Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: cuso4 on 05/07/2003 19:47:21
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Right, this is an interesting one.
Say if you drill a hole through the centre of the earth and drop a ball into the hole, what will happen to the ball?
I think some of you guys have heard this one before. And Tom, you can't answer because you know the answer already.
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Wouldn't it stop in the middle (gravity) and be squished by the pressure?
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The middle would have a little equilibrium spot where it would float as though no gravity?
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Nope, they are not the answer I'm looking for. When the ball is dropped, it accelerates and then reaches a terminal speed at the centre. But the ball is still moving so will not stay in the centre.
Give it another try.
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Okay, well the ball will accelerate towards the centre, keep going, be pulled back, probablt go past the centre then turn around, eventually ending up at an equilibrium in the centre. Is that right?
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I'm with Quantum's reasoning on this one. I reckon that, assuming there are no 'losses' on the way as the ball moves (friction or air resistence) then it will accelerate all the way to the centre, reach maximum kinetic energy, then continue out the other side to the equivalent potential energy on the other side, and so on...bouncing back and forth along the length of the hole.
Chris
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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Yep, Chris you're right. My Chemistry/AG's Physic teacher told us this quiz, he actually used me as an example. When "I've" reached the middle of the Earth, there are no gravity acting on me the force is balanced. However I'll keep moving to the southern-hemisphere because all that kinetic energy don't just disappear (if we start from the north) and now head facing downward and going up if can imagin. Then gradually decelerating and reach the surface to only be pull back by the gravity towards the centre again.
It sounded quite painful when he said it.
Tom
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Well done Chris, the ball oscillates along the length of the hole.
Now, which is the most dense metal known?
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Er Iron is pretty dense...
Chris
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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Erm... yeah iron is pretty dense but it's not the most dense. Any other offers?
Angel (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fsmilies.networkessence.net%2Fs%2Fcontrib%2Fruinkai%2FbiggrinangelA.gif&hash=7a3ab31861328a98db23edcb21639ab9)
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Er... is it Lead ?
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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Osmium
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Wow, Donnah how do you know that? It is Osmium.
Tom
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I've got another question:
Space shuttles don't blast away vertically, they are projected at an angle like projectiles. Once the accelerator on the shuttle ran out, the shuttle starts falling to the earth. So why doesn't it hit the ground?
This is actually simple if you think about it carefully.
Angel
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The shuttle doesn't fall because it is blasted so far/hard that the earth moves a little in its orbit under the rocket. the rocket falls toward, but misses it. It gets pulled towards it again, the earth moves again, the rocket keeps circling and circling, trying to fall but just not being able to. If the rocked isn't blasted hard enough it won't go high enough to take longer and the earth won't move as far and it will catch the earth when it falls towards it. If it is blasted too hard the energy will take it away and it won't slow down in the atmosphere enough to have the energy taking it away be less than the diminishing gravity in order to be pulled back so it won't be pulled back, when it gets out of the atmosphere nothing will slow it down except the earth's gravity and the energy will be too much for the gravity to pull it back ... if that makes sense. I'm not sure about the blasted too hard one someone correct me if I'm wrong I didn't learn it just reasoned but it may be wrong. Everyone should know how things get into orbit! It's something you just pick up when young :-)
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Quantum, the shuttle would fall but because the Earth's surface is curved so the shuttle wouldn't hit the ground. The shuttle just keep on falling and yes orbiting the Earth.
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Right, let's think about this one:
An astronaut was reparing a part of a satellite in space, he lost his connection (a rope say) to the space shuttle. All he's got are his tools, how can he get back to the shuttle?
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By chucking his tools away in the opposite direction to the space ship. The equal and opposite force he generates by throwing the tools will propel him towards the shuttle. That said, perhaps he'd better throw one tool at a time in order to make small corrections to his trajectory in case he goes 'off course' !
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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He could "swim" by moving his tool hard ibehind him, moving them slowly in front, then hard behind him again, that way he wouldn't lose his tools. If you sit in a chair that can spin, wave your arms really hard in the direction you don't want to go and you'll move in the other direction. Bring them slowly back and repeat. Just by swinging your arms you can make yourself spin right around. :-)
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Well done Chris, that was the answer I'm looking for. But Quantum I think your method could also work too.
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Hmmm what about the molten rock and metal that would get released while drilling the whole??? Wouldn't this fry the ball and probably the majority of the earth?[:p] lol
he he
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quote:
Originally posted by cuso4
Well done Chris, the ball oscillates along the length of the hole.
Of course it would (assuming no friction etc., and pole-to-pole tunnel to avoid rotation/coriolis effects), but in what motion?
Well, 1 of the beauties of the inverse-square-of-distance in the law of gravitation is that all mass of a (sphere or) spheric shell can be thought of as concentrated in the centre, as felt by particles outside the sphere/shell, whereas particles inside the shell don't feel any net gravitation.
When our ball is at distance R from the centre, the gravitation force is proportional to
(mass closer to centre than ball) / R-square
Assuming uniform density: R-cube / R-square = R.
The force being proporional to displacement from equilibrium position, we have a harmonic oscillator. If a little friction is present, the motion will damp out gradually (exponentially), with a constant period.
quote:
Originally posted by cuso4
Now, which is the most dense metal known?
quote:
Originally posted by Donnah
Osmium
Osmium must be considerably more expensive than depleted uranium.
Uranium, being denser than lead, is sometimes used as ammo.
Depleted uranium is surely cheaper, and probably safer, than natural uranium, but it still causes political fall-out.
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Yep, the ball would exhibit simple harmonic motion wouldn't it ?
And about the political fallout - great line, I'll have to remember that. I think we can assume that the military have done their sums and come up with the cheapest answer, politically and literally.]
Chris
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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Hey guys, I got another good one. Have a go.
In my physics lessons, I've been learning about gravity. The gravitational attractive force becomes less as you move away from the Earth's surface. So does this mean as you approach the Earth's centre the gravitation pull becomes bigger? Please explain.
Angel
"Anyone who has never made a mistake has never tried anything new." -Albert Einstein
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I suppose yes, that is right. And there is an equilibrium when you are an infitessimally small (how to you spell that?) point in the very centre?
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Actually, as you go in toward the center of the earth (or any sphere of matter) the gravitational acceleration you experience, toward the center of mass, drops linearly to zero at the exact center. This is because the gravitational acceleration due to the whole body is canceling itself out as you go in. Indeed you reach equilibrium.
I wish I had a way to draw this, but here goes with a description:
If you plot the gravitational acceleration versus distance from the center of mass of a sphere (i.e. the earth), the plot would increase in a straight line starting at zero at the center of mass and reach a maximum (9.8 m/s2 for earth) at the surface of the earth. Then the gravitational acceleration would start decreasing with the inverse square of distance (1/R2) as you went farther along the axis. This means it would decrease more rapidly near the surface and then less rapidly as you move away from the surface of the sphere.
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John
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John is right (Sorry Quantum, nice try anyway). As you go toward the centre of the Earth, the mass beneath you is decreasing so the attraction force decreases and the mass above you is increasing. And it will indeed reach an equilibrium.
"Anyone who has never made a mistake has never tried anything new." -Albert Einstein
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Now this question is probably for the chemists.
Esters can be made by reacting an alchol with a carboxylic acid in the presence of concentrated H2SO4 (act as a catalyst) with water as the by-product. Why couldn't mineral acids (that's HCl, HNO3, H2SO4) be used?
Angel
"Anyone who has never made a mistake has never tried anything new." -Albert Einstein
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The formation of an ester linkage is energetically favourable because water is produced with the formation of an OH bond (OH+H -> H2O) plus a C-O bond. The formation of water (which is removed by the strong acid) shifts the equilibrium in favour of the formation of more ester.
But with the mineral acids, you would have to break a sulphur-oxygen or nitrogen-oxygen bond before even having vacant electrons to participate in the bond, let alone a stable product to mop up the protons. It is not energetically favourable. In the case of HCl, it couldn't form a link anyway because chlorine can only make one bond.
Chris
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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Chris, your answer is right but not what I'm looking for.
H+ ions from a strong acid will dehydrate the alcohol forming an alkene.
Angel
"Anyone who has never made a mistake has never tried anything new." -Albert Einstein
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But you make an ester in the presence of a strong acid (e.g. sulphuric) as you outlined above.
Chris
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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Maybe you need more acid to dehydrate the alcohol? But a srong acid will definitely convert the alcohol into alkene. Perhaps cannabinoid can explain.
Angel
"Anyone who has never made a mistake has never tried anything new." -Albert Einstein
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Probably H20 can form with H2SO4 far more H-bonds and dipole-dipole bonds than with other strong acids so the enthalpy of mixing is in this case far more negative.
Ok you smart guys, I see you are familiar with chemistry, answer this question: if you heat tablet of aspirin, acetic acit is produced, you can smell it. How is this possible, because there in tablet is no water? Structure of aspirine is: put on benzene ring -COOH group on C atom no.1 and -O-CO-CH3 group on the C-atom no.2 (orto position). You know that for hydrolysis of esters water is needed!
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What's the structure of acetic acid?
"Anyone who has never made a mistake has never tried anything new." -Albert Einstein
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Who told you, copper sulfate, that you need acid for elimination? You need nucleophile, that's base (OH-). You eat CH3COOH every day so shame on you you don't know what this compound represent.
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Hey! I didn't know ethanoic acid is the same as acetic acid![:(!] I always known the structure as ethanoic acid.
OK, I know the answer now. An organic acid has to be used because that's what an ester is: RCOOR' so the acid has to be an carboxylic acid.
Moving on. Who can tell me which compound (acid or alcohol) does the oxygen (not the C=O) in ester come from? And how can you prove it?
Angel
"Anyone who has never made a mistake has never tried anything new." -Albert Einstein
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No one is going to have a go?
Then I will reveal the answer.
The oxygen actually come from the alcohol and this is proven by using an alcohol with a radioisotope of oxygen, O18. And then detected using a Geiger counter.
Angel
"Anyone who has never made a mistake has never tried anything new." -Albert Einstein
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Angel,you revealed the answer too quickly,I lost my chance,but do you know why it's not coming from the acid? I could never get the answer from JKS![V]
Qing
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Angel,have you got more brain teasers?
Qing
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hi
I think that the ball will standstill at the centre of the earth as there is equal gravitationl pull from all sides of the earth.
Angel remember one thing that the maximum depth the borehole has been sunk may be 10 to 15 kilometers,it took nearly ten months. Then how you are going to borehole to the centre of the earth.
Am i correct.
hi iam a student of geology and currently doing my post graduate degree in remotesensing
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Unless of course one of his tools is a teleporter. Oh wait, that's from another older thread. ;)
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quote:
Originally posted by Quantumcat
He could "swim" by moving his tool hard ibehind him, moving them slowly in front, then hard behind him again, that way he wouldn't lose his tools. If you sit in a chair that can spin, wave your arms really hard in the direction you don't want to go and you'll move in the other direction. Bring them slowly back and repeat. Just by swinging your arms you can make yourself spin right around. :-)
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Errm- i'm gonna have to disagree with you on this one quantum- the only reason it works on a swivel chair is because there is an atmposphere here on earth. If we consider the momentum of the astronaut and his tools as 0, the astronaut cannot gain any momentum (by conservation of momentum) unless an equal momentum is imparted in the opposite direction. On the swivel chair, you impart this momentum to the countless number of air molecules, but in space, there is no such medium! The only way he could get back is by chucking his tools!
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-Edgar Allan Poe