[heythere]

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

[esprit fort]

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.

[chris]

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

[cuso4 (OP)]

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

[Quantumcat]

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?

Am I dead? Am I alive? I'm both!

[tweener]

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.


----
John

[cuso4 (OP)]

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

[cuso4 (OP)]

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

[chris]

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

[cuso4 (OP)]

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

[chris]

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

[cuso4 (OP)]

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

[tom]

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!

[cuso4 (OP)]

What's the structure of acetic acid?

"Anyone who has never made a mistake has never tried anything new." -Albert Einstein

[tom]

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.

[cuso4 (OP)]

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

[cuso4 (OP)]

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

[Qing]

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

[Qing]

Angel,have you got more brain teasers?

Qing

[nandakumar]

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