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» The Geek Culture Forums!   » Techno-Talking   » Science!   » Trivia game! Fun while learning, the essence of a geek. (Page 2)

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Author Topic: Trivia game! Fun while learning, the essence of a geek.
Jace Raven

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Icon 1 posted November 26, 2003 11:15      Profile for Jace Raven         Edit/Delete Post   Reply With Quote 
ok, unless im missing something, dragon, your last post said and did absolutly nothing.

but on a different note:

Two bricks are separated by three parallel wooden sticks of circular cross sections. The sticks are positioned as shown in the picture, separated from the ends of the brick and from each other by distances l1, l2, l3, l4. The weight of the top brick is P. What are the forces applied by each stick on the brick.

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dragonman97

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Icon 1 posted November 26, 2003 11:51      Profile for dragonman97   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by Jace Raven:
ok, unless im missing something, dragon, your last post said and did absolutly nothing.

You haven't been around here much, have you? [Wink]

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Jace Raven

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Icon 1 posted November 26, 2003 12:26      Profile for Jace Raven         Edit/Delete Post   Reply With Quote 
your right i havn't, Notice: "Nebie Larva" under my avatar.

can you answer the question?

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Stereo

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Icon 1 posted November 26, 2003 13:25      Profile for Stereo     Send New Private Message       Edit/Delete Post   Reply With Quote 
Let's see if I remember my first year of mechanical engineering :

The weight supported by the first stick is: (l1 + l2/2)* P/(l1 + l2 + l3 + l4)

Second: (l2/2 + l3/2)* P/(l1 + l2 + l3 + l4)

Third: (l3/2 + l4)* P/(l1 + l2 + l3 + l4)

This sounds right to me, but it's been so long, I might have it all wrong. And that reminds me why I switched to computer science.

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Jace Raven

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Icon 1 posted November 26, 2003 13:46      Profile for Jace Raven         Edit/Delete Post   Reply With Quote 
close very close, too simplified.

your missing the pint where the rods hit the brick, call them x1 and x2, top and bottom, ill post the answer at 1330

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Jace Raven

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Icon 1 posted December 04, 2003 14:57      Profile for Jace Raven         Edit/Delete Post   Reply With Quote 
The answer :

For the sake of simplicity we introduce the coordinates Xi(i=1...3) of the points, where the rods touch the surface of the upper brick. They are defined as the horizontal positions of those points with respect to the center of the brick. The Y-axis is directed downwards from the brick's center. If we assume that the bricks and the rods are perfect rigid bodies then the conditions for equilibrium read:
(1) SUM( Fi) = P(force balance), and:
(2) SUM( Fi*X i) = 0 (torques balance),
where Fiare the forces of normal reaction exerted from the rods on the upper brick. It is evident that if the number of rods is 3 or more, the two equations are insufficient to determine F's unequivocally (the problem is statically undefined).

To cope with the problem we must go beyond the rigid body approximation. Let us to assume that the rods acquire some small deformation when the upper brick is put on them. We will neglect the deformations of the surfaces of the bricks since as a rule the ceramic material of the bricks is rather stiff compared to the wood.
It can be shown that the deformation of the rod is a linear function of the force, despite the fact that it has only a "point contact" with the brick. (This is explained in "Comment 1" at the bottom of this page.) Thus we can treat the rods as elastic springs of equal stiffness K, and assume that the Hook's law is satisfied: Fi= K*U i, where Uiis the deformation of the i-th rod. We assume that when the upper brick is laid onto the rods, due to their deformations, it's center is lowered by a small amount Y, and its surface tilts a little bit at an angle Awith respect to the horizontal (the later effect takes place if the rods are placed asymmetrically with respect to the center of the brick). Then the deformation of the i-th rod is:
Ui= Y + A*X i.
By substituting the forces Fiobtained from the Hook's law in Eqn. (1) and (2) we obtain the values of Yand A:
Y = (P/(3K))*D/(D - M 2);
A = - (P/(NK))*M/(D - M 2);
where D = SUM (X i2)/3 and M = SUM (X i)/3 . Finally we obtain the forces of reaction:
(3) Fi= (P/3)*(D - X i*M)/(D - M 2).
It is evident from the last expression that if the rods are placed symmetrically with respect to the center of the brick, then the weight of the brick is spread uniformly among them with equal portions of P/3 . A*X i.


Comment 1: Contacts involving cylinders or spheres were treated in 19th century by H. Hertz. You can find this treatment in most elasticity textbooks (e.g., the book by Landau and Lifshitz). What is special in this case is that we have a point contact , which upon application of force broadens into a contact with finite area. For the case of a contact between two spheres, or a contact between a sphere and infinitely rigid plane, this leads to conclusion the the displacement (deformation of the sphere) is proportional to the force in the power 2/3. (The prefactor in this relation depends both on the elastic properties of the sphere and on its radius.)
The situation is quite different in the "two-dimensional" case of cylinder. It can be derived from the general formalism that treats contact of ellipsoids, or can be considered directly as was done by H. Poritsky in J. Appl. Mech. 17 , p. 191 (1950). In this paper it has been shown that the displacement is simply proportional to the force applied to the cylinder. Thus the simple linear relation between the force and deformation used in the above derivation is justified. The only pathology caused by the presence of the point contact is related to the dependence of the proportionality constant on the properties of the cylinder: As in the case of a "regular" contact the force constant is proportional to the elastic constant (Young modulus) of the stick. However, for the point the force constant very weakly (logarithmically) depends on the diameter of the stick.

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littlefish
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Icon 1 posted December 04, 2003 15:10      Profile for littlefish   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
OK, so the bricks don't deform, and you are neglecting the acceleration caused by placing the brick onto the rods? Sounds like a poor approximation to me. And you are ignoring windchill factors, flux dependance, the correolis effect and the thermal expansion coeffecient of the wood, which would alter it's compression characteristics. ;P

Stereo sounded close enough to me!

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Jace Raven

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Icon 1 posted December 04, 2003 21:17      Profile for Jace Raven         Edit/Delete Post   Reply With Quote 
well then..... [shake head]

allow me to recalculate [Razz] [weep]

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Stereo

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Icon 1 posted January 26, 2004 07:04      Profile for Stereo     Send New Private Message       Edit/Delete Post   Reply With Quote 
In an attempt to revive this forum I seem to have killed with the article post (sorry!), I will finally use my turn to post a geek/science question.

I couldn't find one that would be tough enough yet open enough to be valuable, until I saw LOTR/ROTK. When watching it, I notice at least two scientific impossibilities (I'm not talking magic or the like here, but problems with the understanding of 'normal' physics) in some effects and actions.

So, the winner of this round will be the one who find and explains the biggest errors and/or the greatest number of them. Bonus points for errors from FOTR and TTT.

Enjoy!

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TMBWITW,PB

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Icon 1 posted January 26, 2004 11:09      Profile for TMBWITW,PB     Send New Private Message       Edit/Delete Post   Reply With Quote 
There is the fact that oliphaunts that large wouldn't be able to stand, let alone charge into battle. Those things were at least 18 feet high and the tallest elephant I've ever seen was more like 9 feet. (shoulder measurements) With double the height you get 4 times the surface area and 8 times the mass. That means problems with dissapating heat and bones being able to support the animal.

Other than that I really didn't care to look for impossibilities. Anything impossible I'm going to explain away with magic and creative license. [Big Grin]

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Jace Raven

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Icon 1 posted January 26, 2004 12:16      Profile for Jace Raven         Edit/Delete Post   Reply With Quote 
While were on LOTR I have a question. I havn't read the book and i was wondering if i was missing something,
Where did frodo go with gandalf and the elves at the end of rotk?

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csk

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Icon 1 posted January 26, 2004 12:55      Profile for csk     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by Jace Raven:
While were on LOTR I have a question. I havn't read the book and i was wondering if i was missing something,
Where did frodo go with gandalf and the elves at the end of rotk?

Into the West (cue Annie Lennox), but I think that the final destination was Valinor. See here for more information.

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Jace Raven

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Icon 1 posted January 26, 2004 13:15      Profile for Jace Raven         Edit/Delete Post   Reply With Quote 
WHOA! this is deep!!!
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supergoo

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Icon 1 posted January 26, 2004 15:56      Profile for supergoo     Send New Private Message       Edit/Delete Post   Reply With Quote 
In the fourth age, a journey to Valinor was a one-way ticket. That's why Pippin, Merry, and Sam were so upset at the end of the book: once Frodo and Gandalf left, they could never come back. Although I think Sam eventually went to Valinor in one of the appendicies, but I'm not sure about that one. I know Legolas and Gimli left Middle-Earth together but I'm not sure if they went to Valinor or not.

As far as physical impossibilites go, I'm still wondering how those catapulted rocks made that big of an impact on the walls of Minas-Tirith.

You can always go here for some insane Tolkien Trivia.

-supergoo

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csk

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Icon 1 posted January 26, 2004 16:16      Profile for csk     Send New Private Message       Edit/Delete Post   Reply With Quote 
Yep, all three of them went into the West (possibly at different times). The site I linked in the last post has bios on all the characters, including when they went to Valinor. Just look under the first letter of the character's name.

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Xanthine

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Icon 1 posted January 26, 2004 17:06      Profile for Xanthine     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by supergoo:
As far as physical impossibilites go, I'm still wondering how those catapulted rocks made that big of an impact on the walls of Minas-Tirith.

F = ma. 'Nuff said.

I wasn't looking for any gaping scientifici errors. Oliphaunts are indeed to big to exist, as was Shelob (an invertabrate that size can't breath). The Eagels were too big to fly as well, I believe, and the poison gases coming off that volcano would have killed Frodo and Sam before the Eagles got them (if the radiant heat from the lava didn't fry them first, that is). Oh yeah, and that whole business with the Ents tearing down walls and diverting rivers in TTT... Never mind the whole magic ring bit.

However, Elves, Dwarves, Hobbits, Orcs, Trolls, Dark Lords and Wizards don't exist either. It's a fantasy movie. Many of those wild and impossible things came out of Tolkien's imagination to begin with, so if you wanna be all realistic, you can take it up with the man himself. [Smile] What is scientifically possible does not really apply to Middle Earth.

I enjoyed the movies immensely. It was wonderful to suspend my disbelief, and lay aside the skepticism I approach the rest of my life with for a good three hours and soak it all in.

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GameMaster
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Icon 1 posted January 26, 2004 17:47      Profile for GameMaster   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
Sppungster, that is akin to: "And how come no can tell superman is superman just cuz he takes off his glasses" (while him flying arround is perfectly natural).

I know the nine rings were in the service of the dark loard, and in the books it was also said that he had the dwarfs rings... I haven't finished the book (that is the three volumes) but haven't started on the rest of extra information (except when a foot note lead to something I thought I'd like to know along the way). My question, not trivia, just curiousness, when and how did Sarumon get the Dwarf's rings? I assume one was with The King Under the Moutian... but I am not sure of this.

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The Famous Druid

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Icon 1 posted January 26, 2004 17:58      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by GameMaster:
Sppungster, that is akin to: "And how come no can tell superman is superman just cuz he takes off his glasses" (while him flying arround is perfectly natural).

There was a great scene in 'Lois and Clarke' where the time-travelling villain from the future reveals the sercret of Supermans identity to Lois.

(Glasses off) "Superman!"
(Glasses on) "Clarke !"
(Glasses off) "Superman!"
(Glasses on) "Clarke !"
(Glasses off) "Superman!"
(Glasses on) "Clarke !"

"How stupid are you ?????"

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dragonman97

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Icon 1 posted January 26, 2004 18:37      Profile for dragonman97   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by The Famous Druid:
quote:
Originally posted by GameMaster:
Sppungster, that is akin to: "And how come no can tell superman is superman just cuz he takes off his glasses" (while him flying arround is perfectly natural).

There was a great scene in 'Lois and Clarke' where the time-travelling villain from the future reveals the sercret of Supermans identity to Lois.

(Glasses off) "Superman!"
(Glasses on) "Clarke !"
(Glasses off) "Superman!"
(Glasses on) "Clarke !"
(Glasses off) "Superman!"
(Glasses on) "Clarke !"

"How stupid are you ?????"

I remember that one well - I loved that [Smile] .

But don't forget - Superman also slicks his hair back, where as Clark keeps it styled [Razz] . I mean, that just makes it so radically different [Wink] . Oh, and he struts/flies around in tights, as opposed to strolling by in a suit, and I think he also talks with a more stern voice. Clearly, we'd never recognize him by his /face/...

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Beth
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Icon 1 posted January 26, 2004 19:02      Profile for Beth   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
What? People are talking about LOTR? Where have I been? Good grief, I'm slipping. (Did I ever have a grip in the first place?) Aaaaanyway.

quote:
I know the nine rings were in the service of the dark loard, and in the books it was also said that he had the dwarfs rings...
I know it's already been brought up, but if you ever want to fill in any gaps in your Tolkien-knowledge, the Encyclopedia of Arda is the place to go. Everything you might want to know. Probably more, in fact. [Big Grin]

That being said, I'll explain it briefly: Sauron tricked the Elves into creating sixteen magic rings (seven for the dwarf-lords, nine for the men) which they thought were going to be used for good, but Sauron secretely made his own One Ring which had power over the sixteen. However, the Elves also have three of their own magic rings, which are NOT controlled by the One.

Um... I'm going to stop now, otherwise I might end up re-telling the entire history of Middle-Earth. And that's a lot of text! [Wink]

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Stereo

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Icon 1 posted January 26, 2004 19:02      Profile for Stereo     Send New Private Message       Edit/Delete Post   Reply With Quote 
Well, Supergoo is right about the rocks hitting the wall. It's not much f = ma itself but more about inertia. Those rocks were hitting high, barely after taking their descending path - not much speed other than their horizontal one. Add that (normal) citadels walls can be up to 4 or 5 meters wide... The rocks would leave a hole, but the top of the walls shouldn't fall. That is, unless they used no mortar whatsoever.

As for the size of the animals, remember some dinausaurs were up to six time the size of an elephant (or is that of a blue whale? my memory's failing me), so I will easily believe an oliphant could live. It may not have the physiology of our elephants. Still, the second major physics problem is related to the oliphants. Hint: it's about how one gets killed.

The fumes from the volcano is a good one too, Xanthine, though I wonder if the opening would be sufficient to bring enough fresh air for one to survive. But I agree that no one could survive on a little island of rock surrounded by lava more than a minute or two.

(As for the Ents. I put it onto Tolkien's magic - special ability of species.)

Anymore contenders?

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Xanthine

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Icon 1 posted January 26, 2004 19:35      Profile for Xanthine     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by GameMaster:
My question, not trivia, just curiousness, when and how did Sarumon get the Dwarf's rings? I assume one was with The King Under the Moutian... but I am not sure of this.

Saruman didn't get anybody's rings. He tried to take the One Ring but he captured the wrong pair of Hobbits.

It was said that each of the seven great dwarfd hoards was founded on one single gold ring, but those hoards were lost long ago. Sauron obtained three (or maybe four) dwarf rings through conquest. The remainder were lost to the dragons. Recall that these magic rings had been in existence for more than 1000 years by the time LOTR starts. Plenty of time for things that should not be forgotten to be lost. [Razz]

One of those dwarf rings was indeed taken from Thror (or maybe Thrain...the father of the lead dwarf in the Hobbit) when he got captured and imprisoned by Sauron, aka the Necromancer, in Dol Guldur. Gandalf did come to rescue this sorry dwarf, but he was too late. I do believe however, that that's how Gandalf got the map used by Bilbo and Co. in The Hobbit.

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Orpheus
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Icon 1 posted January 26, 2004 20:30      Profile for Orpheus     Send New Private Message       Edit/Delete Post   Reply With Quote 
The trebuchets used by both sides were pretty unbelievable. IRL steel ones can send cars and pianos flying, but there is no way wooden trebuchets could send boulders the size of small houses flying much less for a few hundred meters. Though if the trebuchet could generate enough power to send these flying without tearing itself apart, then yes a boulder that size I think could tear straight through the buildings of Minas Tirith as depicted.

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GameMaster
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Icon 1 posted January 26, 2004 21:22      Profile for GameMaster   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
Saruman didn't get anybody's rings. He tried to take the One Ring but he captured the wrong pair of Hobbits.
That was a typo.... I know what I was asking was about sauron.

It was said that each of the seven great dwarfd hoards was founded on one single gold ring, but those hoards were lost long ago. Sauron obtained three (or maybe four) dwarf rings through conquest. The remainder were lost to the dragons. Recall that these magic rings had been in existence for more than 1000 years by the time LOTR starts. Plenty of time for things that should not be forgotten to be lost. [Razz]
Right, and I realize that the wearer of all the rings (and all people of power) are tempted and drawn into the rings more than others... But, it didn't explain when the four were captured.

One of those dwarf rings was indeed taken from Thror (or maybe Thrain...the father of the lead dwarf in the Hobbit) when he got captured and imprisoned by Sauron, aka the Necromancer, in Dol Guldur. Gandalf did come to rescue this sorry dwarf, but he was too late. I do believe however, that that's how Gandalf got the map used by Bilbo and Co. in The Hobbit.
The Necromancer of Dol Guldur wasn't Sauron, was he? I thought him to be a minnion of Sauron's... I also know that a few people in the Dark-Lord's service were promised rings of power for their deeds, (Saruman was, until the Ents came).

I really liked the idea of Tom Bombadil, an old wise, living long before and after all else dies... but having little to do with anyone else at all, save the fair lady of the river. I am, however, glad that they didn't include it in the films; as it would have been a realy long movie and would have been hard to get someone to play the role well... Dancing and Singing, and keeping it light, but showing the hidden wisdom of MANY MANY ages.

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csk

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Icon 1 posted January 26, 2004 21:26      Profile for csk     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by The Famous Druid:
[QUOTE]There was a great scene in 'Lois and Clarke' where the time-travelling villain from the future reveals the sercret of Supermans identity to Lois.

(Glasses off) "Superman!"
(Glasses on) "Clarke !"
(Glasses off) "Superman!"
(Glasses on) "Clarke !"
(Glasses off) "Superman!"
(Glasses on) "Clarke !"

"How stupid are you ?????"

Umm, that was actually "How dumb was she?"

</closet Lois and Clarke fan>

Edit: Come to think of it, I once saw a link of slashdot (where else) which looked at the physics of what would happen if Superman/Clarke bonked Lois. I'm not going to google for the link from work, but suffice it to say the conclusion was that Lois should get her lovin' elsewhere, for her own physical safety [Big Grin]

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