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.
有些超級英雄 可以憑自己的意思長到高樓般的巨大 那真是非常嚇人! 但是身為一個科學家 一定要找出 那些多出來的物質是哪裡來的 質量守恆定律告訴我們 物質不能被製造 也不能被消滅 這也就是說英雄的重量 並不會因為他的大小改變而改變 比如說 當我們烤一個鬆軟的海綿蛋糕時 就算做出來的美味蛋糕 體積會比進烤箱前的蛋糕麵糊大的多 體積會比進烤箱前的蛋糕麵糊大的多 但其實蛋糕麵糊的重量 仍然跟蛋糕的重量加上蒸發的水分 是一樣的 在化學公式裡 分子會重新排列而產生新的合成物 但是所有元素所佔的數量是一樣的 當保護我們的英雄 從(大約)180公分變大成 540公分時 他的身高成長了三倍 因為英雄一定是立體地變大 所以根據伽利略平方立方法則 ──3x3x3等於27 他的體重應該會變成 他原有體重的27倍 所以說 當保護我們的超級英雄變成巨人時 我們面臨兩種可能性 一種是英雄變成540公分時 仍只有當他還是人類大小時的 90公斤重 第二種可能性則是英雄在540公分時 ──90公斤重乘以27倍等於2430公斤 他體重是2430公斤 也就是說他在180公分時 他體重仍然是2430公斤 跟他一起坐電梯 而不讓電梯超載的鈴聲響起是不可能的 第二種可能性 似乎在科學上比較合理一點點 但它仍要被質疑 英雄該如何走過一個公園 爾不陷入地面的呢? 畢竟他在泥土上產生的壓力 是由他坦克般的體重 除以他腳底的面積 而究~竟他穿哪種超級威的襪子跟鞋子 可以承受英雄在跑步時 拉動2430公斤的身體產生的摩擦力 仍保持完整呢? 他....真的能跑嗎? 我絕對不會想知道他到底怎麼找到 那些在他變大時也同時伸縮自如的內褲 現在 我們來探究一下 剛剛提到的兩種可能性的"密度" 密度的定義是重量除以體積 人類的身體是由骨骼跟肌肉組成的 這都有相對固定的密度 在第一種可能性中 如果英雄一直都是90公斤 他變身前會有正常的骨骼跟肌肉 當他變大時 如果他仍然是90公斤重 他基本上把自己變成了一隻 巨大膨鬆的泰迪熊 在第二種可能性中 如果英雄一直是2430公斤 那他在540公分時 他的雙腳將支撐2430公斤重的骨骼跟肌肉 他在移動時,這個重量會 施加在腿骨上造成骨頭間不同的角度 骨頭雖然堅硬 卻不具有延展性 也就是說他們沒有辦法彎曲 所以他們很容易就會斷掉了 韌帶們也暴露在被撕裂的危險性中 高樓大廈之所以能屹立不搖 是因為他們有鋼鐵支架 而且不會在叢林裡東奔西跑和跳來跳去 反過來說保護我們的英雄 只要任何一次降落時角度不對 他就註定墜毀了! 假設他的身體功能跟哺乳類一樣 他的心臟就需要推動大量的血液 到全身來提供足夠的氧氣 讓他能移動2430公斤的身體 這需要非常大量的能量 因此他每天需要消耗 27倍3000卡的食物 差不多等於150個大麥克漢堡 ──27x3000=81000 一個大麥克漢堡約550卡 81000除以550約等於147 他將不會有時間去打擊罪犯 因為他會不斷地吃吃吃 而且要朝九晚五不停地工作賺錢 才能買得起他吃光的所有食物 那麼 其他那些可以把身體轉變成 石頭或沙子的超級英雄是怎麼回事呢? 這個嘛~ 地球上的每個東西 都是由許多元素所構成 這些元素是由 原子核的質子數來定義的 這也是我們排出元素表的方式 氫有1個質子 氦 2個質子 鋰 3個質子 依此類推 一般常見的沙子中最主要的成分是 二氧化矽 而在人體是由 65%氧氣 18%碳 10%氫 及7%其他多樣的(包含0.002%矽)元素 所組成 在化學反應裡 元素們會重新排列產生新物質 所以 他到底是從哪裡得到 這些變成沙子所需要的矽呢 所以 他到底是從哪裡得到 這些變成沙子所需要的矽呢 當然我們可以經由核融合或核分裂的方式 來改變許多元素 然而 核融合需要極多的熱力 通常只發生在外太空的星球 為了能在短時間內利用核融合 環境的溫度 一定要比太陽更熱 每個無辜的路人都會被炸成馬鈴薯片了! 瞬間核分裂也沒有比較好 因為它常產生許多放射性物質 保護我們的英雄會成為 一個具語音功能的行動型核電廠 最終會傷害每一個他想救的人 你會真心想要太陽般炙熱的溫度 或放射性核電廠在你體內嗎? 現在我們來聊聊 你下次想探索哪個超能力物理課呢? 改變身體大小及組成 超極速 飛行 超強大的力量 永生 及 隱身能力