For example, why can you slap a fly mid-air and it’ll probably survive just fine, but if you scaled the same amount of force to the size of a human’s size/weight, they’d probably die?
In: 14
Look at a column. The strength of a column is related to how thick it is, not how tall it is. If it’s radius was doubled, it’d be able to hold a lot more weight, but if it was twice as tall, that doesn’t make it stronger.
To be more specific, it’s strength is related to the area of its cross-section. Since areas are 2D, when you scale them up, they get bigger by the square of the scaling factor. Simply put: scaling a shape by 2 increases its area by 2^(2) = 4. So scaling the radius of a column by 2 increases the cross-sectional area by 4, and it’s 4 times as strong.
But weight is related to volume, which is 3D, so it scales up by the *cube* of the scaling factor. Scaling a 3D shape up by 2 increases its volume by 2^(3) = 8. So scaling the radius *and* height of a column by 2 increases its volume, and therefore weight, by 8. It weighs 8 times as much.
So scaling something up increases its weight much faster than it increases its strength. So more of its strength must be used to support that weight, until it is so heavy it can’t even support that weight with its given strength so it collapses.
Conversely, scaling it down decreases its weight faster than its strength, so more of its strength is freed up to do other things, like resist a swatting human hand.
Latest Answers