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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.

• 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

• 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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