Thread: Question about something crazy

Well it kinda stupid.. because its a wierd thing i saw it in my dream where i had a lesson from my professor where he asked what would happen if i entered a tube that went right through the core of the air.

Now id like to know what realy happen if it could actualy happen.
I think a person would bounce in there[near the core(suppose there is no heat)]
and there would be no way he could stand still... or at least in balance(F=0)

I am on early high school and my physics isnt of high level so i would like no flaming :P

I do not understand the question. Can you give more details? Remember I was not in the dream so I have some catching up to do.

"core of the air"?

i think he means 'core of the earth'.

Well i heard that if you drill a hole from a point on the earth straight through the center and out the other side, and you insulate/protect it well enough, and you fall through the hole it will take almost exactly 42 minutes to complete the journey edge to edge. This is true for all starting and finishing points.
It also works if you drill a 'chord' through the earth, i.e. connecting two points on the circumference without going through the centre, obviously it has to be reasonably deep, but it's still 42 minutes!

As for being in the core...i'd say zero g is a possibility, either that or you get killed by crab people.

Assuming zero air resistance and a perfectly homogenous earth, you'll fall right through to the other side and back, perpetual pendulum style. At the core you will indeed experience zero gravity due to Newton's shell theorem. It states that if you are inside of a giant ping pong ball that you will not experience any net gravitational pull from the ping pong ball, no matter where inside of it you are. This applies to you while you are falling, in that the effect of gravity on you would be as if a layer of the thickness of the rock above you around the earth is continually being skimmed off.

why did i type core of the air... wanted to type earth how dit that happen....-_-
well anyways the tube should be in theeqyator. the earth will have to do its usual stuff(spin around its self and around the sun) suppose that the tube wont be affected by the heat and i am falling inside it.will i stop at the core or with the speed i go from the pull be thrown outside the other side?and just out of quriosity how much speed would i have by the time i reached the core (all supposing me entering the tube)

If we can forget about all of the reality problems like friction, the rotation of the earth which would push you to one side of the tunnel then the other and the fact that you would come out one big burnt piece of toast there is a few neat ideas in this exercise.

If you were inside a hollowed out earth or massive shell with a uniform density you would feel a sum of zero force acting on you. You do not have to be in the center for this to work. If you are closer to one side, then you are closer to less of the shell than you are far from. It just happens that a force like which is proportional to one over the distance squared will balance this out. One one side you, you have more mass but it is farther away, on the other side you have less mass but it is closer.

Show when we do this problem we only have to worry about the mass that is closers to the center of the earth than you are as you fall.

Lets assume a uniform density for the mass of the earth (This is of coarse wrong but it makes the math easier.)

Force of gravity between you, and the earth within a radius

Notice the volume of a sphere times the density to give the mass of the part of the earth within the distance (Why the minus sign? We put our coordinate axis at the center of the earth and the force is pulling to the center and our axis goes positive away from the center.)

Simplify:

Now notice the force you would feel is proportional to your distance from the center. This is just like a spring.

Use Newton's second law with the force above: . Notice the drops out!



This is simple harmonic motion with
which gives a period of


I'm too lazy to plug the numbers in because the fun part is over. But why don't you plug the numbers in and see if you get the same time as you have been told.

One import idea. Because we are working with gravity it will take you and a massive object like a the Bush library the same time to fall through. Remember when the canceled?

i just remembered where i heard that 42 minutes thing if you want a source:

http://www.bbc.co.uk/dna/h2g2/A2960633

trust h2g2 to find every instance of 42 anywhere, ever.

It also turns out that 42 minutes not only applies to any starting and finishing points on earth, but any starting point on any gravitational body...weird.

Edit: Just used excel to Goal seek 42 minutes in that period equation and got an average density of 39 tonnes per metre cubed. sound about right?

Also, if 42 minutes is constant for all gravitational bodies as h2g2 would have me believe, how can density come into it?

Originally Posted by JekPorkins

It also turns out that 42 minutes not only applies to any starting and finishing points on earth, but any starting point on any gravitational body...weird.

The density have to be the same. So It would be slower on Saturn but about the same on the moon. See math above.