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  • 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.

Some superheroes can grow

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B2 TED-Ed weight nuclear weighs body size

【TED-Ed】If superpowers were real: Body mass - Joy Lin

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    姚易辰 posted on 2013/08/28
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