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Nov 7, 2022, 3:15:04 AM11/7/22

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In my drawing

https://www.geogebra.org/m/vkz6htmu

the two springs A and B (with mass) have the same length at rest: 8.

Spring A is in the remote space and maintains its length 8.

Spring B is stationary in a well in the center of the Earth.

Is spring B in free fall even though it is stationary?

Spring B contracts with respect to its resting length, as it does in my

drawing?

https://www.geogebra.org/m/vkz6htmu

the two springs A and B (with mass) have the same length at rest: 8.

Spring A is in the remote space and maintains its length 8.

Spring B is stationary in a well in the center of the Earth.

Is spring B in free fall even though it is stationary?

Spring B contracts with respect to its resting length, as it does in my

drawing?

Nov 8, 2022, 10:25:17 AM11/8/22

to

the earth.

To say that spring B is in free fall is ignoring the fact that it extends over

an extended volume of space, and thus parts experience gravitational

strains that other parts don't. Certainly the ends of the spring are not

"in free fall", although you might argue that the center of gravity is.

Rich L.

Nov 8, 2022, 11:44:15 AM11/8/22

to

But also Einstein's elevator extends over an extended volume of space

and, therefore, only its center is in free fall but not the top and

bottom ends, where gravity is different.

So, if we can't say my spring is in free fall, we can't say it for

Einstein's elevator either!

Luigi

[[Mod. note -- If Einstein's elevator were as big as the Earth, then

you'd be right. But the size of Einstein's elevator is much less than

the size of the Earth (= the spatial scale over which the gravitational

field varies).

In the presence of non-uniform gravitational fields, "free fall" is a

*local* phenomenon, i.e., it's rigorously defined (only) in terms of a

limit where the size of our experimental region (i.e., the "elevator")

goes to zero.

-- jt]]

Nov 9, 2022, 4:21:14 PM11/9/22

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Luigi Fortunati marted=EC 08/11/2022 alle ore 01:44:10 ha scritto:

I added a slider to modify the length of the spring at will: you say it

is in "free fall" only when it is at zero and for no other value?

[[Mod. note --

No, I am saying that unless the spring is infinitesimally small, some

part(s) of the spring may be in free fall AND other part(s) may (in

practice, are very likely to) be not-in-free-fall. More generally,

we need to be precise as to *what* either is or isn't in free-fall:

simplying saying "the spring" isn't sufficiently precise. I expanded

on this reasoning in a separate posting in this thread, which has not

yet appeared.

-- jt]]

is in "free fall" only when it is at zero and for no other value?

[[Mod. note --

No, I am saying that unless the spring is infinitesimally small, some

part(s) of the spring may be in free fall AND other part(s) may (in

practice, are very likely to) be not-in-free-fall. More generally,

we need to be precise as to *what* either is or isn't in free-fall:

simplying saying "the spring" isn't sufficiently precise. I expanded

on this reasoning in a separate posting in this thread, which has not

yet appeared.

-- jt]]

Nov 10, 2022, 5:59:28 AM11/10/22

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I'll start with the easy question: Yes, spring B contracts with

respect to its resting length, because it's in a spatially-variable

gravitational field which points down at the top of spring B, and

up at the bottom of spring B.

Now to the trickier question: what about "free fall"?

The concept of "being in free fall" is easy for a point mass.

But Luigi is asking about extended bodies (bodies with non-trivial

size and internal structure). Here there are different ways to think

about what "being in free fall" means. In particular, we need to

distinguish between two quite different questions:

Question #1: Is the object's center of mass in free-fall? This is

true if and only:

(a) the net non-gravitational force acting on the object (i.e., the

vector sum of all non-gravitational forces acting on the object)

is zero. Or, we could say;

(b) the net *external* non-gravitational force acting on the object

(i.e., the vector sum of all *external* non-gravitational forces

acting on the object, where "external" means "applied by something

that's not itself part of the object") is zero.

[Note that formulations (a) and (b) are actually exactly

equivalent, because the vector sum of all *internal*

non-gravitational forces acting on an object (i.e., forces

where one part of the object exerts a force on another part

of the object), must be zero by Newton's 2nd law.

In practice, formulation (b) is usually more convenient,

because it lets us ignore internal forces, e.g., in this

case it lets us ignore the forces one part of spring B

exerts on another part of spring B.]

The answer to Question #1 for Luigi's spring B is "yes": spring B's

center of mass is in free-fall, because there are no non-gravitational

forces acting on the spring.

Question #2: Is each part (or some specific part(s)) of the object

in free-fall? For some small part X of the object (small enough that

we can neglect it's internal structure, and assume that the gravitational

field is constant across it's diameter), X is in free-fall if and only if

the (vector) sum of any external non-gravitational forces acting on X is

zero.

If X is any part of spring B other than the part right at the center of

the Earth, then the answer to question #2 is "no": there is a non-zero

net force exerted on X by other parts of the spring.

SUMMARY:

The center-of-mass of Luigi's spring B *is* in free fall, but almost all

of the individual parts of spring B are *not* in free fall. A common

(albeit slightly imprecise) shorthand terminology for this is to say that

"spring B is in free-fall in a tidal gravitational field".

--

-- "Jonathan Thornburg [remove -color to reply]" <dr.j.th...@gmail-pink.com>

currently on the west coast of Canada

"Why would you sell anyone your inevitable always increasing asset?"

-- Derek Whittom, 2022-04-25

Nov 11, 2022, 6:28:21 AM11/11/22

to

Jonathan Thornburg [remove -color to reply] giovedì 10/11/2022 alle ore> Luigi Fortunati <fortuna...@gmail.com> wrote:

>> In my drawing

>> https://www.geogebra.org/m/vkz6htmu

>> ,,,the two springs A and B (with mass) have the same length at rest: 8.
>> In my drawing

>> https://www.geogebra.org/m/vkz6htmu

Nov 15, 2022, 3:46:02 AM11/15/22

to

Jonathan Thornburg [remove -color to reply] giovedì 10/11/2022 alle ore 11:59:25 ha scritto:

> Luigi Fortunati <fortuna...@gmail.com> wrote:

>> In my drawing

>> https://www.geogebra.org/m/vkz6htmu

>> the two springs A and B (with mass) have the same length at rest: 8.

>>

>> Spring A is in the remote space and maintains its length 8.

>>

>> Spring B is stationary in a well in the center of the Earth.

>>

>> Is spring B in free fall even though it is stationary?

>>

>> Spring B contracts with respect to its resting length, as it does in my

>> drawing?

> .....
> Luigi Fortunati <fortuna...@gmail.com> wrote:

>> In my drawing

>> https://www.geogebra.org/m/vkz6htmu

>> the two springs A and B (with mass) have the same length at rest: 8.

>>

>> Spring A is in the remote space and maintains its length 8.

>>

>> Spring B is stationary in a well in the center of the Earth.

>>

>> Is spring B in free fall even though it is stationary?

>>

>> Spring B contracts with respect to its resting length, as it does in my

>> drawing?

> Question #2: Is each part (or some specific part(s)) of the object

> in free-fall? For some small part X of the object (small enough that

> we can neglect it's internal structure, and assume that the gravitational

> field is constant across it's diameter), X is in free-fall if and only if

> the (vector) sum of any external non-gravitational forces acting on X is

> zero.

>

> If X is any part of spring B other than the part right at the center of

> the Earth, then the answer to question #2 is "no": there is a non-zero

> net force exerted on X by other parts of the spring.

>

> SUMMARY:

>

> The center-of-mass of Luigi's spring B *is* in free fall, but almost all

> of the individual parts of spring B are *not* in free fall.

Based on what you yourself write, an extended body (without external
> in free-fall? For some small part X of the object (small enough that

> we can neglect it's internal structure, and assume that the gravitational

> field is constant across it's diameter), X is in free-fall if and only if

> the (vector) sum of any external non-gravitational forces acting on X is

> zero.

>

> If X is any part of spring B other than the part right at the center of

> the Earth, then the answer to question #2 is "no": there is a non-zero

> net force exerted on X by other parts of the spring.

>

> SUMMARY:

>

> The center-of-mass of Luigi's spring B *is* in free fall, but almost all

> of the individual parts of spring B are *not* in free fall.

constraints) in remote space is entirely in free fall in every single

particle (none excluded), while the same extended body that falls into a

well on the Earth, is not entirely in free fall because (almost) all its

own particles (although without external constraints) bind each other!

All of this confirms what I wrote: free fall near gravitational masses

is *different* from free fall in remote space.

Nov 15, 2022, 7:17:25 AM11/15/22

to

In article <tkv9hj$16lt$1...@gioia.aioe.org>, Luigi Fortunati

gravitational masses. All such discussions explicitly or implicitly

assume that the tidal effects are "small enough". In other words, in

the limit of arbitrarily small tidal effects, the two are equivalent.

<fortuna...@gmail.com> writes:

> Based on what you yourself write, an extended body (without external

> constraints) in remote space is entirely in free fall in every single

> particle (none excluded), while the same extended body that falls into a

> well on the Earth, is not entirely in free fall because (almost) all its

> own particles (although without external constraints) bind each other!

>

> All of this confirms what I wrote: free fall near gravitational masses

> is *different* from free fall in remote space.

The difference is that tidal effects have to be taken into account near
> Based on what you yourself write, an extended body (without external

> constraints) in remote space is entirely in free fall in every single

> particle (none excluded), while the same extended body that falls into a

> well on the Earth, is not entirely in free fall because (almost) all its

> own particles (although without external constraints) bind each other!

>

> All of this confirms what I wrote: free fall near gravitational masses

> is *different* from free fall in remote space.

gravitational masses. All such discussions explicitly or implicitly

assume that the tidal effects are "small enough". In other words, in

the limit of arbitrarily small tidal effects, the two are equivalent.

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