An ant may be able to survive me flicking it – but proportionally-speaking, I would not be able to survive such a thing. Is it happenstance that this is the case? Is there a “perfect” size for this universe?

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An ant may be able to survive me flicking it – but proportionally-speaking, I would not be able to survive such a thing. Is it happenstance that this is the case? Is there a “perfect” size for this universe?

In: Physics

6 Answers

Anonymous 0 Comments

The short answer is: the ant is much ‘tougher’ than you because it is much smaller than you are.

But there are two reasons why the ant is tougher. There are a couple of factors at play:

**1). First is the Square Cube Law, or the Law of Scaling, or Law of Proportions**

Let’s say we shrunk you down to the size of an ant using a ray gun like Wayne Szalinski’s in the movie *Honey, I Shrunk the Kids*. Once you got your bearings, you would quickly realize that you are MUCH stronger (and tougher) relative to your size than you were when you were ‘big’. *In truth, you’d actually die immediately, but that’s another story.* The reason you’re so ‘tough’ now is because your surface to volume ratio is much *higher*. In other words there’s *more of you*, relative to your weight and volume.

To illustrate this point further, imagine (small-shrunken) you and (big not-shrunken) me standing on opposite ends of a diving board and we both do belly flops into a pool. You wouldn’t feel much when your belly hits the water because your belly only has to support your body weight, which is about a milligram or so. I, on the other hand, would feel the pain. My belly would have to support almost 200 pounds.

**2). The second (and less important) factor at play here is what we call “terminal velocity”.**

This effect is also related to mass and surface area. But, it is more about how an object’s speed (and acceleration) is is affected by gravity and the surrounding air. Remember, when we shrink you, there’s *more of you relative to your weight* (proportionally less volume). This means that as your shrunken self falls, the air is interacting more with your body relative to your weight than mine.

To illustrate, we’ll use the same example of the diving board above. Only this time, you are diving into a drained swimming pool (no water). When you jump, you won’t fall very fast, because relative to your weight, there’s more surface area to slow you down, and the air stops you from speeding up too fast. You stay at that speed and can’t go any faster. When you hit the concrete pool bottom, it won’t hurt too much because you weren’t going fast enough. In fact, you’d be ok if you jumped off the top of the CN Tower into the drained pool because your top speed or “terminal velocity” wouldn’t be “fast enough” to hurt you when you hit the concrete. The air resistance to mass is higher for small animals like ants, which is why they can’t be seriously injured from being dropped from any height.

TDLR:

Proportionally, an ant has more surface area and less weight, and more importantly, less volume which makes it tougher.

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