34 replies to this topic

[olli]

well i reserched this and i found this out.

well basically lets ignore the fact that this wont happen and pretend it is possible.

imagine that we got a huge drill and drilled from the south pole all the way down to exactly the same point directly underneth it in the north pole, so there would be a hole going through the centre of the earth, and we droppped a ball down. what would happen? well, the ball would of course begin to fall because of gravity pulling it down. imagine it falling down a well. it would go through the crust, the mantle, the outer core and it would reach the innner core. now, theoretically, hypothetically etc the exact centre of the earth is zero gravity(if it was a perfect sphere), because of the hydrostatic equillibriam (forces pulling inwards and pushing outwards). now the ball would reach this point and it would still carry in through it, because in zero gravity objects have a constant velocity and never ever stop moving or slow down(e.g in space). they will only change direction if they come into contact with another object. so because it gained a lot of G.P.E and kinetic energy falling down and down, it would have reached a point where it cant speed up any more, its terminal velocity. so it would enter the zero gravity and move in the direction of travel, but no gravity would be pulling it down. eventually it will become further and further away from the point of zero gravity and it will continue falling, because gravity is present again. eventually it would get to the end of the other hole. now the ball would come just up to the top of the hole, so it would be level with it. and then, the whole process repeats again, and the ball would fall back down towards the other hole, as just imagine it again being dropped down a well on the other side of the earth. however, when it gets there,(the hole on the other side) it will come up to a point which is lower than the top of the hole, and then it falls again. so each tiime it gets further and further away frim each hole so it goes up a bit, down a bit, then up a little bit less and down a little bit less etc, so it fluctuates in the earth. eventually it will beocme nearer and nearer to the core, where the would be zero gravity, so it will just stay there as there is no force pulling it up or down, and it has very little energy left.

this is called dampened harmonic vibrations.

Simple Harmonic Motion, if there was no friction present. meaning it would ossailate between the two points for ever and not loose distance between them

who knew??

Edited by olli, 21 March 2007 - 08:31 AM.

[duke_Qa]

you are ignoring the fact that friction takes energy from an object in motion unless its in total vacuum. it would most likely by the time it has come to the center of the planet have so little gravitational pull and high friction that it would practically stop without bouncing at all.

if you had some tube going through the planet which gave the ball zero friction and being in total vacuum you would in theory be able to be quite close to what you are imagining, but there will probably still be losses because of the planet moving and gravitational pull going in the wrong directions etc. etc.

simple harmonic? seems closer to a normal sine movement, though its probably the same.

[olli]

its a theory obviously this wouldnt happen. i know about the friction and obviously the intense heat from the mantle and outer core would melt the ball, so lets say its a tube. gravity would still pull it down regardless. its simple harmonic because each time it would fall the same distance away from the top hole and the bottom hole. maybe they are the same thing. say hole A is at the top of the earth and hole B is at the bottom, it will start falling from B, when it reaches hole B. then it would get to hole A and it would only come up say a meter away from the hole, whereas when it was origionally dropped it (from ground height- not from someone standing up) it was level with it.

and it wouldnt bounce, its going down a hole, it wouldnt come into contact with anything (if it travels in a straight line)

[Bart]

eventually it will become further and further away from the point of zero gravity and it will continue falling, because gravity is present again.

it would not continue falling, because then the gravity is in the other direction however, because it still has speed, it will indeed reach the other side of the earth's surface before actually turning around

if you do take friction into account, it would eventually hover in the earth's center

[CodeCat]

Seems like a classic example of a dampened harmonic vibration to me.

v(t) = a * sin (2pi * f * t) / e^(d * t)

[Bart]

not if there is no friction, then it will go on forever

[olli]

it wont go on forever, as in it wount fall from hole A and go straight through B and fly into the sky. you arent getting what im saying.

imangine a tube. it would fall down the tube until it gets to the hole on the other side, but instead of falling out, it would shoot back up and become further and further away from each end of the tube, and yes eventually is would hover in the middle, when it has no Kinetic or Gravitaional potential energy.

its not a vibration, its a motion, but yes it is like that if you plot it on a graph. its called Simple harmonic motion. but that is what it would look like.

[Mastermind]

If there is no friction then yes, it would go on oscillating between point A and point B forever. Since you seem to be saying there is air resistance, then yes, it would be damped harmonic oscillation.

[Bart]

it would go on oscillating

indeed, that is what i mean with "it goes on forever", not that it would fly straight to the sky

eventually is would hover in the middle, when it has no Kinetic or Gravitaional potential energy.

that will happen if you do take friction into account. if not, then...it will go on forever

ts not a vibration, its a motion

it is a vibration. btw, vibration is motion too

[Calamity_Jones]

It would still be damped Simple Harmonic Motion, even in a vacuum. The gravity of the Earth would still be applied to the ball.

CodeCats description is pretty much exactly what would happen, or put into words, quoth olli:

it will come up to a point which is lower than the top of the hole, and then it falls again. so each tiime it gets further and further away frim each hole so it goes up a bit, down a bit, then up a little bit less and down a little bit less etc, so it fluctuates in the earth. eventually it will beocme nearer and nearer to the core, where the would be zero gravity, so it will just stay there as there is no force pulling it up or down, and it has very little energy left.

Vibration and what the ball is doing are both forms of oscillation, and Codecats diagram is just damped oscillation. The same as plucking a guitar string, jelly wobbling after you poke it, waves in a bucket of water you drop a stone into... all the same basic kinda thing.

[Mastermind]

Again, in a case of zero friction, there would be nothing to damp the oscillation. The object would convert all of its gravitational potential to kinetic energy when it reached the center, and would revert to all potential when it reached the other side. There would be no force reducing the energy, so by conservation of energy it must reach the same potential on the opposite side. If you had a hole with air, then it would be damped.

[olli]

lol...ok lets get something straight all of these are theorys. of course its never going to happen so were all discusing what could happen no one is right or wrong

this will happen regardless of friction because its the gravitational pull of the earth, and the point of zero gravity would be quite small. so it will go on oscillating and becoming further and further away from each point, weather friction is there or not. all the friction would do is stop it from traveling at a certain speed, so it would take longer.

when you throw a ball out of a plane, does it stop cause of air resistance or friction? no, because all it does is stop it from going even faster, so it reaches its terminal velocity,

"it is a vibration. btw, vibration is motion too"

yes i know this. it has the behavoir and charisteristics of a dampened harmonic vibration, but its not vibrations that make this happen. thats why its a motion. but for arguements sake, we can call it a dampened harmonic vibration because there the same thing.

EDIT: spelling mistake which contradictided myself

Edited by olli, 18 March 2007 - 07:59 AM.

[Mastermind]

The point is that when you throw a ball out of a plane, it starts with some gravitational potential energy. For the ball to stop at a terminal velocity some of that potential has to be used up as something other than kinetic energy. That is friction due to air resistance, which generates heat.

The assumptions an infinite equal magnitude oscillation is based on:
Point A and Point B are equidistant from the center of the earth (ie the Gravitational potential at each is equal).
The tube between A and B is frictionless
There is no other energy loss due to odd things like the ball deforming or what have you.
When you start at Point A, the ball has a certain potential energy, and 0 kinetic energy. As the ball falls, that potential decreases, and is converted to kinetic energy. When you reach the center of the earth, the potential energy is 0. The kinetic energy is at a maximum, which is the same as the initial potential energy. Since you have momentum away from the center, the ball continues travelling. Since there is no friction, the only reason the ball will stop is the opposing force of gravity. You will remove all of the energy when you reach Point B. At this point, you again have all potential energy, and no kinetic energy. You will repeat this process infinitely, as energy cannot be created or destroyed.

In the case of air resistance you convert a fraction of your potential energy to heat, which is a different form of energy, which reduces the kinetic energy relative to the potential at the center, which means you won't go as high the other way.

[duke_Qa]

also remember that gravitational forces work as a friction in itself, especially if you're in the middle of the planet where all gravity will pull in all directions. the best way to avoid this friction would be if the planet was a 1meter thick disc with a tube the length of earth through it, it would take alot longer time before the ball would get through, but it would in theory oscillate for a longer time.

[Bart]

so it will go on oscillating and becoming further and further away from each point, weather friction is there or not

it will only get further away if there is friction

when you throw a ball out of a plane, does it stop cause of air resistance or friction? no, because all it does is stop it from going even faster, so it reaches its terminal velocity,

you say it yourself: friction is what causes the ball to stop accelerating (reach it's terminal velocity). if there is no friction, the speed of the ball will be unlimited (although, i wonder what would happen if it hit the speed of light )

but its not vibrations that make this happen

a vibration is just a motion where the direction of the force/acceleration on an object keeps switching around (a little more than that, but you get my point), so that's what this is

we can call it a dampened harmonic vibration because there the same thing.

if there is no friction, this is an (undampened) harmonic vibration

That is friction due to air resistance, which generates heat.

indeed, and on top of that the air is mass too, which excercises some force on the ball

energy cannot be created or destroyed.

unless of course you convert it to/from mass

no one is right or wrong

the laws of science, particular those about motion like Newton's laws, are pretty much accepted as fact. if i say "when i release a ball it will fall to the ground with a constant speed", that's theory too, but scientist will definitely say I am wrong

[olli]

ok one thing, lest stop saying there would be no friction, because im sure there would be air in the hole, there for friction would be present. which is why my theory; that it would ossilate between the two points and get further away from each point on the top and eventually come to rest in the middle is what i think would happen.

"you say it yourself: friction is what causes the ball to stop accelerating (reach it's terminal velocity). if there is no friction, the speed of the ball will be unlimited (although, i wonder what would happen if it hit the speed of light shiftee.gif)"

yes, correct i didnt say otherwise. i probably didnt explain it clear enough. what i was saying was if you threw the ball out the plane, it will accelerate. then it will rezch its terminal velocity cause it has low acceleration, because of the friction. i was saying that just because you havr friction present, it doenst just slow down to 1 mile an hour or stop.

"a vibration is just a motion where the direction of the force/acceleration on an object keeps switching around (a little more than that, but you get my point), so that's what this is wink.gif"

yes, but this is larger scale, so im calling it a motion. its the same, it has the same meaning. im not disputing that fact. its just what the sources said. call it what you like, but in my posts i calle it simple harmonic motion. it has the same appreence as a dampened harmonic motion graph.

"if there is no friction, this is an (undampened) harmonic vibration"

if there was no friction it would just keep acceleration very rapidly to each point and it wouldnt slow down. so it would happen a lot lot faster, but i think it would still come to rest in the moddle eventually because of the gravity. its there regardless if its in a vacuum or not.

and yes energy would be lost as heat and other things, but that wont wont stop it from coming to rest in the middle after ossilating and moving further away from each point. this is basically what would happen.
G.P.E>>>>>K.E>>>>Heat energy. then it starts again when it gets to the other end. if some K.E is lost as heat, its means it doesnt move as fast and isnt falling as fast, but gravity will still pull it down regardless.

thats my theory any way taking into account these things being present; with air resistance/friction present. no obstacles in the way. and it fell in a perfectly straight line from point A to B and points A and B were exactly the same distance away. the ball was a perfect sphere and if the earth was a perfect sphere.

[Bart]

it's your situation, and from your post i read that there is no friction. if you had said so earlier, a lot of this discussion would have been unneccesary

if there was no friction it would just keep acceleration very rapidly to each point and it wouldnt slow down. so it would happen a lot lot faster, but i think it would still come to rest in the moddle eventually because of the gravity. its there regardless if its in a vacuum or not.

if there was no friction, it would not come to rest in the middle. you see, when you release the ball it has speed 0, and then the gravity pulls it inward. however, when it is in the center, it goes trough (because of the speed). the gravity will then start to slow it down, but that will take the exact same distance/time as it took to accelerate it, which results in the ball stopping at the other side of the earth. then, the process repeats

[olli]

i didnt mention friction because i thought you would realise and take into account that if there was a gaping hole in the earth air would be present meaing friction would occur

"if there was no friction, it would not come to rest in the middle. you see, when you release the ball it has speed 0, and then the gravity pulls it inward. however, when it is in the center, it goes trough (because of the speed). the gravity will then start to slow it down, but that will take the exact same distance/time as it took to accelerate it, which results in the ball stopping at the other side of the earth. then, the process repeats"

that could be a theory yes, but to me it sounds exactly the same as what im describing, even with friction presnt. but in more detail.

Edited by olli, 19 March 2007 - 07:39 PM.

[Bart]

to me it sounds exactly the same as what im describing,

how can it? your theory is that the ball stops, mine is that it goes on forever

[olli]

it would only go on forever if gravity was not present. friction has nothing to do with it. like i said it only takes longer if friction is present. if it didnt have any gravitational pull, it wouldnt be a planet. or any thing large enough to have a gravitational pull.