Some superheroes can grow to the size of a building at will. That's very intimidating! But a scientist must ask where the extra material is coming from. The Law of Conservation of Mass implies that mass can neither be created nor destroyed, which means that our hero's mass will not change just because his size changes. For instance, when we bake a fluffy sponge cake, even though the resulting delicious treat is much bigger in size than the cake batter that went into the oven, the weight of the cake batter should still equal the weight of the cake plus the moisture that has evaporated. In a chemical equation, molecules rearrange to make new compounds, but all the components should still be accounted for. When our hero expands from 6 feet tall to 18 feet tall, his height triples. Galileo's Square Cube Law says his weight will be 27 - 3 times 3 times 3 equals 27 - times his regular weight since he has to expand in all three dimensions. So, when our superhero transforms into a giant, we are dealing with two possibilities. Our hero towering at 18 feet still only weighs 200 pounds, the original weight in this human form. Now, option two, our hero weighs 5,400 pounds - 200 pounds times 27 equals 5,400 pounds - when he is 18 feet tall, which means he also weighs 5,400 pounds when he is 6 feet tall. Nobody can get in the same elevator with him without the alarm going off. Now, option two seems a little more scientifically plausible, but it begs the question, how does he ever walk through the park without sinking into the ground since the pressure he is exerting on the soil is calculated by his mass divided by the area of the bottom of his feet? And what kind of super socks and super shoes is he putting on his feet to withstand all the friction that results from dragging his 5,400 pound body against the road when he runs? And can he even run? And I won't even ask how he finds pants flexible enough to withstand the expansion. Now, let's explore the density of the two options mentioned above. Density is defined as mass divided by volume. The human body is made out of bones and flesh, which has a relatively set density. In option one, if the hero weighs 200 pounds all the time, then he would be bones and flesh at normal size. When he expands to a bigger size while still weighing 200 pounds, he essentially turns himself into a giant, fluffy teddy bear. In option two, if the hero weighs 5,400 pounds all the time, then he would be bones and flesh at 18 feet with 5,400 pounds of weight supported by two legs. The weight would be exerted on the leg bones at different angles as he moves. Bones, while hard, are not malleable, meaning they do not bend, so they break easily. The tendons would also be at risk of tearing. Tall buildings stay standing because they have steel frames and do not run and jump around in the jungle. Our hero, on the other hand, one landing at a bad angle and he's down. Assuming his bodily function is the same as any mammal's, his heart would need to pump a large amount of blood throughout his body to provide enough oxygen for him to move 5,400 pounds of body weight around. This would take tremendous energy, which he would need to provide by consuming 27 times 3,000 calories of food every day. Now, that is roughly 150 Big Macs. 27 times 3,000 calculated equals 81,000 calculated slash 550 calories equals 147. He wouldn't have time to fight crime because he would be eating all the time and working a 9-to-5 job in order to afford all the food he eats. And what about superheroes who can turn their bodies into rocks or sand? Well, everything on Earth is made out of elements. And what defines each element is the number of protons in the nucleus. That is how our periodic table is organized. Hydrogen has one proton, helium, two protons, lithium, three protons, and so on. The primary component of the most common form of sand is silicon dioxide. Meanwhile, the human body consists of 65% oxygen, 18% carbon, 10% hydrogen, and 7% of various other elements including 0.002% of silicon. In a chemical reaction, the elements recombine to make new compounds. So, where is he getting all this silicon necessary to make the sand? Sure, we can alter elements by nuclear fusion or nuclear fission. However, nuclear fusion requires so much heat, the only natural occurrence of this process is in stars. In order to utilize fusion in a short amount of time, the temperature of the area needs to be hotter than the Sun. Every innocent bystander will be burned to a crisp. Rapid nuclear fission is not any better since it often results in many radioactive particles. Our hero would become a walking, talking nuclear power plant, ultimately harming every person he tries to save. And do you really want the heat of the Sun or a radioactive nuclear plant inside of your body? Now, which superpower physics lesson will you explore next? Shifting body size and content, super speed, flight, super strength, immortality, and invisibility.
Neki heroji mogu da narastu do veličine zgrade kada požele. To je veoma zastrašujuće! Ali naučnik mora da se zapita odakle potiče taj dodatni materijal. Zakon održanja mase kaže da masa ne može da se stvori ni uništi, što znači da se masa našeg heroja neće promeniti samo zato što se menja njegova veličina. Na primer, kada pravimo paperjasti biskvit, iako je ukusna poslastica koju dobijemo puno veća od testa koje je ubačeno u rernu, težina testa bi svejedno trebalo biti jednaka težini kolača plus vlazi koja je isparila. U hemijskim jednačinama, molekuli se preraspoređuju da naprave nova jedinjenja, ali još uvek moraju biti prisutne sve komponente. Kada se naš heroj rastegne sa 180cm na 5,5 metara visine, njegova visina se utrostručuje. Galilejev zakon kvadrata na kub kaže da će njegova težina biti 27 puta - 3 puta 3 puta 3 je 27 puta više od njegove redovne težine pošto mora da se raširi u sve tri dimenzije. Kada se naš superheroj pretvori u džina, postoje dve mogućnosti. Naš heroj ima 5,5 metara i još uvek ima 90kg, što je njegova prvobitna ljudska težina. U opciji broj dva, naš heroj ima 2450kg, 90kg puta 27 jednako je 2450kg - kada ima 5,5 metara visine, što znači da tu težinu ima i kada ima 180cm visine. Niko ne može da uđe u lift sa njime a da se ne oglasi alarm. Opcija dva se čini kao da je naučno verovatnija, ali ističe pitanje - kako on može da prođe kroz park a da ne potone u zemlju pošto se pritisak koji on vrši na tlo računa tako što se njegova masa podeli sa površinom na dnu njegovih stopala? I kakve super čarape i cipele obuva na svoja stopala kada mogu da izdrže svo trenje koje nastaje od tegljenja njegovog tela od 2450kg po putu kada on potrči? Da li on uopšte može da trči? Neću ni da pitam kako pronalazi pantalone koje su dovoljno rastegljive da izdrže širenje. Hajde sada da istražimo gustinu za pomenute dve opcije. Gustina se definiše kao masa podeljena sa zapreminom. Ljudsko telo sastoji se iz kosti i mesa, koje imaju prilično tačno određenu gustinu. U prvoj opciji, ako heroj stalno ima 90kg, onda bi njegove kosti i meso bili normalne veličine. Kada se proširi na veću veličinu, a da još uvek ima 90kg, zapravo sebe pretvara u ogromnog pufnastog medveda igračku. U opciji broj dva, ako heroj stalno ima 2450kg, onda bi bio kosti i meso na 5,5 metara visine sa 2450kg težine koju drže dve noge. Težinu bi održavale kosti nogu na različitim uglovima dok se kreće. Iako su čvrste, kosti nisu savitljive, što znači da se ne krive i lako pucaju. Tetive bi se takođe lako pokidale. Visoke zgrade stoje u mestu jer imaju čelične okvire i na trče i ne skaču po džungli. Sa druge strane, naš junak, dovoljno je da se jednom dočeka na noge pod lošim uglom i pao je. Pod pretpostavkom da su mu funkcije tela iste kao kod drugih sisara, njegovo srce moralo bi da pumpa velike količine krvi kroz telo kako bi obezbedilo dovoljno kiseonika da pokreće njegovo telo od 2450kg. Ovo bi zahtevalo neverovatnu energiju koju bi morao da dobije konzumiranjem 27 puta 3000 kalorija iz hrane svakog dana. To je oko 150 Bigmekova. 27 puta 3000 jednako je 81 000 podeljeno sa 550 kalorija, to je 147. Ne bi imao vremena da se bori sa zločinom pošto bi stalno jeo i radio od 9 do 5 kako bi priuštio svu hranu koju jede. A šta je sa superherojima koji mogu svoja tela da pretvore u stene ili pesak? Pa, sve na Zemlji sačinjeno je od elemenata. Ono što definiše svaki element je broj protona u jezgru. Tako je organizovan naš periodni sistem. Vodonik ima jedan proton, helijum ima dva, litijum tri protona, i tako dalje. Primarni sastojak najčešćeg oblika peska je silicijum dioksid. Sa druge strane, ljudsko telo se sastoji od 65% kiseonika, 18% ugljenika, 10% vodonika i 7% raznih drugih elemenata, uključujući i 0,002% silicijuma. U hemijskoj reakciji, elementi se kombinuju kako bi napravili nova jedinjenja. Odakle mu onda sav taj silicijum koji je potreban da se napravi pesak? Naravno, možemo izmeniti elemente putem nuklearne fuzije ili fisije. Ipak, nuklearna fuzija zahteva toliko toplote da je jedina prirodna pojava ovog procesa u zvezdama. Kako bi se iskoristila fuzija u kratkom vremenskom roku, temperatura površine mora da bude vrelija od Sunca. Svaki nevini posmatrač bio bi potpuno spržen. Brza nuklearna fisija nije ništa bolja pošto često za posledicu ima mnogo radioaktivnih čestica. Naš heroj bi postao nuklearna elektrana koja hoda i priča i na kraju bi naškodio svakoj osobi koju pokuša da spasi. A da li zaita želite vrelinu Sunca ili radioaktivnu nuklearnu elektranu unutar vašeg tela? Sada, koju ćete lekciju o supermoćima iz fizike istražiti nakon ove? Menjanje veličine i sadržaja tela, superbrzina, let, nadljudska snaga, besmrtnost ili nevidljivost.