. As you note, it has very small mass, and it’s moving very slowly. So if m is small and v is small, m*v is going to be really really small.
[/QUOTE]

And…really, really cute!

[QUOTE=Really Not All That Bright]
Sure, but the amount of energy required is reduced in proportion to its size.
[/QUOTE]

Not all natural phenomena scale in direct proportion to one another - if an ant were scaled up magically to human size, it wouldn’t even be able to lift its own body off the ground.

Take an idealised cubic container - scale it up in every way so that it’s twice the size - that is, twice as wide across as before - if your grow-ray is working properly, the container’s wall thickness is also now doubled. but the contained volume is eight times what it was previously.

Keep doing that and obviously, you quickly reach a point where the walls lack the structural strength to contain the contents, or even to support their own weight.

This sort of thing happens in many different ways - it’s the reason that surface tension can pull a raindrop into a spherical shape, but not a whole bucketful of water. It’s the reason ants can carry many multiples of their own body weight, but humans or elephants can’t.

[QUOTE=tdn]
For another, I don’t think they have brains in the traditional sense that mammals do. They don’t have tiny little brains inside of tiny little skulls.
[/QUOTE]

Well, they don’t have skulls, but they do have tiny little brains in their tiny little heads.

[QUOTE=Annie-Xmas]
Pick up ant.
Put in model airplane
Put plane on very fast moving treadmill.
Stop treadmill suddenly.
Check out ant’s brain.
[/QUOTE]
PROFIT!

[QUOTE=Fish]
It would also be 23,887,872 times its previous mass (because it expanded 288 times in three dimensions). Such an ant who previously weighed 1/20 of an ounce would now weigh 37 tons, requiring a cool million newtons of force to move and 1,998 horsepower to do the quarter-mile.

Those silly numbers illustrate the danger of trying to scale human-size physics to ant-size. Relative speed aside, ants have much less mass.
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I don’t think a regular house ant is anywhere close to 1/20th of an ounce. A weight of .25 milligrams would be closer to the mark.

Still. The example is illustrative; scaling up the linear (one-dimensional) speed may not apply when you also have to scale up the (three-dimensional) mass.

[QUOTE=Fish]
Still. The example is illustrative; scaling up the linear (one-dimensional) speed may not apply when you also have to scale up the (three-dimensional) mass.
[/QUOTE]

Point taken.

[QUOTE=tdn]
Send it to the Marianas Trench for 20 minutes. That ought to addle its little ganglion good!
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Didn’t that already happen?

[QUOTE=Tyrrell McAllister]
Didn’t that already happen?
[/QUOTE]

Once.

Isn’t this happening?