Earth and You: Physics

[stormbind]

Actually even without friction you would end up in the center of the earth, because your gravity would pull the earth in the direction of your ossilation, eventually imparting your momentum to it.

That's making the assumption that gravity is affection the person, which cannot really be assumed given that other matter-related forces are not affecting them

 

[betazed]

I have been reading this thread for a couple of days. The original post left too many things ambiguous, so here is the idealized scenario and a more interesting question

Imagine you are in empty space. 100 kms away suddenly a microscopic black hole appears. You are of course pulled towards it. By the time you reach it of course you would have picked up quite some speed, enough that you can pierce the black hole with 0 resistance (it is atomic size anyway and can go right thru your body). So of course you continue on the other side of the black hole and decelerate as you go. Eventually you turn around and come back. You will continue this ocillatory motion.

Now here is the question? Will this motion continue forever in the absence of friction between you and the hole (i.e. you do not lose any energy because of friction between the hole and you).

The answer is no. You will come to a stop at the hole in due time. Can anyone explain why?

 

[Bozo Erectus]

Now here is the question? Will this motion continue forever in the absence of friction between you and the hole (i.e. you do not lose any energy because of friction between the hole and you).

The answer is no. You will come to a stop at the hole in due time. Can anyone explain why?

Because you wont have 100 kilometers to accelerate on subsequent passes?

Edit: with every subsequent pass, the pull of the blackholes gravity will further shorten the distance between you and the blackhole, therefore, your speed will gradually decrease until its zero.

 

[Aphex_Twin]

@betazed

Now let's see if I'm getting the hang of this Physics thing

If a black hole is microscopic in size then it must have a huge mass to shrink it so much, hence it has a very wide event horizon (wider than 100 km) and past the event horizon all movement happends in one direction, towards the center of the hole and gradually decelerated.

 

[betazed]

Because you wont have 100 kilometers to accelerate on subsequent passes?

Edit: with every subsequent pass, the pull of the blackholes gravity will further shorten the distance between you and the blackhole, therefore, your speed will gradually decrease until its zero.

Nope. It is very much like a spring (an approximate simple harmonic oscillator -in fact for short distances it is exactly a SHO).

Remember, While the pull is slowing you down while you are going away it is also speeding you up when you are coming towards it. Going towards the black hole you gain kinetic energy which will let you go past it and go to a distance (while decelerating) almost equal to how far you started from it originally. Except at each pass you will lose a slight amount of kinetic energy and hence each pass will traverse lesser and lesser.

How and why is this kinetic energy lost?

@betazed

Now let's see if I'm getting the hang of this Physics thing

If a black hole is microscopic in size then it must have a huge mass to shrink it so much, hence it has a very wide event horizon (wider than 100 km) and past the event horizon all movement happends in one direction, towards the center of the hole and gradually decelerated.

Not quite; for a microscopic hole the horizon is also microscopic. You can imagine a atomic size horizon. Hence the hole can go right thru you without stopping.

 

[Bozo Erectus]

Nope. It is very much like a spring (an approximate simple harmonic oscillator -in fact for short distances it is exactly a SHO).

Remember, While the pull is slowing you down while you are going away it is also speeding you up when you are coming towards it. Going towards the black hole you gain kinetic energy which will let you go past it and go to a distance (while decelerating) almost equal to how far you started from it originally. Except at each pass you will lose a slight amount of kinetic energy and hence each pass will traverse lesser and lesser.

How and why is this kinetic energy lost?

The deceleration has more to do with space and not the actual blackhole itself, right? Hmmm...I can picture it by imagining a ball rolling on a surface with a depression in it, but its difficult to put into words...because of the warping of space around the blackhole? Some of the kinetic energy is transferred to the warped space around the hole? Damn! My head hurts!

edit: the resistance from space, the same way a rolling ball imparts some kinetic energy to the surface its rolling on.

 

[Aphex_Twin]

I thought you meant a black hole made from a collapsed star. So the microscopic black hole would have to be acted upon from the outside to maintain it's compression, right?

How and why is this kinetic energy lost?

Kinetic energy is transfered to the travelling man. As he is aproaching the hole he will be distorted by the tidal forces. By the time he reaches the center he would be one compressed pile of stuff. But what if he were an indistructible solid?

 

[betazed]

@DP: You are thinking too much. Here is a hint.

The smaller the body that is pushed back and forth the longer it will take to come to rest. Hence the dimensions of the body is the key.

@Aphex: you are almost there.

 

[Bozo Erectus]

Inertia! A small object has less mass and thus less inertia!

edit: a larger body would be able to break free from the blackholes gravity because it has greater inertia!

 

[betazed]

edit: a larger body would be able to break free from the blackholes gravity because it has greater inertia!

If that were true then a larger body would come to rest later than a smaller body. I said that in actuality it is the opposite.

Here this pic should help. the small arrows are the forces acting on a box as its approaches the small hole. Three events are pictured in succession.

 

[Aphex_Twin]

Betazed, if the microscopic black hole has a microscopic event horizon then it's mass would be puny. How exactly would the man be compressed and incorporated into it?

 

[Bozo Erectus]

Ok, the leading arrow in the first diagram is the gravity from the blackhole right? Whats does the second arrow represent? Momentum?

 

[Aphex_Twin]

Ok, so there is no compression. The box will be slightly deformed on each run, taking away kinetic energy from the system. Eventually both the box and the black hole would be at rest towards each other.

But if the deformations are smaller than one cuanta of energy then it would be as if the box (man) would be an indestructible solid.

 

[betazed]

Betazed, if the microscopic black hole has a microscopic event horizon then it's mass would be puny. How exactly would the man be compressed and incorporated into it?

Well, a microscopic black hole can have the mass of several mountains put together, but that the actual mass of the hole is not a factor in our discussion.

DP: the leading arrow on top shows the motion of the box. the small circle is the hole. I have pictured three successive instants as the box crosses the hole from left to right. The small arrows are the forces working on the box.

 

[Bozo Erectus]

Oh well, I give up, Im way out of my league

 

[betazed]

The box will be slightly deformed on each run, taking away kinetic energy from the system. Eventually both the box and the black hole would be at rest towards each other.

Bingo! the box will be alternately compressed and expanded by the tidal forces. This will heat it up and hence transfer its kinetic energy to heat energy.

Now you know the answer to the question of the first post of this thread.

 

[Chairman Meow]

I'm curious to know what speed would one's body have(let's say someone weighting 90-100kgr), while he's approaching the core of the earth.

11,200 m/s, or 25,000 mph. You would find it by using the formulas for kinetic energy and gravitational force:

F = GMm/d^2
To find energy from force, you simply multiply by displacement (actually it's a bit more complicated than that, but I'll stay out of calculus for this...).

Then you have E=GMm/d=1/2mv^2
This can be simplified to v=sqrt(2GM/d).
where G=gravitational constant= 6.6742 × 10^−11 N·m2/kg2
M=mass of the earth=6 x 10^24 kg
and d=distance to the center=6.38 x 10^6 m.

edit - it's useful to read the entire thread... microbe already answered it...

 

[kryszcztov]

Bingo! the box will be alternately compressed and expanded by the tidal forces. This will heat it up and hence transfer its kinetic energy to heat energy.

Now you know the answer to the question of the first post of this thread.

The microscopic blackhole isn't even needed, uh ? We could imagine a giant tube going from one point of the Earth's surface down to the other side of the world, and the travelling man jumping into it. That way, no need to go through some matter...

As I understand it, everytime a solid (or even a liquid, or a gas ?) is deformed by some kind of tidal waves, it is heated and thus loses noble energy (related to entropy's increase ?). It happens eg. when gravity acts on it. So my question : since all matter is concerned with gravitational forces, is the whole matter of the universe constantly heated ? I suppose that the matter doesn't have to be in motion (like myself, typing this on my chair), or does it have to be moving (so as to deform the matter) ?

Further, can we relate it to the fact that we can't reach the absolute zero ? Because all the matter would be heated all the time ? Even if the object isn't moving, every nanoscopic particles being part of the object does move, and so could be heated in the same way as moving macroscopic objects ? Would this be some nice theory that I don't know or I have forgotten, or is this total BS ?

 

[Perfection]

If it were a black hole wouldn't it just never come out even if it was indestructible, simply because spacetime is so curved it would have to travel an infinite distance to get there?

 

[Bozo Erectus]

Because you wont have 100 kilometers to accelerate on subsequent passes?

Edit: with every subsequent pass, the pull of the blackholes gravity will further shorten the distance between you and the blackhole, therefore, your speed will gradually decrease until its zero.

I was thinking about this later in the day (good thing nobody said, 'Hey DP, penny for your thoughts' because I would have replied 'Well I was wondering what would happen if I popped into space 100 kilometers away from a microscopic blackhole' and then the person would have slowly backed away ). Wouldnt what I said above actually decelerate the body much quicker than the compression and expansion you were talking about? Yes the body will accelerate and boomarang away from the blackhole, but wouldnt it decelerate slightly with each pass? Wouldnt a perpetual pendulum like back and forth violate some sort of physical law? The braking caused by the gravity of the receding blackhole would gradually cut its velocity to zero wouldnt it?