Question for a boffin scientist!?

Question

If you could drill a whole right through the earth and it's core, from the north pole to the south. The whole would be 100 metres in diameter and would be made of an alloy which did no melt or get react with the magma core. It's a hyperthetical question but:: What would happen if a man jumped onto the whole that went straight through the earth and out the other side. Would gravity eventually stop him at the centre or would he come flying out the other side??????

Answer 1

In a perfect frictionless world he'd go all the way thru and stop exactly at the other side, then start falling again.

If you think about this is 2 dimensions:

A----------------C------------------B
^
If the man starts at A, the whole Earth (A-B) is pulling him towards B.

As he is falling towards the centre of the earth (C) there is some earth pulling him towards A but most of the earth is pulling him to B.

A----------------C------------------B
^
By the time he reaches C there are equal amounts of earth on either side pulling him in both directions. But he is already moving very fast so he'll fly past the centre on his way to B.

From C to B the thing works in reverse, most of the earth is pulling him back towards A (and an ever decreasing amount is pulling towards B). This slows him down.

If we assume the earth is perfectly simmetrical (can't spell) the speed picked up on the way to C is perfectly cancelled out on the way to B. So by the time he reaches the other side he is at a stand still. Grab the side quick or you'll go back the other way...

Answer 2

Unless there was some way of removing air resistance, he'd never make it out the other side because some of the energy he'd need to get back up to the surface on the other side will have been dissipated, so he'd only make it part of the way up.

On the way down he'd accelerate until passing through the centre point after which he'd decelerate at the same rate. If this was allowed to continue, his position would continue to oscillate about the centre of the earth until air resistance and / or any other friction slowed him to a stop. He'd then be suspended at the centre.

Cheers.

Answer 3

He'd be stuck in the centre, but after "bouncing" between both sides of the Earth's gravitational centre. He'd accelerate until he reached terminal velocity, then after passing the centre of the Earth, he'd begin to decelerate, as he is technically going upwards, like throwing a ball straight up into the air, he will decelerate until he stops, then he will accelerate to the Earth's centre, pass it, and decelerate again, but a bit lower than before. After doing this for a while with the "bouncing" getting lower and lower, he will eventually stop in the Earth's centre.

That's my theory anyway...

Answer 4

When you lift a 100 pound weight say one foot you increase its potential energy by 100 foot-pounds. When you throw a stone you increase its speed and kinetic energy. As the pendulum of a clock swings to-and-fro it has either potential energy at the top of its swing (zero velocity but maximum height). At the bottom of the swing it has kinetic energy (maximum velocity but minimum height). It oscillates between pure potential energy (position) and pure kinetic energy (motion).

Your man would also oscillate between pure potential energy (at North Pole), pure kinetic energy (at earth's center) and pure potential energy (at the South Pole). Of course air resistance would reduce his energy and the oscillations would decrease with time until he had lost all his energy and remained at the center of the earthy (where gravitational attraction is zero!).

Answer 5

Easy, you would eventually come to rest in the middle. Think centre of gravity...