Jayne Mansfield (1933-1967) is a physics problem all by herself.
True. But, her daughter's a hotty.
> Jayne Mansfield (1933-1967) is a physics problem all by herself.
Yes, but one still needs to consider lunar gravity tides.
LOL.
The bar on the back of semi-trailers is known as the "Mansfield Bar". It prevents a car from traveling underneath a semi-trailer.
> The bar on the back of semi-trailers is known as the "Mansfield Bar". It prevents a car from traveling underneath a semi-trailer.
When you consider the effect of lunar gravity, you'll recognize that the flow is an alternating in-and-out movement. I'm not making this stuff up. Isaac Newton posted the details on his blog, and with photos.
I've read in a textbook that if you had this hypothetical hole and no air, water, or earth rotation, and dropped a ball into it the ball would oscillate between the ends of the tube with a period of 84 minutes. The acceleration is positive until it reaches center, and then negative until it reaches the other side. This may suggest something about the posed problem.
Also, the steady state would be water standing at the earth's surface on each side. So the question is what happens between these extremes.
With a column of water, the acceleration would increase until the leading edge of the water got to the center, and then decrease. But the acceleration wouldn't go to zero until the water had filled the hole all the way to the other side so there was an equal amount of water being pulled each direction. Thus the velocity would be a maximum when the acceleration is no longer positive, i.e. the water reached the opposite side and it would make a tremendous geyser.
You are using the point mass equivalent of the body, which is only valid outside the body. The gravitation at the center of a a uniform sphere is zero. Also true if the sphere is not uniform but has radial symmetry.
Well Jayne had a well-known repeated issue with her center front mass escaping Earth's gravitational pull.
My excuse is that I posted my response while standing in line at a Panda Express in Stockton, CA, after watching two 15U baseball games, one of which was delayed for 45 minutes while the center fielder for the other team was removed by ambulance after fracturing his skull on the left fielder's knee. We're told he'll be okay once they drill a couple of holes in his skull to relieve pressure from the bleeding. The doc mom of one of our players -- who arrived at the ballpark after the ambulance had already left -- said that if left untreated, he likely would have died within an hour.
All these years I've been fearing injury from a bat or a ball, and then something as pedestrian as two kids running into each other nearly cost one of them his life.
Back to the subject at hand: with time to reflect, I now agree with what Bill said.
One thing no one that I see has mentioned that makes much of the analysis incomplete.
The center of the earth is probably very very hot. As water or anything nears the core it will superheat and probably explode back up the hole in a way to make any other human solvable event insignifcant.
Pethaps spewing the internal guts of the earth out into the atmosphere entering us into an almost instant new ice age.
Great Idea? no thanks.
Already addressed in OP
"and assume the pipe is insulated so the high temperatures in the earth's core don't turn the water to steam."
Is the weight of the remaining water in the Indian Ocean greater than the force of gravity. I think the Indian Ocean may go dry before the hole is filled in which case the water would settle at the lowest point of gravity vs the weight of the water column. You can escape the gravitation pull of earth if the speed of acceleration overcomes the force of gravity
Should submit this question to xkcd's "What if?"
He answers a new question each Tuesday. Usually about physics/math type problems.
Some examples:
How long would the Sun last if a giant water hose were focused upon it?
> One thing no one that I see has mentioned that makes much of the analysis incomplete.
> The center of the earth is probably very very hot. As water or anything nears the core it will superheat and probably explode back up the hole in a way to make any other human solvable event insignifcant.
>
> Pethaps spewing the internal guts of the earth out into the atmosphere entering us into an almost instant new ice age.
>
> Great Idea? no thanks.
As mentioned in the original post, assume the pipe is insulated.
> Is the weight of the remaining water in the Indian Ocean greater than the force of gravity. I think the Indian Ocean may go dry before the hole is filled in which case the water would settle at the lowest point of gravity vs the weight of the water column. You can escape the gravitation pull of earth if the speed of acceleration overcomes the force of gravity
Even a large diameter hole 7900 miles deep would centainly not empty all the worlds oceans.
> My only way to answer that question is to go back to the universally accepted Newton's Law of Gravitation. If mass of water reaches the center of earth then the distance between their centers of gravity collapses to zero thus leaving the universal formula with zero value denominator. In such a case, force of gravitation reaches infinity.
Gravity goes to zero at the center of the arth, not infinity.
Exactly!
> I've read in a textbook that if you had this hypothetical hole and no air, water, or earth rotation, and dropped a ball into it the ball would oscillate between the ends of the tube with a period of 84 minutes. The acceleration is positive until it reaches center, and then negative until it reaches the other side. This may suggest something about the posed problem.
>
> Also, the steady state would be water standing at the earth's surface on each side. So the question is what happens between these extremes.
>
> With a column of water, the acceleration would increase until the leading edge of the water got to the center, and then decrease. But the acceleration wouldn't go to zero until the water had filled the hole all the way to the other side so there was an equal amount of water being pulled each direction. Thus the velocity would be a maximum when the acceleration is no longer positive, i.e. the water reached the opposite side and it would make a tremendous geyser.
We are in agreement. Now I just need to convince the nayseyers that we are right!
7 BILLION PEOPLE--THAT'S A LOT OF JUMPERS....
This is a hypothetical problem because....you'd never get a permit for it...
Since we are talking hypothetically, you would need a hole approximately 404 KM in diameter to empty the oceans.