Lightwizard:
There was a scientific reason why I gave the size of the hole and the size of the lead ball. Also, the additional three pieces of data that I mentioned, especially the precessional wobble will assist with an answer to this question.
ok, so do we get an answer?
i already answered the question.
As part of that perpetual motion comes the flows of our rivers. Man has harnessed that 'energy,' but I'm not sure what detriment to the earth. c.i.
Several people gave insightful answers, but the question remains unanswered in my opinion. The fountains of lava seem likely, but the question infers this problem is somehow solved "drop the lead ball into the hole dead center" The Earth is a big gyroscope so we get coriolis causing the ball to bounce off the wall, likely before the first mile. Hot lead is not very elastic, nor is the hot inside surface of the hole, but I would still expect the the ball to hit the side of the hole at perhaps 1000 MPH several times per mile. This would abrade the lead ball reducing it's diameter to perhaps 1/1000 of an inch in perhaps 20 miles of dropping. The high surface area to mass would cause the ball to slow to perhaps one millionth of a mile per hour in the perhaps 15 atmospheres of air pressure. The ball would behave like a dust mote and begin moving upward if the hole had even a slight updraft. Alternately the dust mote would continue to descend until it hung up on the surface of the hole or reached the center as lead vapor after a few million years. The cloud of lead vapor would have little tendency to over shoot the center, so it would not oscillate significantly in the zero gravity at the center. The lead molecules would mostly be absorbed by the wall material leaving scarsely a trace anywhere including the center. Can someone explain the dylexia answer or was she teasing? Please refute, embellish or comment. Neil
Actually, the heat close to the center of the earth would push the lead ball back out of the hole.
The Earth's mass behaves from the point of view of gravitation, as though it were concentrated at the center of mass of the Earth, which presumably is somewhere near the geometric center. Using the simplifying approximation that there is no heat and that the center of mass lies within the hole, near the center, the ball would accelerate until it reached the center and then decelerate after it passed the hole. With no friction at all and perfect symmetry, it would hit zero speed just as it approached the top of the hole on the other side. Once at a speed of zero, it would begin to accelerate in the opposite direction, back towards the hole. It would oscillate, as someone said, like a harmonic oscillator, but the motion would die out due to friction with the air, and it would come to rest in the center. The rotation of the Earth would have no effect, since you specified that the hole is along the Earth's axis of rotation. This is a very unstable situation, though, because if for any reason the ball struck the sides of the hole, its motion would damp out much more quickly.
Pneumatic pressure is very powerful.
With taking all the three conditions into account, I will say the ball must melt "ultimately."
Brandon9000 wrote:The Earth's mass behaves from the point of view of gravitation, as though it were concentrated at the center of mass of the Earth, which presumably is somewhere near the geometric center.
This is only true when you are outside of the Earth. If you are inside the Earth, the math is quite different.
I stand corrected. A majority agree negligible gyroscopic effect and coriolis on or near the axis of rotation.
As it is a lead ball, it will reach supersonic speed six? seconds after being dropped. The turbulence will cause it to hit the wall once, then repeatedly due the elasticity of the ball and wall. The ball will get hot due to air friction even if the conditions are standard temperature and pressure (two more improbables to go with perfect alignment, no lava, a non abrasive wall and rock pressure would crush the hole, unless it was lined with unobtainium)
The volume of near zero gravity near the center is quite large, so the ball (cloud of lead vapor?) would not overshoot the center by much so the oscillation would be damped out quickly by standard pressure and instantly by the 2000? atmospheres of air pressure we would expect at the center of the Earth.
The perpetual oscillations will occur only if the hole has a perfect vacuum and the wall has no friction. Wall friction is unimportant if the alignment is prefect to parts per google, which is also improbable.
The lead ball will melt if the ambient, over most of the length of the hole, exceeds 327 degrees C which is the melting point of lead, even if the hole is a perfect vacuum. Surface tension will keep the molten ball intact, until it hits the wall unless air turbulence is severe. After the lead ball is scattered into tiny pieces, they will evaporate (minutes to years) as lead has significant vapor pressure over a wide range of pressure and temperature. The lead molecules will cling to and/or be absorbed by the enormous wall area of the inside of the hole, unless the unobtainium has another improbable property. Neil
Ok, Let me have a take at this:
1. Gravity: outside Earth, gravity is F=m * MG/r^2
but inside it linearly falls off toward the center, where it is zero.
So given vacuum, totally symmetrical Earth, no wobble, the ball would go straight through, accelerating to the center, decelerating from there, and reaching 0 on the other side.
Any abnormalities inside Earth (earth is not a perfect sphere, density is not uniform) will cause the vector of gravity not being parallel to the hole (tunnel) all the time and the ball might strike the wall.
This can be avoided by drilling the hole in such a way that it follows the path of an object in free fall through the Earth (geodesic).
Also there is wobble in Earth's rotation - meaning there is no fixed axis of rotation and such a tunnel is impossible. Because of relatively small amount of time needed (about 80 minutes) wobble might not play a significant role in the first several hours.
Now the real problems start with the introduction of air. At ground level, the air would be 'normal' , but increasing in pressure and density enormously toward the center. Because of air the ball would reach terminal velocity fairly soon and from poisson eq. we can see that this velocity would get lower toward the center, because of lower gravity, and higher air viscosity.
At a certain depth the viscosity would be so great that the ball would move as in water, and deeper even as in wax - and so on.
Because of this, the ball would stop somewhere around the center.
Further, the temperatures down the tunnel, and heat created by friction, would cause lead to melt long before reaching middle ground, dissolving into tiny drops of lead, even further slowing the object. Molten drops of lead would wobble thus causing aerodynamic effects which would throw them at the walls where they would stick.
Not counting any molten lava streams down below the Earth's crust...
@Lightwizard,
Don't forget you are drop a metal object through another object with a metal core, on a planet that is travelling through the Sun's very significant electro magnetic field.
So will you get rather large eddy currents that set up a magnet field in opposition to the Earth's and act like a major break - or will being inside a Metal ball shield you?
Who knows Faraday's laws well?
