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Food And Discovery
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00:00This video contains the answers to my four revolutionary riddles, so if you
00:06haven't seen the riddles yet, you should probably watch them before you watch the
00:09answers. It's okay, I'll wait, just click this card up here. Now when I filmed the
00:15riddles, I also filmed the solutions at the same time, but that was before I
00:20received your 15,000 comments and dozens of video responses, so I'm reshooting
00:25parts of this solutions video to incorporate the results I saw in the
00:28comments and to use some of your video responses to help explain the solutions.
00:33Let's get to it. Okay, by looking at the comments, for number one, over 15% of you
00:39said a cylinder containing sand. Now this contains some powder, see how it rolls.
00:47It doesn't seem to roll very far before it stops and then it won't roll again
00:54because I think the sand just kind of levels off in there. Maybe you were
00:59thinking a bigger kind of sand like this small gravelly stones. Let's try that.
01:11That actually rolls pretty well. Nearly 25% of you said a cylinder half full of water, so
01:18let's try that. This rolls very well, so it's not water. Nearly 45% of you said a cylinder half full of a
01:30viscous liquid. Here I have a half full container of honey, so let's see how it rolls.
01:36That's not bad. It's rolling and it's stopping and it's rolling some more. This is a pretty good guess and I
01:48think the behavior is not exactly the same as the mystery cylinder, but it definitely is similar and
01:55that's no coincidence. The mystery cylinder actually contains honey and ping pong balls. There are two ping pong
02:05balls submerged in this honey. So if I place that on the ramp, the center of gravity is not above the
02:14point of contact with the ramp and so it rolls forward, but now because those ping pong balls are
02:20in the front, they change the center of gravity and so it's exactly under the point of contact and so
02:27it stops briefly. But then as the viscosity of the honey allows those ping pong balls to move up,
02:33the center of gravity shifts forwards again allowing this little container to roll. So that is the trick
02:39of the mystery cylinder. Pretty easy if you want to try it out at home. Now I challenged you to run
02:46two laps of this track where the first lap you could go as slowly as you like, but the second
02:50lap you had to go much faster such that your total average speed was twice the speed of your first lap.
02:56Now when I was first asked this question by Simon Pampana, it took me a long time and scribbling on paper
03:02and just something didn't seem to work out and that's because you can't actually do this. It's
03:10impossible. I mean you might think I could run 3v1 for my second lap and that would mean my total
03:16average speed is 2v1. The problem is you can't just add the two velocities together and divide by two
03:21because you spent much more time in your first lap so that velocity is weighted more heavily into the
03:28average. So you'd have to run, well, impossibly fast. Let me explain. The velocity of the first lap
03:35was the distance around the track divided by t1, the time it took you. Now if you want your total
03:40average time to be twice v1, well then it needs to be 2d over t1. You need to run twice the distance
03:48in the same amount of time as it took you to run the first lap, but you've already run that first lap
03:53and so you have no time remaining to run the second lap. Even if you went the speed of light,
03:58you would not be able to increase your total average speed up to twice the velocity of your
04:05first lap. It is just mathematically impossible. So this may seem like a bit of a trick question,
04:11but the point to me is how doable it sounds, how it seems like something you should be able to do,
04:17but you can't. It's actually impossible. Riddle number four, the question about the train, was
04:24actually answered pretty well, with most people mentioning something to do with the wheels. But
04:28of course that makes sense in a series of riddles which are about rotation, rotational motion. Some
04:34people though did point out that maybe it was the steam that was going backwards, or maybe air molecules
04:40in the train, and that is actually a pretty clever point. However, I wouldn't really consider the air in the
04:45train part of the train. So indeed, the part of the train that is moving backwards is the flange part
04:53of the wheel which is below the rail. That is the part of the train which is moving backwards. To
05:00understand why, you just think about a spinning wheel. The top of the wheel is moving forwards at
05:05speed 2v and the bottom of the wheel is not moving forward at all. It is stationary with respect to the
05:11track. And that is what we call rolling without slipping, and that's how most wheels work. At
05:16least that's how they're designed to work. Now in the case of trains, they have to have flanges so the
05:23train doesn't fall off its rails. But of course when these pieces come around during the rotation of the
05:28wheel, they actually extend beyond the rail and therefore they are going backwards with respect to the
05:34ground. So the part of the train that's moving backwards is always changing, but it's always that part of the
05:41flange that part that extends beyond the wheel that is below the level of the track. So what happens
05:47when you pull the bottom pedal of a bike backwards? Well about 45% of you thought that the bike would
05:54move backwards, about a quarter said it would move forwards, and a quarter said the bike wouldn't move
06:00at all. And five percent said it depends on something. So let's give it a shot and see what happens.
06:07I'm going to pull backwards on the bike pedal in three, two, one...
06:15Whoa! The bike did indeed move back. And for virtually all bikes, this is what you will find.
06:22But the explanation is not just as simple as, well the net force on the bike is back, so therefore it
06:27has to accelerate backwards. And to prove that that logic doesn't work, we'll just have a look at this
06:33video by George Hart. Watch this. Again, I pull the same pedal backward, but now the bike moves forward.
06:41I'll put a link to the full video here and a link to his website in the description. So the reason the
06:46bike moves backwards is because of the way these gears are set up, the diameter of the tire, and also
06:52the distance on this crank to the pedal itself. Because as a bike moves forwards,
06:58the pedal, even when you're pushing back on it, never actually moves backwards with respect to the
07:05ground. It's always moving forwards. So if you drag a string behind the pedal of a bike moving forward,
07:12the string is always moving forward. Now just play that movie backward in your mind,
07:17and it may be clear how pulling the string backward could make the bike move backward. They move forward
07:22together, so they move backward together. Another way to think about this is to consider the path traced
07:26out by the pedal as the bike moves forward. This is called the trochoid. For all ordinary bikes,
07:32the pedals are moving much slower than the tires, so the pedal is always going forward with respect to
07:37the ground. But George modified his bike so the ratio of the pedal to the wheel radius was greater than
07:43the ratio of the front sprocket to the back sprocket. And this ultra-low gear changes the trochoid so the
07:50pedal does actually go backwards with respect to the ground as the bike goes forwards. And that's why he
07:56could pull back on the pedal and make the bike go forwards. And this is the same reason why if you
08:01were to pull backwards on the flange of a train wheel, you could actually get the train to move
08:06forwards if you pulled backwards with enough force. For all normal bicycles, pulling back like this on
08:12the bottom pedal will cause the bicycle to move backwards. But depending on the gear ratio, you can get
08:18the bike to move forwards. So it was those people who said it depends on the ratio of these gears and
08:25the size of this crank to the radius of the back wheel that were actually the most correct.
08:48заход in the clinch.
08:52So I'm going to give you a little bit of a little bit of a little bit of an engine for
08:53you to get there.
08:54So
08:56you can get there.
08:58You can get there.
08:59So
09:00do
09:02you
09:04get there.
09:08go
09:10you
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