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.
Nekateri junaki lahko postanejo veliki kot hiša, če hočejo. To je prav strašljivo! A znanstvenik se bo vprašal, od kod ves ta dodatni material. Zakon o ohranitvi mase pravi, da se mase ne da ustvariti niti uničiti, kar pomeni, da se junakova masa ne bo spremenila, tudi če se on poveča. Recimo, ko spečemo rahel biskvit, je okusen pečeni posladek veliko večji od testa, ki smo ga dali v pečico, a teža testa bi morala ostati enaka teži peciva, če dodamo izparelo vlago. V kemijskih enačbah se molekule razporedijo v nove spojine, a izgubiti se ne sme nobena. Ko naš junak zraste z 1,80 metra na 5,5 metra, postane trikrat višji. Galilejev zakon o razmerju med površino in prostornino pravi, da bo 27-krat težji (3 x 3 x 3 = 27) od prvotne teže, saj se poveča v vseh treh dimenzijah. Ko naš junak postane velikan, sta torej dve možnosti. Pri višini 5,5 metra bo še vedno težak le 100 kg, kolikor je tehtal prej. Ali pa bo težak 2700 kg (100 kg x 27 = 2700 kg ), pri dobrih petih metrih višine, kar pomeni, da tehta 2700 kg, tudi ko je visok le 1,80 metra. Nihče ne more v dvigalo z njim, ne da bi sprožil alarm. Druga možnost se zdi znanstveno malce bolj verjetna, a postavi se vprašanje, kako lahko gre skozi park, ne da bi se pogreznil v tla, saj je pritisk na podlago količnik njegove mase in površine njegovih podplatov. In kakšne super nogavice in čevlje mora imeti, da preživi trenje s tlemi, ki nastane, ko svojih 2700 kg s tekom premika naprej? Ali sploh lahko teče? Da sploh ne vprašam, kje najde take hlače, da se razširijo, ko se on poveča. Poglejmo še gostoto obeh zgornjih možnosti. Gostota je količnik mase in prostornine. Človeško telo sestavljajo kosti in meso, kar ima relativno stalno gostoto. Pri prvi možnosti ima junak vedno 100 kg in pri normalni velikosti so ga same kosti in meso. Ko se poveča, še vedno pri teži 100 kg, se v bistvu spremeni v velikanskega puhastega medveda. Če pa junak ves čas tehta 2700 kg, bo iz kosti in mesa pri 5,5 metra in dve nogi bosta nosili teh 2700 kg. Noge bodo med hojo težo čutile pod različnimi koti. Kosti so trdne, niso pa prožne, se pravi, da se ne upognejo in se hitro zlomijo. Tudi vezi bi se lahko raztrgale. Visoke stavbe zdržijo, ker imajo jeklen okvir in ne tekajo in skačejo po džungli. Naš junak pa bo v težavah, če pristane pod napačnim kotom. Če ima telesne funkcije kot sesalci, mora njegovo srce prečrpati veliko krvi skozi telo, da priskrbi kisik, tako da svojih 2700 kg sploh lahko premika. To zahteva neznansko veliko energije, ki jo bo dobil le, če poje za 27 x 3000 kalorij hrane na dan. To je okoli 150 big macov. 27 x 3000 je 81000, 81000 deljeno s 550 kalorij pa je 147. Ne bi se mogel boriti s kriminalci, ker bi ves čas jedel in delal po osem ur na dan, da bi si lahko kupil vso to hrano. Kaj pa junaki, ki se lahko spremenijo v kamen ali pesek? Vse na Zemlji je iz elementov. Vsak element določa število protonov v jedru. Tako je sestavljen periodni sistem elementov. Vodik ima en proton, helij ima dva, litij ima tri protone in tako naprej. Temeljna sestavina najobičajnejšega peska je silicijev dioksid (kremen). Človeško telo pa je sestavljeno iz 65% kisika, 18% ogljika, 10% vodika in 7% drugih elementov, tudi 0,002% silicija. V kemijskih reakcijah se elementi prerazporedijo v nove spojine. Odkod junak dobi ves ta silicij, ki je potreben za pesek? Seveda lahko elemente spremenimo z jedrsko fuzijo ali jedrsko fizijo. A jedrska fuzija potrebuje toliko vročine, da se lahko sama zgodi le v zvezdah. Za kratkotrajno fuzijo bi morala temperatura okolice biti višja od tiste na Soncu. Vsi opazovalci bodo pečeni kot čips. Hitra jedrska fizija ni nič boljša, ker pogosto ustvari radioaktivne delce. Naš junak bi postal hodeča in govoreča jedrska elektrarna in bi poškodoval vse, ki jih hoče rešiti. Si v telesu res želite Sončevo vročino ali radioaktivno jedrsko elektrarno? Katero nadnaravno moč boste raziskali zdaj? Spreminjanje velikosti in sestave telesa,, super hitrost, letenje, nadnaravno moč, nesmrtnost in nevidnost.