multiplied by the time. if that's true, that means something twice as heavy will fall twice as far in the same time. let's see if that's true. ted, can i have your help? i've got a two-meter stick here, gang. ted, could you hold that two-meter stick up? this is ted barnstorm, ta. [laughter] and what i'm gonna do is i'm gonna hold this one up here, two meters high, and this one meter high, and i'm gonna drop them at the same time. if the resistance is proportional to velocity, they'll hit the ground at the same time because this one will fall twice as far as this, okay? let's try it and see. they did not hit at the same time. so hypothesis, no good. but let's suppose the resistance is compared-- stay right there, ted-- it's compared to the velocity square?

all right? if it's proportional to the velocity square, then that means-- velocity square proportional to resistance proportional to the weight that means the velocity would be proportional to the square root of the weight. can you see that? if that's true, then the distance something falls would be equal to the square root of the weight. so if i had something twice as heavy, that greater distance it falls will be proportional to twice the square root of the weight times the time. but that's proportional to-- and this is that. so if it's true that the resistance is proportional to speed square, then the distance one falls is going to be equal to square root of two times the weight. you know the square root of two is, anyone? 1.4. it turns out to be 1.414, okay, times the little distance.

if that's true, if i hold this thing up 1.4 times higher than this, they should hit the ground at the same time. shall we try it? i've got this marked off. so this distance here is d, and up here turns out to be 1.4 times higher than d. so i'm gonna put the twice as heavy one up here and this down here and drop them, and see if they hit at the same time. ready, mark, set, go. did you see that? at the same time. let's try it one more time. do it on this side. do it on both sides. okay. oh, the heavy one on top, and the light one with the mark right here. okay, ready. one, two, three. see that? same time. this ball here has twice the diameter of this one.

this is twice as high off the table. twice the diameter, that means it has eight times the weight, okay? this one here has eight times as much weight but four times as much area. so what's the ratio? two weights to one area. the same ratio we had over here. i should be able to drop this with one ball, one unit high, the other 1.4 unit high. and when i do that, though-- watch this, gang. they don't fall together. you know why? because they didn't reach their terminal velocities. the balls really are too heavy. so what i could do is i get lighter balls where it reached the terminal velocity right away. when i drop this thing here, it didn't have to go very far at all before it reaches tv, maybe accelerate it for about a centimeter, then it's tv all the way down. so you know what i'm saying? but these things will accelerate all the way to the floor. but if i put these in a more viscous medium,

then it won't accelerate but by a tiny, tiny bit. and we can do that with this container of water. ted. ted and i have been playing around with this a day before yesterday. so what we got here now is we got a couple of spheres, and one is twice the diameter of the other. it means it weighs eight times as much, and it's got a weight-area ratio of 2:1. so when i drop these two things both at the same time, of course, the heavy one will hit first. you see that? but what i'm gonna do-- [laughter] --i'm not gonna drop them. i take this-- [laughter] you guys are wondering, yeah? yeah. ted was doing that yesterday because his arm is-- he got long arms. so we--he had this little thing made out.

isn't that kinda neat, see? oh, yeah. [laughter] here's what we're gonna do. this is ted's idea, by the way. so what we're gonna do, i'm gonna put this up here. oh, no, no. it's my idea to screw it up, okay? [laughter] so i'll put the bottom-- this one here. oh, what we've done is we've measured this off. from here to here is d. and from here to here is 1.4 times d. this is a little bit longer, of course, you can see. and it's at 1.4, same thing we've got with the cops. so let's try it now. right there. there we go. oh. that's why we get this-- oops, more water. oh. oh, we've got some more water. it's good--on that, yeah? [laughter] okay, here we go, gang. the little one here. [laughter]

big one here. and i'm gonna flip this off to the side and see if you don't see them both fall at the same-- yehey, yehey. huh? isn't that nice? okay? so heavy things will fall faster or the same as light things? faster. faster. these fell at the same time because one, of course, was higher. one had to go up a greater distance. ain't that nice? okay. yeah, do it one more time. oh, one more time. yeah. why not? if these were a couple of dead fish and the couple of dead fish were going down, which dead fish would get to the bottom first, the big one or the little one? the big one. the big one. the big one will fall faster, yeah? yeah. do you have any friends that swim? do you have any friends that are like competition swimmers?

do you know any competition swimmers who are-- look at that. do you know any competition swimmers who are small? will this effect of scaling be useful or nonuseful to a small swimmer? two people fall off a cliff in a vacuum, big person, small person. which one hits the ground first? the same. now, two people fall off a cliff in the air, one is heavy, one is light. which one hits the ground? the heavy. i take these two balls here, one is heavy, one is light. which one went faster through the water? heavy. heavy. and the light one, honey, got to do some tricks or something to keep up with the heavy one. that's right. so big boats usually go faster than the small boats. the big fish swim smarter than fast fish. the small fish-- [laughter]

you know a big fish will open up their mouth and just go, right? the little fish can't keep up. the little things have more resistance compared to their strength. the effects of scaling. yehey. [music]