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What do you think is stronger? An ant, or an elephant?
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An elephant can lift more weight than an ant,
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but what about their strength compared to their body size?
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The answer might surprise you.
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An elephant can lift 500kg, which is 10% of its body weight.
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An ant can only lift one millionth as much, but that amount is actually 50 times its body weight!
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Ants use their impressive strength to move food and materials to their colonies.
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How much can you lift?
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The average person, between the size of an ant and an elephant, can only lift about half of its own weight.
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Why is an ant so strong?
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First, we need to understand the principle called the “Square Cube Law”,
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which Galileo came up with over 400 years ago.
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He observed that when an object grows in size, its volume increases faster than its area.
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Let’s picture a cube.
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The area of one face on the cube is the length squared,
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and the volume is the length cubed, hence the square-cube law.
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This cube has sides that are 1cm long.
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The area of a face on the cube is one square cm, and its volume is one cubic cm.
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Now this cube has sides that are twice as long.
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The area of its face is 4 square cm, but the volume is now 8 cubic cm.
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Doubling the length of the sides quadruples the area, but octuples the volume!
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As the object gets bigger, the ratio between its area and volume changes.
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There are important consequences when an object’s volume grows faster than its area,
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because it changes the way it can interact with its surroundings.
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Effects of the square-cube law can be observed in our everyday life.
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For example, in designing buildings.
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We can make small-scale models of buildings out of paper mâche,
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but real houses are made of wood, brick, and metal.
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But why can’t we just build a real house out of paper mâche?
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The amount of weight that a structure can support is relative to the cross-sectional area.
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But the building’s own weight is proportional to volume.
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Since the square-cube law told us that volume increases faster than area,
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a bigger building will weigh more but might not have enough area to support its own weight.
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These two towers are made of the same material, but only the small one can support its own weight!
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Because of this, engineers need to use stronger materials like bricks
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to design real buildings that have larger dimensions.
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For similar reason, an ant can carry more relative to its body weight than an elephant.
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And this is also the reason why monster ants do not exist.
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Strength is proportional to the cross-sectional area of their legs,
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while weight is proportional to their volume.
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Here you see a small ant holding its weight.
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If we now scale up the ant, we see that the ant’s legs can no longer support its weight, and it collapses!
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And hey, look! The small ant can even bring treats back to its friends!
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The square cube law is also observed in aerodynamics,
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which is the science of flying and falling.
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You may have learned that gravity causes matter to fall towards the ground,
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and that gravity makes objects of any mass fall at the same speed.
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Why is it then that in real life some objects seem to fall faster than others?
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A falling object actually experiences two forces, gravity and air resistance, which is also called drag.
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Gravity makes the object fall faster, while drag slows it down.
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The force from gravity is proportional to the volume of an object,
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while drag is proportional to its exposed area.
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Remember again that when things get bigger, volume increases faster than area.
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If we drop these two different sized helicopters from four-stories high, what happens?
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As predicted, the bigger helicopter falls faster, because the drag, which goes with area,
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increases more slowly than weight, which goes with volume.
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Let’s review what we’ve learned today!
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The square-cube law tells us that when an object grows in size,
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its volume increases faster than its area.
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We've seen how this can be applied to buildings, animals, and falling objects.
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Look around you! What else can you explain with the square-cube law?
