0:00:00.000,0:00:01.839 - [Instructor] Beach balls float on water, 0:00:01.839,0:00:04.510 icebergs float on water,[br]certain things float on water, 0:00:04.510,0:00:07.337 whereas others, like a steel ball, sinks. 0:00:07.337,0:00:10.410 Why? Why do certain things[br]float and certain things sink? 0:00:10.410,0:00:12.114 And also, if you consider[br]the things that are floating, 0:00:12.114,0:00:14.743 sometimes, most of the[br]object is above the water, 0:00:14.743,0:00:17.350 like the beach ball, but[br]when it comes to the iceberg, 0:00:17.350,0:00:20.303 look, most of the object is[br]submerged below the water. 0:00:20.303,0:00:23.085 So what controls how much[br]of that object is above 0:00:23.085,0:00:24.863 and how much of it is submerged? 0:00:24.863,0:00:26.194 Now, you probably know the answer 0:00:26.194,0:00:29.554 has something to do with[br]density, but why density? 0:00:29.554,0:00:31.140 Why does density matter? 0:00:31.140,0:00:33.014 What is the deeper reason behind this? 0:00:33.014,0:00:35.040 That's what we wanna[br]figure out in this video, 0:00:35.040,0:00:35.873 so let's begin. 0:00:35.873,0:00:38.237 So, let's start by submerging[br]an object inside a fluid. 0:00:38.237,0:00:40.234 Let's consider water to be our fluid, 0:00:40.234,0:00:42.155 and let's submerge a cubicle object. 0:00:42.155,0:00:45.606 A cube because it's a nice[br]shape. Easier to analyze, okay? 0:00:45.606,0:00:47.992 We know that the water[br]is going to start pushing 0:00:47.992,0:00:50.602 on this cube in all the[br]directions perpendicular 0:00:50.602,0:00:51.617 to the surface. 0:00:51.617,0:00:53.492 And if we calculate that force per area, 0:00:53.492,0:00:55.108 we call that as the pressure. 0:00:55.108,0:00:56.058 Now, the important thing 0:00:56.058,0:00:58.734 is that the pressure increases with depth. 0:00:58.734,0:01:01.344 So, let's see how that affects the cube. 0:01:01.344,0:01:02.918 First, let's consider[br]the horizontal forces. 0:01:02.918,0:01:04.590 For example, consider[br]the forces on the left 0:01:04.590,0:01:06.117 and the right side of the cube. 0:01:06.117,0:01:07.752 The forces would look somewhat like this. 0:01:07.752,0:01:10.680 Look, the pressure is[br]increasing with the depth, 0:01:10.680,0:01:14.244 but notice the forces[br]pretty much cancel out. 0:01:14.244,0:01:15.093 And the same thing is gonna happen 0:01:15.093,0:01:17.323 with the front and back[br]surface of the cube as well, 0:01:17.323,0:01:19.744 so all the horizontal forces cancel out. 0:01:19.744,0:01:22.243 But what about the top[br]and the bottom surface? 0:01:22.243,0:01:23.240 Well, let's see. 0:01:23.240,0:01:25.106 The pressure on the top is smaller 0:01:25.106,0:01:27.750 than the pressure from the bottom. 0:01:27.750,0:01:31.088 And because the surface[br]area is exactly the same 0:01:31.088,0:01:32.991 on both the top and the bottom, 0:01:32.991,0:01:36.183 the forces from the bottom will be larger 0:01:36.183,0:01:38.679 than the force from the top. 0:01:38.679,0:01:41.085 And therefore, now the[br]forces don't cancel out. 0:01:41.085,0:01:45.570 Instead, there is a net[br]force acting upwards. 0:01:45.570,0:01:48.240 And that net force that's acting upwards 0:01:48.240,0:01:50.989 is what we call the buoyant force. 0:01:50.989,0:01:55.351 This is the force that[br]tends to make things float. 0:01:55.351,0:01:57.927 It tends to make things buoyant. 0:01:57.927,0:01:59.982 That's what the b stands for over here. 0:01:59.982,0:02:02.760 And so, notice where does[br]the buoyant force come from? 0:02:02.760,0:02:06.753 It ultimately comes from the[br]fact that as you go deeper, 0:02:06.753,0:02:09.042 the pressure increases. 0:02:09.042,0:02:11.607 That is where it all comes from. 0:02:11.607,0:02:13.836 Now, although we did[br]this analysis for a cube, 0:02:13.836,0:02:17.495 this would be true for any[br]object of any arbitrary shape. 0:02:17.495,0:02:18.993 Even if you take some kind of a rock, 0:02:18.993,0:02:20.737 which has some random shape, 0:02:20.737,0:02:22.775 the fact is the pressure from the top 0:02:22.775,0:02:25.290 is smaller than the[br]pressure from the bottom. 0:02:25.290,0:02:26.916 And so, when you look at all the forces, 0:02:26.916,0:02:30.495 eventually, there will be[br]a net force acting upward, 0:02:30.495,0:02:32.351 the buoyant force. 0:02:32.351,0:02:33.743 Now comes the big question, 0:02:33.743,0:02:35.996 because of this buoyant[br]force, how do we know 0:02:35.996,0:02:38.601 whether this object is[br]going to float or sink? 0:02:38.601,0:02:42.396 Well, it depends upon the[br]weight of this object. 0:02:42.396,0:02:44.740 If the weight of this object 0:02:44.740,0:02:47.897 is smaller than the buoyant force, 0:02:47.897,0:02:49.737 well, then the buoyant force wins. 0:02:49.737,0:02:51.780 The net force will now be upwards, 0:02:51.780,0:02:54.611 and as a result, the object[br]will accelerate upwards, 0:02:54.611,0:02:56.829 making it float. 0:02:56.829,0:03:01.101 On the other hand, if the[br]weight of the object is larger 0:03:01.101,0:03:04.241 than the buoyant force,[br]then the weight wins 0:03:04.241,0:03:06.657 and therefore, the object[br]will accelerate down, 0:03:06.657,0:03:09.418 in other words, the object will sink, 0:03:09.418,0:03:10.667 which means all we need to do 0:03:10.667,0:03:12.746 is figure out what the buoyant force is. 0:03:12.746,0:03:14.321 If we can do that, we can predict 0:03:14.321,0:03:16.759 whether an object is[br]going to float or sink. 0:03:16.759,0:03:18.792 But how do we figure out[br]what the buoyant force 0:03:18.792,0:03:21.499 is going to be, especially[br]when the objects 0:03:21.499,0:03:23.337 have irregular shapes like this? 0:03:23.337,0:03:25.290 Well, here's a way to think about it. 0:03:25.290,0:03:28.234 Imagine that instead of having a rock, 0:03:28.234,0:03:30.491 if I had a styrofoam over here, 0:03:30.491,0:03:32.743 but of exactly the same shape 0:03:32.743,0:03:36.673 and volume submerged in the[br]same liquid, in the same fluid, 0:03:36.673,0:03:38.809 the question to think about is, 0:03:38.809,0:03:41.709 would the buoyant force[br]now be the same as before 0:03:41.709,0:03:43.289 or would it be different? 0:03:43.289,0:03:45.853 Why don't you pause the[br]video and think about this? 0:03:45.853,0:03:47.497 All right, at first, it might feel like, 0:03:47.497,0:03:49.495 "Hey, I have a different[br]substance altogether, 0:03:49.495,0:03:51.994 so the buoyant force must[br]be different, obviously." 0:03:51.994,0:03:53.018 But think about it, 0:03:53.018,0:03:54.385 the buoyant force,[br]where does it come from? 0:03:54.385,0:03:57.090 It comes from the pressure[br]differences, isn't it? 0:03:57.090,0:03:58.845 And what does pressure depend on? 0:03:58.845,0:04:02.880 Well, the pressure only[br]depends upon the depth. 0:04:02.880,0:04:06.034 And so if you have the[br]exact same shape as before, 0:04:06.034,0:04:09.278 then all the forces will be[br]exactly the same, and therefore, 0:04:09.278,0:04:11.942 the pressure would be[br]exactly the same as before, 0:04:11.942,0:04:13.905 and therefore, the buoyant force 0:04:13.905,0:04:16.141 would be exactly the same as before. 0:04:16.141,0:04:17.677 So, this is the key insight. 0:04:17.677,0:04:19.182 This means that the buoyant force 0:04:19.182,0:04:22.065 has nothing to do with what[br]material you have submerged. 0:04:22.065,0:04:25.879 All that matters is the[br]shape of the material. 0:04:25.879,0:04:27.247 If the shape remains the same, 0:04:27.247,0:04:29.107 then regardless of what material it is, 0:04:29.107,0:04:31.491 the buoyant force should be the same. 0:04:31.491,0:04:34.598 Okay, the buoyant force does[br]not depend upon the material, 0:04:34.598,0:04:36.492 how can we use that insight? 0:04:36.492,0:04:40.141 Well, now, in this exact same shape, 0:04:40.141,0:04:44.562 let's fill water. (laughs) 0:04:44.562,0:04:46.734 Well, the buoyant force is[br]gonna be the same as before, 0:04:46.734,0:04:50.792 but this time, we know[br]that this particular piece 0:04:50.792,0:04:54.159 of water is in equilibrium[br]because, remember, 0:04:54.159,0:04:55.345 this is just water. 0:04:55.345,0:04:57.495 It's static. It's not moving at all. 0:04:57.495,0:05:00.134 This piece of water is neither[br]sinking nor it's floating. 0:05:00.134,0:05:02.938 It's not accelerating upwards,[br]which means it's static. 0:05:02.938,0:05:05.604 And therefore, this[br]means this piece of water 0:05:05.604,0:05:07.328 is in equilibrium. 0:05:07.328,0:05:10.290 So, the weight of this piece of water 0:05:10.290,0:05:13.286 must be exactly equal 0:05:13.286,0:05:15.238 to the buoyant force. 0:05:15.238,0:05:16.360 And there we have it. 0:05:16.360,0:05:20.347 We have figured out what[br]the buoyant force must be. 0:05:20.347,0:05:21.846 For this particular shape, 0:05:21.846,0:05:23.859 it doesn't matter what[br]you put inside this, 0:05:23.859,0:05:26.875 the buoyant force should equal the weight 0:05:26.875,0:05:29.737 of this fluid. 0:05:29.737,0:05:32.488 In other words, when you fill this object, 0:05:32.488,0:05:35.760 when you fill this space with some object, 0:05:35.760,0:05:39.270 that fluid got displaced somewhere, 0:05:39.270,0:05:43.996 and the weight of that fluid[br]that got displaced literally 0:05:43.996,0:05:46.598 is the buoyant force. 0:05:46.598,0:05:47.916 Isn't it amazing? 0:05:47.916,0:05:50.853 Long story short, the buoyant[br]force acting on any object 0:05:50.853,0:05:55.410 will always equal the weight[br]of the fluid that it displaces. 0:05:55.410,0:05:59.557 And this is what we call[br]the Archimedes' principle. 0:05:59.557,0:06:01.587 So now let's see if we[br]can use this insight 0:06:01.587,0:06:03.556 to figure out when will an object float 0:06:03.556,0:06:05.600 and when it'll sink, okay? 0:06:05.600,0:06:07.566 So, we know that if the[br]weight of the object 0:06:07.566,0:06:10.332 is larger than the buoyant[br]force, in other words, 0:06:10.332,0:06:12.993 larger than the weight of[br]the fluid it displaces, 0:06:12.993,0:06:14.743 the object is going to sink. 0:06:14.743,0:06:17.495 So this is a sinking case,[br]but when will this happen? 0:06:17.495,0:06:20.238 When will the object have more[br]weight compared to the fluid 0:06:20.238,0:06:21.486 that it's displacing? 0:06:21.486,0:06:22.990 Well, what is weight? 0:06:22.990,0:06:24.685 Weight is just mass times gravity. 0:06:24.685,0:06:26.838 So we can plug mg over here. 0:06:26.838,0:06:28.325 This represents the mass of the object, 0:06:28.325,0:06:30.643 and this represents the mass of the fluid 0:06:30.643,0:06:31.993 that got displaced. 0:06:31.993,0:06:35.555 But we know that mass is[br]the density times volume. 0:06:35.555,0:06:36.638 So we can replace masses 0:06:36.638,0:06:39.799 with density of the object[br]times the volume of the object, 0:06:39.799,0:06:41.811 and the density of the fluid displaced 0:06:41.811,0:06:43.597 times the volume of the fluid displaced. 0:06:43.597,0:06:45.232 But here's the key thing, 0:06:45.232,0:06:48.368 the volume of the fluid[br]displaced is exactly the same 0:06:48.368,0:06:51.060 as the volume of the object, right? 0:06:51.060,0:06:53.239 And therefore, these things cancel out, 0:06:53.239,0:06:55.875 and look what the condition becomes. 0:06:55.875,0:06:56.893 The condition for sinking 0:06:56.893,0:06:59.576 is the density of the[br]object should be larger 0:06:59.576,0:07:01.395 than the density of the[br]fluid it's submerged in. 0:07:01.395,0:07:04.810 When that happens, the object will sink. 0:07:04.810,0:07:06.997 But can we now understand why? 0:07:06.997,0:07:08.661 Well, because if the density of the object 0:07:08.661,0:07:10.583 is larger than that of the fluid, 0:07:10.583,0:07:12.576 then the weight of the object 0:07:12.576,0:07:14.894 will be larger than[br]the weight of the fluid 0:07:14.894,0:07:17.730 that it displaces when[br]it's completely submerged. 0:07:17.730,0:07:19.923 And as a result, its weight wins. 0:07:19.923,0:07:21.870 Its weight will be larger[br]than the buoyant force 0:07:21.870,0:07:24.570 and that's why it ends up sinking. 0:07:24.570,0:07:26.545 And this is why a steel[br]ball sinks in water 0:07:26.545,0:07:29.501 because it has a higher[br]density than water. 0:07:29.501,0:07:31.383 But what if an object has a lower density 0:07:31.383,0:07:33.007 than the fluid it's submerged in? 0:07:33.007,0:07:35.644 Well, then its weight would be lower 0:07:35.644,0:07:38.100 than the weight of the[br]fluid that it displaces, 0:07:38.100,0:07:39.740 and therefore, the buoyant[br]force will be larger 0:07:39.740,0:07:41.066 and the whole object will accelerate up. 0:07:41.066,0:07:44.164 In other words, this is the[br]condition for flotation. 0:07:44.164,0:07:45.806 This is the reason why beach balls 0:07:45.806,0:07:47.509 and icebergs float in water 0:07:47.509,0:07:50.745 because they have a density[br]that's smaller than water. 0:07:50.745,0:07:52.195 And now, look, we have[br]the complete equation 0:07:52.195,0:07:53.353 for the buoyant force. 0:07:53.353,0:07:55.578 The buoyant force is the[br]weight of the fluid displaced, 0:07:55.578,0:07:59.890 which is the density of the[br]fluid times the volume times g. 0:07:59.890,0:08:02.230 And so this is the expression[br]for the buoyant force. 0:08:02.230,0:08:03.352 And again, this helps us see 0:08:03.352,0:08:04.995 why it's the density that matters 0:08:04.995,0:08:06.484 because, look, the weight[br]of the displaced fluid 0:08:06.484,0:08:08.488 will have the exact same volume 0:08:08.488,0:08:10.605 as the weight of the submerged object. 0:08:10.605,0:08:11.742 The volumes cancel out, 0:08:11.742,0:08:14.245 and that's why it's eventually[br]the density that decides 0:08:14.245,0:08:16.100 whether something's[br]going to sink or float. 0:08:16.100,0:08:18.402 So it all comes from the[br]Archimedes' principle, 0:08:18.402,0:08:21.780 which eventually comes from[br]the pressure differences. 0:08:21.780,0:08:22.647 Amazing, right? 0:08:22.647,0:08:24.240 But now, let's think about[br]what's going to happen 0:08:24.240,0:08:25.248 to this object. 0:08:25.248,0:08:27.671 We know it's going to[br]start accelerating up, 0:08:27.671,0:08:29.490 but when will it stop? 0:08:29.490,0:08:30.356 Well, let's see. 0:08:30.356,0:08:32.740 As long as the whole[br]thing is submerged inside, 0:08:32.740,0:08:34.809 the buoyant force stays the same. 0:08:34.809,0:08:38.943 But now, as it starts[br]coming above the surface, 0:08:38.943,0:08:42.465 it starts displacing lesser fluid. 0:08:42.465,0:08:43.413 Can you see that? 0:08:43.413,0:08:46.170 It now only displaces this[br]much amount of the fluid, 0:08:46.170,0:08:49.489 and therefore, the buoyant[br]force will become smaller. 0:08:49.489,0:08:51.612 But as long as it's still[br]larger than the weight, 0:08:51.612,0:08:55.200 the object continues accelerating upwards, 0:08:55.200,0:08:57.483 and eventually, at some point, 0:08:57.483,0:08:59.037 the weight of the fluid displaced 0:08:59.037,0:09:02.430 will exactly match the[br]weight of the object, 0:09:02.430,0:09:04.295 and that's when equilibrium is reached 0:09:04.295,0:09:06.595 and the object pretty[br]much stops at that point. 0:09:06.595,0:09:08.497 So look, for an object to float, 0:09:08.497,0:09:11.090 it needs to be submerged[br]enough so that the weight 0:09:11.090,0:09:15.216 of the fluid displaced exactly[br]equals the object's weight. 0:09:15.216,0:09:16.252 Does that make sense? 0:09:16.252,0:09:17.350 Now, consider the beach ball. 0:09:17.350,0:09:21.753 It has a very low density,[br]so the amount of water needed 0:09:21.753,0:09:25.252 to match the weight of the[br]beach ball is very little. 0:09:25.252,0:09:27.504 So only a small portion[br]needs to be submerged 0:09:27.504,0:09:29.238 because by then, the weight of the water 0:09:29.238,0:09:32.491 that has been displaced[br]already equals the weight 0:09:32.491,0:09:33.989 of the entire beach ball 0:09:33.989,0:09:37.669 because the beach ball has a[br]much smaller density compared 0:09:37.669,0:09:38.544 to the water. 0:09:38.544,0:09:39.835 That's the whole idea. 0:09:39.835,0:09:42.241 On the other hand, if[br]you consider an iceberg, 0:09:42.241,0:09:46.647 it has a density very, very[br]close to that of water. 0:09:46.647,0:09:49.738 And so now, to displace the[br]water equal to its weight, 0:09:49.738,0:09:52.834 you need to submerge a lot more. 0:09:52.834,0:09:55.495 Pretty much the entire[br]thing needs to be submerged 0:09:55.495,0:09:58.662 because its density is very,[br]very close to that of water. 0:09:58.662,0:10:00.351 It's still less, that's why it's floating, 0:10:00.351,0:10:01.936 but it's very close to that of water. 0:10:01.936,0:10:04.483 So, higher the density of the object, 0:10:04.483,0:10:06.836 more it needs to be submerged 0:10:06.836,0:10:09.238 so that it can be in equilibrium. 0:10:09.238,0:10:10.743 So, if you put it all together, 0:10:10.743,0:10:12.410 we can say that when[br]the density of an object 0:10:12.410,0:10:15.588 is smaller than density of the[br]fluid, it will be floating. 0:10:15.588,0:10:17.641 And the amount of the[br]objects submerged depends 0:10:17.641,0:10:19.498 on how small the density is. 0:10:19.498,0:10:21.113 If the density of the[br]object is very tiny compared 0:10:21.113,0:10:22.530 to the density of the fluid, 0:10:22.530,0:10:23.739 it'll be submerged just a little bit. 0:10:23.739,0:10:25.659 On the other hand, if[br]the density is very close 0:10:25.659,0:10:27.223 to the density of the[br]fluid, but still smaller, 0:10:27.223,0:10:29.040 it needs to be smaller[br]for it to be floating, 0:10:29.040,0:10:31.742 but if it's close enough, then[br]most of it will be submerged. 0:10:31.742,0:10:34.503 On the other hand, if the[br]density of the object is higher 0:10:34.503,0:10:35.853 than the density of the fluid itself, 0:10:35.853,0:10:37.244 then the object will sink. 0:10:37.244,0:10:38.743 And by the way, in all the examples, 0:10:38.743,0:10:40.242 we have taken water as our fluid, 0:10:40.242,0:10:42.653 but this would work for any fluid, okay? 0:10:42.653,0:10:44.153 For example, air is also a fluid, 0:10:44.153,0:10:46.120 so it can also put a buoyant force. 0:10:46.120,0:10:48.253 But since air has a very[br]low density compared 0:10:48.253,0:10:50.825 to everyday objects, we[br]don't usually notice it. 0:10:50.825,0:10:53.738 But if you consider a[br]helium balloon, its density, 0:10:53.738,0:10:56.142 helium density is smaller[br]than that of the air. 0:10:56.142,0:10:58.993 And now, as a result of[br]that, helium tends to float, 0:10:58.993,0:11:01.499 and that's why helium[br]balloons tend to rise up. 0:11:01.499,0:11:03.107 But now is an interesting question, 0:11:03.107,0:11:06.428 what if the density of the[br]object exactly equals the density 0:11:06.428,0:11:07.304 of the fluid? 0:11:07.304,0:11:08.250 What happens then? 0:11:08.250,0:11:10.243 Well, now, if you completely submerge it, 0:11:10.243,0:11:13.598 it will neither float nor sink. 0:11:13.598,0:11:16.343 We call this the neutral buoyancy. 0:11:16.343,0:11:20.489 That object will just stay[br]at that particular depth, 0:11:20.489,0:11:22.620 and that's exactly how submarines 0:11:22.620,0:11:24.744 can stay at a particular depth. 0:11:24.744,0:11:28.340 They do that by changing[br]their average density. 0:11:28.340,0:11:29.848 If they want to sink, 0:11:29.848,0:11:31.845 they will increase their average density 0:11:31.845,0:11:36.231 by allowing water to flood their tanks. 0:11:36.231,0:11:37.064 On the other hand, 0:11:37.064,0:11:40.489 if it now needs to come towards[br]the surface of the water, 0:11:40.489,0:11:42.491 then it'll decrease its average density. 0:11:42.491,0:11:44.996 It does so by now using compressed air 0:11:44.996,0:11:47.231 to force the water out. 0:11:47.231,0:11:49.614 And by carefully balancing[br]the amount of water 0:11:49.614,0:11:51.422 and air inside its tanks, 0:11:51.422,0:11:54.740 it can also make sure that[br]its density exactly equals out 0:11:54.740,0:11:57.740 of the surrounding water,[br]maintaining neutral buoyancy, 0:11:57.740,0:12:00.493 and in which case, it'll[br]stay at a particular depth. 0:12:00.493,0:12:02.115 That's amazing, right? 0:12:02.115,0:12:04.901 Now, instead of submarine,[br]imagine you were wearing a suit 0:12:04.901,0:12:07.843 which could also maintain[br]neutral buoyancy in water. 0:12:07.843,0:12:10.182 Then you would be, just[br]like the submarine, 0:12:10.182,0:12:12.482 stay at a particular location in water, 0:12:12.482,0:12:14.895 not going down nor going up. 0:12:14.895,0:12:18.495 In other words, you would[br]kind of feel weightless, 0:12:18.495,0:12:20.106 which means now you can train 0:12:20.106,0:12:22.490 for the weightless environments[br]that you would face 0:12:22.490,0:12:23.828 in the space stations. 0:12:23.828,0:12:24.999 And that's exactly 0:12:24.999,0:12:28.614 what the NASA's Neutral Buoyancy Lab does. 0:12:28.614,0:12:30.593 It's a giant swimming pool inside 0:12:30.593,0:12:33.600 which astronauts can[br]maintain neutral buoyancy 0:12:33.600,0:12:34.872 and train for the weightless environment. 0:12:34.872,0:12:37.182 It's not perfect, but it's way better 0:12:37.182,0:12:40.323 and more realistic than training[br]on the ground, for example.