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.
一些超级英雄 可以随意的把身体变成一座楼那么大 这可真吓人 但是科学家会问 那些多余的物质从哪里来? 质量守恒定律表明 质量既不能凭空创造 也不能凭空消失 这意味着我们的英雄的质量 并不会因为他身体大小的改变而改变 举个例子,当我们烤松软的海绵蛋糕的时候 即使烤出来的美味蛋糕 比烤之前的蛋糕糊 大了许多 蛋糕糊的重量仍然应该 等于烤出来的蛋糕的重量 加上蒸发掉的水分的重量 在化学方程式中 分子们重新组合来制造新的化合物 但是反应前后所有物质的质量之和仍然不会变 当我们的英雄从 6英尺高 变到18英尺高 他的身高变成原来的三倍 根据伽利略的平方立方定律计算 他的重量会变为原来的27倍 3x3x3=27 乘上他原来的重量 因为他必须在三个维度都变大 因此,当我们的超级英雄变成一个巨人 有两种可能性 我们的超级英雄有18英尺那么高 但只有200磅那么重 和他没变大的时候一样重 还有,第二种可能,我们的英雄重5400磅 200磅乘7=5400磅 当他高18英尺的时候 这也意味着在他只有6英尺高的时候 他还是重5400磅 如果不想超载 他就只能自己坐电梯 现在,第二种可能性 看起来更佳符合科学事实 但是这种情况依旧回避了一些问题 在他在公园散步的时候 他如何保持自己不会陷进地里? 由于他对泥土施加的压强 等于他的质量 除以他脚底的面积 而且他得穿什么样的超级袜子和超级鞋 才能承受得了他在奔跑的时候 他那5400磅的身体 和道路之间的摩擦? 他能跑步么? 我不会问他能不能找到足够有弹性的裤子 来承受他的变形 现在,我们探究一下 之前我们提到的两种情况中的密度 密度的定义是质量除以体积 人的身体由骨头和血肉组成 这两部分的密度都是确定了的 第一种情况中,如果这个英雄一直都重200磅 那么他的骨头和血肉都和正常一样 当他变大之后 而且仍然只有200磅 他基本上就是把自己 变成了一个超大超软的泰迪熊 在第二种可能中,如果这位英雄 一直都重5,400磅 那么,当他的身高18英尺时 他需要用两条腿支撑5,400磅的身体 当他从不同角度活动时 腿骨需要承受如此之大的重量 骨,又硬又没有延展性 这代表它们无法弯曲 因此它们易碎 筋也有可能被撕裂 高大的建筑之所以可以耸立 是因为他们有钢架 并且不会在丛林里跑跑跳跳 而我们的英雄呢 一旦从一个不太好的角度着了陆 他就会摔倒 假设他的身体构造和哺乳动物的一样 他的心脏需要提供大量的血液 在身体里循环来提供足够的氧气 来支持他那5,400磅的身体行动 这将需要他 每天通过吃27x3000卡路里的食物 来提供这巨大的能量 粗略地计算大概是150个巨无霸汉堡所含的能量 27x3000=81000 81000÷550 =147 他将没有时间和罪犯斗争 因为他所有的时间都用来吃东西了 并且找一份朝九晚五的工作 来支付在他食物上的花销 那么,像那些可以 把身体变成沙子或者石头的超级英雄呢 地球上的所有东西都由各种各样的元素组成 而决定每一种元素种类的 是原子核中的质子数 这也是元素周期表排列的规则 氢元素有一个质子 氦元素,两个质子 锂元素,三个质子 等等 沙子最基本形式的基础成分 是二氧化硅 然而,人体由 65%的氧元素 18%的碳元素 10%的氢元素 和7%的其它种类的元素组成 包括0.002%的硅元素 在化学反应中 元素重新组合形成新的物质 那么,他要从哪弄到这些必要的硅元素 来制造沙子 当然,我们可以通过核裂变或核聚变 来改变元素的种类 然而,核聚变需要非常高的温度 以至于唯一可以自发聚变的地方在星体上 为了在短时间内进行聚变 反应区域的温度 需要比太阳还高 每个无辜的旁观者都会被烧成脆片 快速的核聚变反应有很多缺点 因为它会产生许多放射性微粒 我们的英雄就会变成 一个会行走,会说话的核电站 基本上会伤害每一个他试图去救的人 并且你真的想要太阳那么高的热度 或者一个放射性的核电站在你身体里面么? 现在,你还想参加哪一种 超能力的课程? 改变身体的大小和构成身体的物质 超快的速度 飞行 力大无比 长生不老 还是 隐身