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bagpiperNL
830731.  Mon Jul 11, 2011 6:48 pm Reply with quote

Wheelera wrote:
...
At the centre of the Earth all the planet will be around us, pulling us equally in all directions. We will be weightless. And because the decrease in the downwards pull has been so gradual we will arrive with zero velocity, and zero momentum to carry us through this weightless zone. (Recent modelling with our grandson's plasticine has confirmed this expectation.)

We are now trapped, forever.
42 minutes? 43 minutes? Trapped in a weightless void at the centre of our tunnel. I just hope you remembered to bring some sandwiches.

Anthony Wheeler


I was thinking the same thing.

When you're falling down one end, you can not accelerate out of the hole at the other end.
The centre of the earth would, theoretically, be the point of zero velocity.

If one approaches the centre, one would decelerate to a point at where there isn't any acceleration at all.

If gravity 'flows' the the centre of the earth, it wouldn't make a difference as from which location you're falling. Fall down from Australia, fall down from Spain, from both directions, you wouldn't be able to reach the other end.

 
Zebra57
830735.  Mon Jul 11, 2011 7:30 pm Reply with quote

Welcome bagpiperNL

 
Arcane
830763.  Mon Jul 11, 2011 11:35 pm Reply with quote

Has anyone offered the thought about what happens when you dig a really big hole? That the sides tend to er, fall in?

Physics aside, which I freely admit I know diddlysquat about, there's some serious scaffolding needed here.

 
samivel
830765.  Tue Jul 12, 2011 12:20 am Reply with quote

That's why it's a thought experiment, not a practical one.

Well, that and the searing heat thing.

 
dr.bob
830801.  Tue Jul 12, 2011 4:58 am Reply with quote

bagpiperNL wrote:
When you're falling down one end, you can not accelerate out of the hole at the other end.
The centre of the earth would, theoretically, be the point of zero velocity.


Errr, no it wouldn't. The centre of the earth would be the point of zero acceleration, but of maximum velocity.

bagpiperNL wrote:
If one approaches the centre, one would decelerate to a point at where there isn't any acceleration at all.


I think you're wrong to use the word "decelerate" here. You're right to say that you would reach a point where there isn't any acceleration at all, but you would be accelerating all the way down to that point. It's simply that your rate of acceleration would be decreasing.

So, at the surface of the earth, you'd be accelerating with 1g. At the centre of the earth, acceleration would be zero, but all the way down to the centre, the acceleration would be non-zero.

Acceleration is the rate of change of velocity. So, even though the acceleration might be very small close to the centre of the earth, your velocity would still be increasing. That's why the centre of the earth would be the point of maximum velocity.

Once you pass the centre, you then start to decelerate, shedding speed until you just reach the surface on the other side, which is the point of maximum deceleration, but zero velocity.

 
Jenny
830936.  Tue Jul 12, 2011 10:55 am Reply with quote

Welcome bagpiperNL :-)

 
aTao
831073.  Tue Jul 12, 2011 5:18 pm Reply with quote

Is there air in the shaft?

 
bagpiperNL
831104.  Tue Jul 12, 2011 7:10 pm Reply with quote

hmm quite interesting this..

I put it to thought: If you are, in any way able to reach the other end of the tunnel/hole, would you have enough speed to get out?

Or would you just be falling back and forth/up and down between the two ends?

Or am I missing the point here?

 
dr.bob
831164.  Wed Jul 13, 2011 5:20 am Reply with quote

You would just be falling back and forth/up and down between the two ends. It all comes down to the conservation of energy.

The principle of the conservation of energy states that energy cannot be either created or destroyed, merely converted from one form to another.

If an object is stationary at the surface of the Earth being held out over a big tunnel running through the centre, it has zero velocity and, hence, zero kinetic energy. However, what it does have is potential energy through being 6,371km away from the gravitational centre of the Earth.

Once you let go of the object, it starts to fall toward the centre. As that happens, its potential energy is converted into kinetic energy. In other words, it gets closer to the centre of the Earth (thereby losing potential energy) and speeds up (i.e. gains kinectic energy). At the centre of the Earth, the potential energy is zero, and the kinetic energy (and, hence, velocity) is at a maximum.

What happens next is that the object moves further away from the centre, towards to Earth's surface on the other side. This slows it down as the kinetic energy is converted back into potential energy. Assuming there are no other forces acting (i.e. friction from the sides of the tube or whatever) then all of the kinetic energy will be converted back into potential energy.

Since energy cannot be created or destroyed, the object will end up with zero kinetic energy (i.e. it will come to a stop) when it has the same amount of potential energy as before. This will happen when it's 6,371km away from the gravitational centre of the Earth, in other words when it's back at the surface on the other side.

 
bagpiperNL
831942.  Fri Jul 15, 2011 4:00 pm Reply with quote

dr.bob wrote:
You would just be falling back and forth/up and down between the two ends. It all comes down to the conservation of energy.

The principle of the conservation of energy states that energy cannot be either created or destroyed, merely converted from one form to another.

If an object is stationary at the surface of the Earth being held out over a big tunnel running through the centre, it has zero velocity and, hence, zero kinetic energy. However, what it does have is potential energy through being 6,371km away from the gravitational centre of the Earth.

Once you let go of the object, it starts to fall toward the centre. As that happens, its potential energy is converted into kinetic energy. In other words, it gets closer to the centre of the Earth (thereby losing potential energy) and speeds up (i.e. gains kinectic energy). At the centre of the Earth, the potential energy is zero, and the kinetic energy (and, hence, velocity) is at a maximum.

What happens next is that the object moves further away from the centre, towards to Earth's surface on the other side. This slows it down as the kinetic energy is converted back into potential energy. Assuming there are no other forces acting (i.e. friction from the sides of the tube or whatever) then all of the kinetic energy will be converted back into potential energy.

Since energy cannot be created or destroyed, the object will end up with zero kinetic energy (i.e. it will come to a stop) when it has the same amount of potential energy as before. This will happen when it's 6,371km away from the gravitational centre of the Earth, in other words when it's back at the surface on the other side.


I get it now.
I also think that your answer, solves the initial question.

I bow to your wisdom ;) (you must have a head as big as Stephen')

 
Ion Zone
831943.  Fri Jul 15, 2011 4:00 pm Reply with quote

Quote:
it was mentioned that if you have a tunnel through the centre of the Earth, an object dropped from one end would emerge at the other in 42 minutes 12 seconds. I did the calculation myself (using just A-level physics and maths) and got 42 minutes 10 seconds instead.


Easy, because QI know trains are always late. (Except in Japan where they are scarily precise)

 
Mikesim2000
874777.  Mon Jan 02, 2012 6:39 pm Reply with quote

Ok so on the show the theory was it would take the same amount of time to get anywhere on the planet... I don't see how this can be true, and the earth is not a perfect sphere so going from a point on the equator to the opposite point on the equator you would have to travel further than if you went from the north to the south pole as the world is squashed right?

Am I wrong ? Is you speed variable with depth, cause that is the only way I can see the travel time remaining the same for the different distances you would travel?

Any QI researchers got a better explanation?

 
suze
874781.  Mon Jan 02, 2012 6:44 pm Reply with quote

If you look at page 1 of this thread, you'll see the formula which is used to work out how long the journey would take. That formula does assume that the Earth is spherical - which it isn't, although it fails so to be by about one third of one per cent.

We were not shown the algebra which would prove the matter, but it was suggested that the difference in time between a journey at the equator and a journey from pole to pole was about two seconds.

 
h1ghju1ce
944310.  Mon Oct 08, 2012 11:24 am Reply with quote

Posital wrote:
Sorry - we've overlooked the fictitious forces since this "tunnel" would need to be considered in a rotational frame of reference (with the exception of the single case going through the poles).

Can someone factor this in? I assert that the time taken would vary by more than two seconds, but wouldn't be enough to cover National Rail's sorry ass...


If you factored it in, you'd be dead :-)

http://www.youtube.com/watch?v=jN-FfJKgis8&feature=relmfu

 
Tas
944346.  Mon Oct 08, 2012 3:40 pm Reply with quote

Given the acceleration/decelaration thing, it would be important to make sure the entrance and exit were equidistant from the centre of the Earth, right? I mean, if one was 'higher' than the other, you'd have too much acceleration/not enough deceleration to stop/reach the other end, right?

:-)

 

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