Remember that Force equals mass times acceleration. F=MA when the water column has equalized the force is zero, so no more acceleration. The force is at its greatest when the water first starts flowing down the hole. You have the force of gravity and the water pressure of the water column in the ocean. When the water reaches the center of the earth the force of gravity starts decreasing because the force on the water on each side of the center cancels itself out. The water will rise until the the force directed "down" is equal to the force directed "up". At this point the water is not moving because there is equal acceleration in both directions. When the velocity has gone to zero because of the balancing forces there is no momentum left.
you are confusing acceleration and force
you are confusing acceleration and force
you posted:
The water will rise until the the force directed "down" is equal to the force directed "up". At this point the water is not moving because there is equal acceleration in both directions.
Actually, The water will accelerate until the the force directed "down" is equal to the force directed "up". At this point the water is no longer accelerating because there is equal force in both directions. Don't confuse No Longer Accelerating with no longer moving.
you are confusing acceleration and force
> you are confusing acceleration and force
>
> you posted:
>
> The water will rise until the the force directed "down" is equal to the force directed "up". At this point the water is not moving because there is equal acceleration in both directions.
>
> Actually, The water will accelerate until the the force directed "down" is equal to the force directed "up". At this point the water is no longer accelerating because there is equal force in both directions. Don't confuse No Longer Accelerating with no longer moving.
No, I'm not confusing them they are directly related. There is an acceleration caused by the force pulling down and one by the force pulling up. At the point at which the forces have equalized the two accelerations are equal. The water may continue moving up momentarily, but it will slow down and return to that point. It won't go gushing out. My point was that momentum has nothing to do with it. Momentum is conserved, but only in a closed system.
Velocity is the integral of acceleration
When the net force and thus the acceleration drops to zero because the columns of water on each side of center are equal, it has been building up velocity for a long time. It no longer builds up more velocity but it is already moving fast. It has momentum (mass times velocity) that must continue until dissipated by opposing forces that gradually slow it down.
Depending on what effects you consider or neglect, it would be moving at hundreds to thousands of miles per hour when it reaches the surface, and certainly gush out.
I tried this at home.
I drilled a hole in a globe and poured water into it which resulted in two things:
1) Water poured all over the table and floor.
2) my wife yelled WHAT ARE YOU DOING!?!
Thanks a lot Perry.
Gee whiz, you didn't put a pipe all the way through the globe to see how it poured out the other end. Or maybe you didn't have the globe over the sink?
Could we get a better thread?
Curved lines are more better!
Keith
hello,
my initial thoughts are that there will be NO column of uniform density water all the way through to the centre of the earth, and no geyser.
as the water is speeding towards the centre of the earth it will (in a vacuum) reach 28440 km/h. the water rushing in at the top of the hole will be starting its journey at 0 km/h and accelerating from there.
in order to maintain a column of uniform density the water would have to be rushing in at the top of the hole at 28440 km/h. this is not going to happen. to maintain the same volume of flow going past any point you wished to observe from, the faster the water is travelling the less dense it must be going past; lots of small droplets going really fast. in effect it should be raining (hard) on you at the centre of the earth.
so as it passes the centre of the earth it starts to slow and become more dense until becoming a solid column again at the other side.
so, i wish to register my guess in advance of the answer as: no. it will not gush out the other side.
:-/
Excellent point. If you don't assume it to remain a column, things really change.
I think I have to concede that it wouldn't stay in a column.
And even if you put a frictionless sliding plug in ahead of the water to try to keep it together, the later water won't keep up with the earlier water and plug. In a vacuum, the voids can be anywhere (a water barometer in atmosphere only stands 32 feet, and in a vacuum no head at all).
