Physics question

[nun]

This is a special case of the two body problem. As the initial velocities are both zero the "orbit" will be a straight line between the two atoms. This "orbit" will pass through the center of mass of the system and so they will collide.

 

[kcowan]

OK now that have have solved that one, what about that 14 trillion $ deficit?

(It is these types of theoretical questions that turned me off school. I quit right after the Masters degree. My buddy who went on to get his PhD in Theoretical Physics eventually was gainfully employed through the delivery of the Charlottesville telephone directories!)

 

[M Paquette]

OK now that have have solved that one, what about that 14 trillion $ deficit?

"First, we assume a spherical cow..."

 

[Zero]

These are the kinds of things my kids come up with:

Assuming two hydrogen atoms starting out motionless at opposite ends of a static universe, with nothing else in the universe and standard gravity. Would they eventually hit each other, and if so, what speed would they hit each other at, and would they still be accelerating when they hit?

(I've no idea; I got a C in physics!)

2Cor521

If I am reading correctly, you say "standard gravity", and if that is the case then someone has to provide information on what populates the "static universe". If there are other masses, as in planets or stars, then there are many gravitional fields and there is certainly no way to answer the question. If it is an empty universe then the only gravity would be the gravity associated with the mass of the atoms. In that case the atoms would begin to accelerate towards each other and collide.

The interesting thing about a question from a child is that they expect there to be "some" answer. Any protestation on your part that there is "no" answer will be interpreted as "dad/mom doesn't know the answer."

 

[ERD50]

The interesting thing about a question from a child is that they expect there to be "some" answer. Any protestation on your part that there is "no" answer will be interpreted as "dad/mom doesn't know the answer."

I bet the kids really didn't mean to complicate the question with the "opposite ends of a static universe" line. I think they really meant to simplify it, something like - 'really, really, really far apart, in a big ol' universe with nothin' else in it, but the conventional formulas for gravity still apply in this universe'.

So, unless some quantum levels need to be exceeded for these very small forces to react, or other forces are stronger, I guess the standard formula applies:

Newton's law of universal gravitation - Wikipedia, the free encyclopedia

F = G*(m1*m2)/r^2
where:
F is the force between the masses,
G is the gravitational constant,
m1 is the first mass,
m2 is the second mass, and
r is the distance between the masses.

Assuming SI units, F is measured in newtons (N), m1 and m2 in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674×10^−11 N(m/kg)^2.

So some tiny force that pulls them together, and the force keeps increasing pulling them harder and harder as they get closer and closer. With even a constant force, they would keep accelerating.

-ERD50

 

[Avalon]

Don't know if there is a 'correct' answer. Interesting subject though.

I posed the question to a person that I consider somewhat 'abnormal' in thought. The reply:

"If they don't miss and orbit each other, then they accelerate continuously since gravity is inversely proportional to the square of the distance between them. Oh, wait. Tricky since supposedly stuff can't go faster than speed of light. Don't know. Light speed shan't limit these atoms."

 

[donheff]

I don't know why anyone would expect them not to come together in the scenario posited. Two atoms, gravity exists, universe is static - gravity would serve to pull the atoms together with no other forces to screw with them. In a classical universe they would accelerate constantly with the final speed depending on the initial distance up to, presumably, the speed of light. But with quantum effects, Katie bar the door. They could jump together instantly or never - but there would be a high probability of collision, at least in most of the universes.

 

[Texas Proud]

I don't want to seem argumentative, but the solutions proposed other than mine do not take account of the two atoms being at opposite ends of a universe. What sort of universe has opposite ends?

Something like this was my first thought..... if you have only two atoms, then the universe is only as 'big' as the distanct between the atoms...

IOW, what else is beyond these atoms? What is an edge to a universe?

But, here is the formula to get the force of gravity...



Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:[3]

, where:

• F is the force between the masses,
• G is the gravitational constant,
• m1 is the first mass,
• m2 is the second mass, and
• r is the distance between the masses.

Edit to add:
OK... I was not the first with the formula... OH WELL....

 

[dpruitt85]

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.

 

[donheff]

So, TP, by your formula there will be a force no matter how far apart they are. As it draws them together the force will increase. So they will increasingly accelerate as they approach. The farther apart they start, the greater their speed at collision (in a classical universe). Who cares about the edge of the universe. We all know that beyond that "there be dragons."

 

[arebelspy]

So, TP, by your formula there will be a force no matter how far apart they are. As it draws them together the force will increase. So they will increasingly accelerate as they approach. The farther apart they start, the greater their speed at collision (in a classical universe). Who cares about the edge of the universe. We all know that beyond that "there be dragons."

Except if the universe is expanding at a faster rate than they move together (which seems very likely, as the distance between them would be so great as to make the attraction between them so small). See my post at the top of page 2.

 

[dpruitt85]

Except if the universe is expanding at a faster rate than they move together. See my post at the top of page 2.

I believe the OP said "static" universe for this question. But you are correct.

 

[Patrick]

OK now that have have solved that one, what about that 14 trillion $ deficit?

Congress will solve it the way they always do - by printing more money.

 

[Amethyst]

Murphy's law says the atoms will only collide if they are trying their best to avoid collision.

A.

 

[Calgary_Girl]

zzzzzzzzzzzzzzz...........

No idea, I flunked Physics because I didn't really care if, where or when "Plane A" would meet "Plane B". Your kids have too much time on their hands...shouldn't they be on Facebook or something?

 

[Nords]

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"...]

 

[ls99]

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

 

[BTravlin]

Thanks, now I have a headache.

 

[Walt34]

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.

 

[arebelspy]

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?

 

[SecondCor521]

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.

2Cor521

 

[KingB]

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.

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.

 

[Calgary_Girl]

I think that subject is Algebra.

This is probably why I failed Physics.

 

[Calgary_Girl]

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 .

 

[nun]

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.