Balancing Quiz: Greed Edition
Greed is a solid gold statue wearing ruby jewelry, who is an enormous cheapskate and will only spend the least possible amount of money. Assume that Greed has a volume of 100,000 cubic centimeters and an infinitely thin regular pentagon with a side length of 1 meter as a base. The density of gold is 19.3 grams per cubic centimeter. Excluding Greed's base and arms, which begin 1 meter below the statue, Greed has mass uniformly distributed along its height.
Assume Greed is 2 meters tall, with an arm span equal to its height. Its cylindrical upper arms, which are 0.5 meters long and have a volume of 2000 cubic centimeters with uniform density, are inclined downwards 30 degrees relative to the ground, and its also-cylindrical lower arms (also 0.5 meters long with 2000 cubic centimeters of volume and uniform density) are inclined upwards 30 degrees relative to the ground.
Greed begins with 2 necklaces upon each of its arms. Each necklace weighs 0.1 kilograms. When Greed acquires a new necklace (each costs 1 ruby), it is placed at the end of its right arm.
The exchange rate of rubies to gold is 10000 gold for 5 rubies. Every time gold is purchased using 5 rubies, the value of this trade drops by 1 gold/ruby, to a minimum value of 500 gold for 5 rubies.
There is a labor cost of 100 gold per necklace (which are commissioned and paid for immediately following each purchase of Greed). However, the company has a special price for returning customers; once the customer has purchased their 4th necklace, they receive a 1% discount on all future necklaces, with an increase in 1% for every time they double their purchased necklace number (e.g. a 2% discount for having purchased 8 necklaces, or a 3% discount for having purchased 16 necklaces).
Given that Greed started out at 500 stock costing 40 rubies (all proceeds go to Greed, who only spends it on necklaces) and every 2 copies of it bought increase the price of Greed by 1 ruby, is Greed still balanced by the time that it is sold out? If not, which copy of Greed sold caused it to become unbalanced?
30 RP goes to the respondent with the most accurate answer. Show your work.
-not main_gi
Greed's total weight without necklaces is 19.3*100000=1930000 g = 1.93 metric tons.
The infinitely thin polygon for all intents and purposes does not exist as it would do absolutely nothing to prevent the greed from falling over as it would literally be incapable of creating any sort of electromagnetic repulsion from the ground at the molecular level so it would literally clip through the floor if greed fell over.
Each arm takes away 2000*19.3=38600 grams, for a total of 154400 grams. This leaves 1775600 g which means his central torso takes up 1775600/19.3 = 92000 cubic centimeters. We know his arm span is 2 meters, but each arm is only 0.5 meters long, so his main torso is 1 meter or 100 cm wide. We also know that it is 2 meters tall (200 cm), so assuming that greed's main torso is approximately an elliptical shape, we have that the area of the ellipse is 92000/200 = 460 cm^2. Given that the area of an ellipse is πab where a is the semimajor axis and b is the semiminor axis, and one of the axis is 1/2 * (100) = 50 cm, we have:
π*50*b=460
b=2.9
Hence, we are left to conclude that Greed is about 3 centimeters thin. Big yikes. A 2 meter tall statue that weighs nearly 2 metric tons cannot possibly balance on a width of 2.9 centimeters, and Greed would face plant into the ground before purchasing a single necklace.
It was at this moment that I read the question again, and noticed that I read it entirely wrong and that Greed obviously doesn't have four arms. However, this makes the question even more clearly absurd, as if both his arms total 1 meter long each, this means that his torso is infinitely thin as his armspan without his torso is already 2 meters. Since we know that vertically he is of uniform density, we can conclude that this Greed is infinitely thick in the forwards/backwards direction and is infinitely thin in the forwards/backwards direction. In other words, Greed does not physically exist except for his arms, which would fall to the ground as the rest of his body utterly clips through its atoms.
The problem has by now simplified significantly. We are now asking if two cyllindrical arms with a 120 degree angle V shape in the middle of them are able to balance on their elbows. In theory, since the arms have uniformly distributed density and are in every way perfectly symmetrical, they are able to balance on the tangent point of the elbow and the ground. However, the moment a single necklace is added to the arm, it will not remain balanced as the base of the elbow is one singular point and will tip even with the smallest weight on one side. Therefore, the first necklace will unbalance Greed. However, it is impossible that a statue of a pair of gold arms is capable of purchasing a necklace in the first place, so Greed will remain balanced for the rest of eternity as a pair of arms who will never gain any more necklaces for the rest of time. Thank you for listening
seeing as ive gotten a total of 5 greeds... 0 of which were from ultra crates somehow (only from diamond boxes and basics)
whereas ive gotten 22 aquarius and 21 waterelemental...
i can easily say: greed is smell bad.
This question is not fun enough for me to try hard, there are just a lot of random details that aren't important to make it more annoying >:( There's an independent physics and math problem so it's really 2 questions. Anyways, since its standing on an infinitely thin polygon, it is not balanced.
I'm going to assume that greeds body is also cylindrical and that the arms are tilted cylinders to avoid intersection (same volume andyway).
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