just meant why do things float okay that could be the subtitle of this brooke we're back to newton's laws all those free body diagram problems where you had the normal and you had the force of friction and you had the force of the the tension and the rope all those things come back around at the very end of this because we're going to add one more force to our catalog of forces and that's the buoyant force okay now the buoyant force is fairly easy but you have to read it carefully okay the buoyant force is equal to the weight because weight is a force yes weight is m g which could be density times volume times g right because density is kilograms per cubic meter or something along that line times the volume of whatever it is times g so it says it's equal to the weight of the displaced fluid all right so we have to start thinking here like a boat in the water okay so you put your boat in the water and part of the boat's in the water part of the boats above the water right the force acting on that boat upward is equal to the weight of the water that was pushed aside by the boat okay if i were to lily take a rock okay when the rock's above the water well there's no buoyant force because it's above the water right when i let go of it it'll plop down in the water right well it doesn't float that's okay right we'll see how f equals m a deals with that but i don't worry about the weight of the rock to calculate the buoyant force okay i'll have to worry about the weight of the rock somewhere along here but not for the buoyant force what what weight do i worry about the weight of water that has the same volume because that rock let's just call it a cubic meter when we put it in the water a cubic meter of water had to move right that amount of water that moved what was the weight of it oh i could calculate because i know it was a cubic meter i could go look up the density of water which you might remember one gram per cubic centimeter right and i could figure out the weight that would be the force that's acting upward on my rock the buoyant force do you have a buoyant force even though it's not floating yes because this does not say it's the it's the weight of the displaced fluid when the object is floating it says the buoyant force is the weight of the displaced fluid where what direction does it point well it's kind of intuitive but we'll give it some physics-y words and say it always opposes gravity or it opposes the acceleration okay mackenzie three in the morning i predict you won't get this wrong but somebody here when doing the homework at three in the morning will get really confused because they'll use the weight of the object not the weight of the displaced fluid okay those are not necessarily the same thing now to help you with that hey we have an example yes i love this example you're gonna hate it because it's got springs in it because oh crap we're back yeah we're back to statics problems with f equals m a with springs and tens all those things right this is a perfect segue into reviewing for the final exam but what i've given you here is um this situation we've got some water says it's in water i've got a cube but the cube is connected to a spring that's connected to the ceiling okay how much is the spring stretched now you're going like who would ever do this i don't know right i suppose a chemist could use this to determine volume or density or something there's also a tendency to go how can we have water in a statics problem we never had that before but this is not accelerating it does not tell me anything about that it asked me about a force and we've seen that in the past when we're asked about what is the force or what is the tension in the rope or what is the right force related we go ah free body diagram what is the free body diagram for my block bailey pick a force all right we would have a spring force how about another one gravity that's always a good one is it's not sitting on the bottom of the container is it is there a normal it's not sitting on the bottom is it no no normal okay and what's the theme of the day buoyant force no uh sorry um well he asked a good question we're going to assume that this object is small enough that the pressure on top and the pressure on the bottom are the same okay if i had a really big object would a submarine be big enough it might come into play if you had a submarine because submarines are actually very tall they've got that tower up there there are multiple stories and there might be a bit of a difference but we're not going to do that in this one that's a good question okay who am i talking to ian a buoyant force yes okay now uh the spring force we don't know do we right we eventually will find the this the stretch by using kx but we don't have a number for it do we have a number for the force of gravity uh what is it we haven't can you help me find it all right all right the volume of the cube let's see that would be 0.2 meters cubed yeah by the way i'm going to remind you that um 1 cubic meter is 10 to the sixth cubic centimeters that's illegible yes how many liters in a cubic meter oh he's giving me the look where would you go to find it back of the book yeah equals 1 000 liters because the leader is actually a volume okay uh what else do i have to do here oh we know the density yes but not oh i got to be careful i got to do this in the right units yes so this would be 10 to the fifth kilograms per cubic uh nope i goofed just a minute just a minute 10 to the fourth grams per cubic meter caitlin can you see where the 10 to the fourth came from a factor of 10 to the third for the kilograms a factor of 10 to the sixth for the centimeters but it's a 10. so it was 10 times 10 to the third divide sorry 10 to the sixth divided by 10 to the third all right so we end up with 10 to the fourth two four eight yes okay times the vol uh times 9.8 meters per second squared and the magic number is equals 784 newtons samantha what's the buoyant force well it's the weight of the displaced fluid right so what's the volume of fluid that was moved off to the side huh 0.2 meters cubed yes what's the what's the um what's the density of water well you'd have to work it out went one gram per cubic centimeter okay now okay yep ten to the third kilograms per cubic meter and gravity 9.8 meters per second squared would give me 78.4 newtons mean the multiplying yeah i you know i picked nice numbers because if i worked it out for 10 i could easily do it for one because it was just divided by 10. right but that 10 to the third comes from saying one gram per cubic centimeter but 10 to the sixth from the size conversion 10 to the third to go from grams to kilograms so it ends up being 10 to the third my goodness we're back to day one doing unit conversions aren't we you don't look happy about that do i need to do it out 10 grams per centimeter cubed times 1 kilogram 10 to the third grams times 10 to the sixth centimeters cubed for one meter cubed equals 10 to the fourth yeah i see a few smiles not a lot but a few okay william all right so what do we have let's see we have minus 784 newtons plus 78.4 newtons plus 500 delta x equals zero can you find the stretch in the spring all right now we do it again yes what you know i post them right uh a rope the same block but now let's see 0.5 meters is out of the water sarah jane oh i don't have a lot of time left what changes in this problem do i still have an upward force from the rope yeah so my free body diagram still looks like f t and mg uh yeah mg i'll leave with that and f b right does the gravitational force change same size same density same mass same gravitational force what changes why right with the buoyant force how what's the what's the weight of the displaced fluid right so the buoyant force would be 0.2 meters times .2 meters times .115 meters times 10 to the third [Music] kilograms per cubic meter times 9.8 right the volume changed so i have to calculate the weight of the displaced fluid well if there's a half a centimeter out of the water that doesn't count so i realize that this is now one point sorry .15 meters and when i go to calculate how much water got pushed away two meters by 0.2 meters by 0.15 meters [Music] oh zero five yeah yeah it can't be that thought okay hey you look stunned no okay is that good all right uh and then we would just do the free body set it equal uh do the sum of the forces equals zero you'd find the tension in the rope okay uh let's see i ended up with four times one and a half ft equals 725.2 newtons but we haven't really verified that so i'll put a couple of question marks by it shelby uh now i have a beach ball tied down to the bottom of the lake so it's completely submerged right have you ever tried to do this at the beach it's really hard isn't it yes there's going to be a lot of tension in there it's the same problem isn't it right the only reason i offer this one to you because it's really no different we just right base oh sorry there are two things in here do we worry about the mass of the beach ball gravity of the beach ball no i mean we could it's pretty small isn't it i mean what's the mass of a beach ball full of air not much okay technically just like your question about is the pressure put the water on top of it yes no okay we're not going to worry about its own mass sometimes the expert ta proms give you a mass for the beach ball but it's insignificant okay all right so that's that's difference number one right mg for the ball is negligible is really small addison what's the volume of a beach ball with radius 1.1 meter uh oh high school geometry yes what's the volume of a sphere nope that's the circumference of a circle what you're guessing too what was it that's the area of a circle volume equals four thirds pi r cubed okay if you can't remember that if it doesn't ring true what are you going to do with it all right say it loud going to write it on the formula sheet yes because you might see spheres you don't know how many moles i actually reverse did it so that there's one mole of gas in there but you don't need i just wanted realistic numbers all right so this is the same problem as the other two right beach ball buoyant force force of gravity but we're going to call that equal to zero and force tension nice one-dimensional problem you just set the two equal and you uh find out what the tension in the rope was are we good yes again no because we're going to assume it's small enough that we'll say the pressure on top and bottom is the same if i give you a skyscraper sized object sitting on the bottom of the ocean then what was the there is one more that we're not going to go through i will tell you the mass of the dirt is 2 000 kilograms now shall keep