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Old 05-14-2011, 01:44 AM   #41
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Your kids have too much time on their hands...shouldn't they be on Facebook or something?
They got that question from the "Post this to your status!" passed along from their FB friends.

Next week's FB status challenge: relativistic acceleration in an inertial frame of reference.

[Note for those who don't remember Justin: "This is sarcasm"...]
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Old 05-14-2011, 08:43 AM   #42
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If the atoms are infinitely far apart (as assumed in the universe) then the gravitational force is 0. In the gravitational force equation with 'r' being infinity and r^2 being infinity, anything divided by infinity is zero. If the force is zero and force equals mass*acceleration, then the acceleration must be zero.

In essence, you must define the distance.

EDIT: However, even if you defined an extremely large distance, say 5 quadrillion light years, the theoretical upper limit for velocity is the speed of light, regardless of acceleration.
Without any qualifications in the field, I like dpruitt's solution.


The question I posed around 1980 to an Astronomer morphed to become a Seismologist (There was slim chance of making a living in astronomy) was:

What is the gravitational pull on my right hand 3 feet away from a bottle of Olympia beer while sitting at a rickety table in The Elbow Room in Unalaska Alaska.

A few minutes of puzzled look, but never got an answer. I think we both were more than three sheets to the wind. Maybe the erstwhile physics majors can figure it out.

Presenting: THE ELBOW ROOM. Inside was a tad more shabby. Photo is from an article in The NY Times.

Unalaska Journal - Safe Harbor on Alaska Fishing Island, Still a Dream Away - NYTimes.com
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Old 05-14-2011, 08:47 AM   #43
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Thanks, now I have a headache.
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Old 05-14-2011, 09:20 AM   #44
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I would tell the kids to do their own damn homework and quit bugging me about trivial stuff.

And stay off the lawn.

This reminds me of my father laughing when I asked my first-grade teacher "How big is infinity?" which he said was "a number so big you can't measure it" which didn't explain a thing. She didn't have a good answer either.
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Old 05-14-2011, 09:35 AM   #45
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I would tell the kids to do their own damn homework and quit bugging me about trivial stuff.

And stay off the lawn.

This reminds me of my father laughing when I asked my first-grade teacher "How big is infinity?" which he said was "a number so big you can't measure it" which didn't explain a thing. She didn't have a good answer either.
Does anyone?
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Old 05-14-2011, 11:15 AM   #46
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Thanks all. I'll have my son read this thread.

The question was not homework related; he just thinks up these questions in his spare time to entertain himself.

To clarify a couple of other things:

1. Yes, the posited universe is supposed to be static to avoid the interaction between gravity and the expanding universe we happen to live in.
2. Yes, the universe is supposed to be empty just to simplify the problem.
3. I don't think he knows about quantum stuff (neither do I actually), so I don't think that was part of his question.
4. He's been talking about terminal velocity lately, so I think his question was more along the lines of would there be anything else to slow down the two atoms / counteract the acceleration due to gravity like there is with a parachutist entering the atmosphere. I think the answer is no, like most posted here.
5. He maybe also wondering if the very tiny gravitational force (due to tiny masses and great distances) would be "enough" to bring the two atoms together. I think the answer is yes, but obviously, depending on the distance, it could take a really long time.

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Old 05-14-2011, 11:33 AM   #47
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zzzzzzzzzzzzzzz...........

No idea, I flunked Physics because I didn't really care if, where or when "Plane A" would meet "Plane B".
I think that subject is Algebra.

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Your kids have too much time on their hands...shouldn't they be on Facebook or something?
Something. I think I will re-arrange DW's kitchen cabinet again.
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Old 05-14-2011, 01:57 PM   #48
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I think that subject is Algebra.

This is probably why I failed Physics.
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Old 05-14-2011, 01:59 PM   #49
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Next week's FB status challenge: relativistic acceleration in an inertial frame of reference.

[Note for those who don't remember Justin: "This is sarcasm"...]
Thanks for the heads up....I will schedule my root canal for that day .
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Old 05-14-2011, 02:40 PM   #50
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The problem gets good if there is some initial velocity. Then the atoms will orbit around their center of mass. The eccentricities and families of shapes these orbits are interesting.

Also terminal velocity isn't relevant in this case as there is no resistive force to counter the motion of the atoms. Terminal velocity is when the resistive force of a fluid (air or water) ie drag equals the gravitational force. When this happens there's no net force acting and the object doesn't accelerate, so the speed is constant. For an atom though it's collisions with other atoms would be more important.
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Old 05-14-2011, 03:23 PM   #51
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With some basic assumptions, like the universe is a sphere, and that it's finite and that the atoms are the only 2 objects in that non-expanding or contracting universe, here is a simple Newtonian view of what should happen.
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Old 05-14-2011, 03:26 PM   #52
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Thanks all. I'll have my son read this thread.
Well, heck, if he's going to come up with these physics questions on his own, then he'll need this indispensable scientific resource too:

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Old 05-14-2011, 03:50 PM   #53
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The question was not homework related; he just thinks up these questions in his spare time to entertain himself.
Cool! You have a future scientist there. Get him some books and encourage the interest!

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1. Yes, the posited universe is supposed to be static to avoid the interaction between gravity and the expanding universe we happen to live in.

2. Yes, the universe is supposed to be empty just to simplify the problem.

3. I don't think he knows about quantum stuff (neither do I actually), so I don't think that was part of his question.

5. He maybe also wondering if the very tiny gravitational force (due to tiny masses and great distances) would be "enough" to bring the two atoms together. I think the answer is yes, but obviously, depending on the distance, it could take a really long time.
He would basically be right, as long as he reduced the scale. For example, two hydrogen atoms in a perfect vacuum inside a shoebox in orbit around the earth would eventually gravitate together, but after an amazingly long time. On the scale of the universe, the stochastic events have even more thousands of zeroes in them, on the divisor side.

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4. He's been talking about terminal velocity lately, so I think his question was more along the lines of would there be anything else to slow down the two atoms / counteract the acceleration due to gravity like there is with a parachutist entering the atmosphere. I think the answer is no, like most posted here.
Well, on the scale of the universe, you have to take into account dark matter and dark energy. Are you going to remove them to allow the two atoms to see each other ? Part of the problem of doing that is that our current physics doesn't know how to identify them, which is a shame since they represent over 90% of the universe (which I would be pretty embarrassed about, if I were an astrophysicist!)
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Old 05-15-2011, 07:49 AM   #54
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Assuming, from what OP has posted, that this is a problem within the framework of Newtonian physics (i.e. neglecting any quantum mechanical or relativistic effects).

First of all, by symmetry, they would collide at a point halfway between the two particles and would each be traveling at the same speed (V), assuming a finite separation as described in post #34 by dpruitt85 and post #30 by ERD50, since the particles have the same mass (M) and are initially at rest. Since the two particles are the only occupants present in the universe, it becomes a conservation of energy problem - the initial gravitational potential energy due to the particles' separation is totally converted into kinetic energy when they collide.

The initial potential energy is the work required to separate the two particles (against the gravitational attraction between them) to a very large distance. This number (to a very close approximation) = GMM / R, where (in the metric system)

G = the gravitational constant = 6.67 x 10^(-11) N(m/kg)^2
M = the mass of a hydrogen atom = 1.674 x 10^(-27) kg
R = the diameter of a hydrogen atom = 10^(-10) m

To find the speed:

2 x ( 0.5 MV^2) = GMM / R

Solving for V (assuming I've done the arithmetic correctly)

V = SQRT ( GM / R) = SQRT ( 6.67 x 1.674 x 10^(-28) ) = 3.3 x 10^(-14) m/s

They ain't going very fast!
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Old 05-15-2011, 08:43 AM   #55
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But, I'd rather talk about in-laws, politics, finance and sex.
Me too - but in the reverse sequence ...
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Old 05-15-2011, 08:47 AM   #56
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Reading this thread, I think I understand why Quants took over Wall St. Lots of intellectual fun trying to solve problems, plus when you are right you get rich and when you are wrong, you blame somebody else.
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Old 05-15-2011, 09:46 AM   #57
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Here is a discussion on a physics (nerd) forum and it devolves into a discussion of two hydrogen atoms at a distance and the question is what would happen due to their attraction. From reading the discussions it seems that lots of folks interpret the physics associated with the atoms differently.

Inside an Atom [Archive] - Physics Forums
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Old 05-15-2011, 10:24 AM   #58
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I think they would come together if they had a sufficient attraction to each other. Whether they would collide or waltz around each other would depend on their conflict management skills.

I got a B+ in physics.

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Old 05-15-2011, 10:28 AM   #59
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Assuming, from what OP has posted, that this is a problem within the framework of Newtonian physics (i.e. neglecting any quantum mechanical or relativistic effects).

First of all, by symmetry, they would collide at a point halfway between the two particles and would each be traveling at the same speed (V), assuming a finite separation as described in post #34 by dpruitt85 and post #30 by ERD50, since the particles have the same mass (M) and are initially at rest. Since the two particles are the only occupants present in the universe, it becomes a conservation of energy problem - the initial gravitational potential energy due to the particles' separation is totally converted into kinetic energy when they collide.

The initial potential energy is the work required to separate the two particles (against the gravitational attraction between them) to a very large distance. This number (to a very close approximation) = GMM / R, where (in the metric system)

G = the gravitational constant = 6.67 x 10^(-11) N(m/kg)^2
M = the mass of a hydrogen atom = 1.674 x 10^(-27) kg
R = the diameter of a hydrogen atom = 10^(-10) m

To find the speed:

2 x ( 0.5 MV^2) = GMM / R

Solving for V (assuming I've done the arithmetic correctly)

V = SQRT ( GM / R) = SQRT ( 6.67 x 1.674 x 10^(-28) ) = 3.3 x 10^(-14) m/s
Huh?
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Old 05-15-2011, 04:25 PM   #60
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2Cor - terminal velocity would be a factor. And you can forget about dark mater since your son stipulated that the universe is empty except for the two atoms. The determining factor (unspecified) is the size of your son's universe. The atoms will continually accelerate towards each other. If the time available for acceleration (i.e. distance) is sufficient, the atoms will approach the speed of light. As they do time will slow down, mass will increase but the atoms can never exceed the speed of light so there is your terminal velocity.
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