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Author Topic: Vertex tower  (Read 3979 times)

Offline clueless

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Vertex tower
« on: 07/09/2013 12:11:59 »
I wrote a riddle, but I'm not sure if the solution is feasible... :I

Vertex tower

A curious man enters a square, tall and wide tower, made in stone. The heavy door closes behind him. Sensing danger, he tries to open the door, to no avail. He looks around. There is a dead elf lying on the floor. He takes a thin, long and sturdy rope from the corpse, made by elves, thinking it might be of use to him. Suddenly, spooky letters appear on the wall: I am Vertex tower. I am alive and I will swallow your soul at midnight. The letters then disappear. The man is chilled to the bone, as he has 3 hrs. to come up with something and save himself. He climbs up the stairway all the way to the flat roof. He thinks of using the rope, which is long enough to climb down the tower, but he has no place to tie the end. He considers tying the rope to the door, but the remaining length isnít long enough to safely climb down, as he would certainly die. He walks down the stairs and tries to open the door again. The door is firmly locked. But then he calms down and tries to come up with a solution to his predicament. He manages to leave the tower before midnight. How did he do it? 


ANSWER: He ties the less heavy elf and throws it off the tower and then he jumps off the tower on the opposite side. So the corpse ascends while the man safely descends down. Is this at all possible? How heavy would the man and the corpse have to be? About half the weight of the man? Is this perhaps impossible because of, I donít know, acceleration, or friction? What do you think? Thanks.  xx(


 

Offline alancalverd

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Re: Vertex tower
« Reply #1 on: 07/09/2013 13:13:18 »
Neat trick!

Ignoring friction, if the elf weighs half as much as the man m, the net graviational force acting on the pair is gm/2 but the mass of the pair is 3m/2, so the man's acceleration will be g/3 instead of g ft/sec^2, which may be survivable - depends on the height of the tower. If not, use a heavier elf. 
 

Offline clueless

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Re: Vertex tower
« Reply #2 on: 07/09/2013 13:51:36 »
Neat trick!
Thanks! :)



Ignoring friction, if the elf weighs half as much as the man m, the net graviational force acting on the pair is gm/2 but the mass of the pair is 3m/2, so the man's acceleration will be g/3 instead of g ft/sec^2, which may be survivable - depends on the height of the tower. If not, use a heavier elf.
I guess you answered my question. :I I I prefer for some reason that the tower is rather tall.  ::)
« Last Edit: 07/09/2013 17:06:08 by clueless »
 

Offline alancalverd

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Re: Vertex tower
« Reply #3 on: 08/09/2013 00:40:02 »
How about getting rid of the elf, talking towers, and other such nonsense, and just requiring the man to escape from a tower with nowhere to fix the rope. The only other object in the tower is his dead identical twin.

Same escape ploy as before, but he removes the corpse's shoes. He now weighs just a pound or so more than the corpse, so his acceleration is very gentle indeed. 

Or make it slightly plausible: the only other thing in the tower is a pile of sand and some sandbags.
« Last Edit: 08/09/2013 00:42:25 by alancalverd »
 

Offline clueless

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Re: Vertex tower
« Reply #4 on: 08/09/2013 10:23:44 »
Or make it slightly plausible: the only other thing in the tower is a pile of sand and some sandbags.
But then he could tie three heavy sandbags with the rope so there would be no need to throw a sandbag off the tower.

Same escape ploy as before, but he removes the corpse's shoes. He now weighs just a pound or so more than the corpse, so his acceleration is very gentle indeed. 
Right. Thanks.
« Last Edit: 09/09/2013 02:08:28 by clueless »
 

Offline alancalverd

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Re: Vertex tower
« Reply #5 on: 09/09/2013 08:31:38 »
Or make it slightly plausible: the only other thing in the tower is a pile of sand and some sandbags.
But then he could tie three heavy sandbags with the rope so there would be no need to throw a sandbag off the tower.

OK if it's a short tower, but climbing down a fixed rope is almost as difficult as climbing up one, and very tiring. Your method gives a gentle passive ride down any distance.
 

Offline clueless

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Re: Vertex tower
« Reply #6 on: 09/09/2013 16:26:53 »
How about getting rid of the elf, talking towers, and other such nonsense, and just requiring the man to escape from a tower with nowhere to fix the rope. The only other object in the tower is his dead identical twin.
A good idea. I modified the riddle accordingly. You can find the riddle in the What Happened section of the Wu forums, under the name Tower. 
 

Offline CliffordK

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Re: Vertex tower
« Reply #7 on: 11/09/2013 06:32:24 »
A lot depends on the length of rope and dimensions of the tower, and the shape of the tower.

For example, if one had a round and smooth tower, toss the elf off one side and jump off the other side, inevitably the rope will slip to one side and you both will find yourselves in freefall. 

Nonetheless, I don't think there would be a "jumping" over the side.  Wait for the elf to get all the way to the bottom, then carefully climb over the opposite side of the tower. 

As far as weights, a lot would depend on the friction in the system.  Going over two squarish edges, your 50% estimate may be good.  Going over a pulley, perhaps 90% would be a better ratio.  If just a single pulley, then you could control the descent by holding onto the upward rope.

What about tying a loop of rope all the way around the tower itself, then climbing down the rope? 

Is the roof perfectly flat, or is there a lip at the edge?  With a lip (and square corners on the lip, tie a few knots in the rope to increase the friction going over the lip, then tie the rope to the elf and just climb down the rope.

How tall is the tower.  Carrying a 100 lb body up 10 flights of stairs to the roof would tucker me out.  Doing it with a 200 lb body would be very difficult indeed, It may have to be quartered to carry a heavy body up.

However, if designed right, perhaps one could just tie the rope to the body where it lay, then just pull one end of the rope up and through the trap door.  No need to carry the body to the roof.
 

Offline clueless

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Re: Vertex tower
« Reply #8 on: 11/09/2013 15:38:42 »
The roof is perfectly flat and the tower is rather tall. I modified the riddle and added four openings near the top of the tower. For now, revision looks like this:

TOWER

A man is searching for his identical twin. He enters a round and tall tower, made in stone. He sees his brother lying dead on the floor. Someone closes and locks the door. The man, scared and sadden by his loss, tries to open the door, to no avail. He then kisses his brother, who recently died, but he canít tell the cause of death. His dead twin is wearing clothes and boots. He takes a thin, long and sturdy rope from the corpse, thinking it might be of use to him. He climbs up the staircase and looks through each of the four wider openings near the top of the tower. He thinks of using the rope, which is long enough to climb down the tower, but he has no place to tie the end. He considers tying the rope to the door, but the remaining length isnít long enough to safely climb down, as he would certainly die. He walks down the stairs and tries to open the door again. The door is firmly locked. But then he calms down and tries to come up with a solution to his predicament. He manages to leave the tower w/o physical injury. How did he do it?
 

Offline CliffordK

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Re: Vertex tower
« Reply #9 on: 11/09/2013 21:06:58 »
Now, with "4 openings" near the top, and some boots????

It shouldn't take much to tie the rope through the openings, perhaps swinging the boots to get it to go through the holes.

There are a lot of variables to expect a single solution.

Now, if is something like an interactive video game, you can make the attempts fail until the player comes up with the "right" solution.
 

Offline clueless

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Re: Vertex tower
« Reply #10 on: 11/09/2013 22:52:50 »
TOWER (revision)

A man is searching for his identical twin. He enters a square and 50 m tall tower, made in stone. There he sees his brother lying dead. He canít tell the cause of death. He then kisses his dead twin and starts to mourn over his loss. While he is bitterly crying, someone closes and locks the door. Scared, he wipes his tears and tries to open the door, to no avail. His dead twin is wearing clothes and boots. He takes a thin, long and sturdy rope from the corpse, thinking it might be of use to him. He climbs up the staircase and looks through the hole near the inaccessible flat top of the tower. He thinks of using the rope, which is a few meters longer than the height of the tower, but he has no place to tie the end. He calms down and tries to come up with a solution to his predicament. He manages to leave the tower w/o physical injury. How did he do it?


Is this better?

 
« Last Edit: 14/10/2013 11:10:22 by clueless »
 

Offline clueless

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Tower II: Dread
« Reply #11 on: 14/10/2013 10:56:13 »
Tower II: Dread

A sturdy tourist lost his way. He has a hunting knife, a padded waist belt and a 100 m long rope in his backpack. He has the feeling throughout the whole morning that someone is following him. He decides to enter a square, wide and 50 m tall tower, thinking view from the tower might tell him in which direction he should go. He climbs up the staircase, disregards the locked window in the middle of the tower and arrives on the top. While he is admiring the view, someone closes and locks the trapdoor. Scared, he tries to open the trapdoor, to no avail. He thinks of using the rope, but he has no place to tie the end since the trapdoor is evenly leveled with the flat top. He then calms down and tries to come up with a solution to his predicament. He manages to leave the tower w/o physical injury. How did he do it?



ANSWER: He cuts the rope to make a girdle that encircles the tower, by tying this shorter piece of rope. He then ties the longer piece of rope on the girdle, lowers the girdle 50 m down and starts to climb down on the opposite side. Is this at all possible because of friction? Probably not, eh? Can you think of another way?
« Last Edit: 14/10/2013 14:07:45 by clueless »
 

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Tower II: Dread
« Reply #11 on: 14/10/2013 10:56:13 »

 

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