Adventure In Science: The Size Of Things (1959)

[Music] if you've read the book Gulliver's Travels by Jonathan Swift you remember that Gulliver said he visited a land of Giants he said they were 12 times taller than he was and therefore 12 times as strong let's see if we can find out if Gulliver was telling the truth the science of physics and measurement can give us the answer first let's look at a boy suppose he's 5T tall and weighs 100 lb now if he were 10 ft tall and his proportions remain the same he'd weigh 800 LB why well this Cube will show us why it's 1 in Long 1 in wide and and 1 in high to double its height and keep its proportions the same we must double its length its width as well as its height we've had to use eight cubes as you can see if our original Cube weighs 1 o then our big Cube must weigh eight times as much or 8 oz when the dimensions of any object regardless of its shape are doubled it will weigh eight times as much so if the boy were twice as tall and kept his same proportions he'd be eight times as heavy but he wouldn't be eight times as strong why well his body is held up by a set of Bones a skeleton the strength of a bone or a muscle depends upon the area of its cross-section a crosssection of a bone is a the slice through it because a cross-section is an area it has only length and width when the small cube doubled in size three dimensions doubled length width and height but its cross-sectional area a slice through it double in only two Dimensions length and width let's see what happens if the size of a large animal increases if the height of this elephant doubles and its length and its width also double its weight like the boys increases in three dimensions or eight times but the cross sectional area of its bones and muscles its strength increases in only two Dimensions or four times thus the weight of a double-sized elephant increases twice as much as its strength that's why doubling the boy's height and keeping his same proportions makes him eight times as heavy but only four times as strong one half as strong proportionately as he was before what if a mouse were as big as a boy a large Mouse on its hind legs May stand about 6 in high if the boy is 5 ft or 60 in high and the mouse is 6 in high then the boy is 10 times taller than the mouse now if the mouse were the boy's size its volume and weight would increase 10 times for the length 10 times for the width and 10 times for the height or 1,000 times but the cross-sectional area of its bones and so its strength would increase only 10 time 10 or 100 times the bones of the mouse would have to support 10 times more weight than they did originally each time our oversized Mouse took a step its bones would snap like toothpicks as you can see big mice have a very dim future here's another example this beetle is very strong it's able to pull a heavy toor wagon now what if the beetle were as big as the boy how strong would it be the beetle is 1 in in length if it were 5 ft or 60 in in length its volume and weight would increase 60 times for the length 60 times for the width 60 times for the height a total of 60 * 60 * 60 or 26,000 times but the strength of muscles like bones depends upon the area of their cross-section the beetle strength would increase 60 times for each of only two Dimensions 60 times for the length and 60 times for the width a total of only 60 * 60 or 3,600 times so a beetle as large as a boy would not have strength enough to lift a glass of milk it couldn't even exist now what happens when we decrease size what if the boy were as small as the beetle the boy's volume and weight would decrease 60 times for each of three dimensions 60 * 60 * 60 or 216,000 times but the cross-sectional area of his muscles would decrease 60 times in only two Dimensions 60 * 60 or 3,600 times since the boy's weight decreased 60 times more than his strength the boy becomes 60 times stronger in proportion to his size than he is now if a body is made smaller in all proportions its strength does not become smaller by the same amount in fact the smaller a body becomes the greater its strength in relation to its weight if a body is made larger in all proportions however the less its relative strength because the relative weight it must carry is greater do you remember our question about Gulliver he said the Giants he visit were 12 times taller and 12 times stronger than he was was guler telling the truth [Music]