okay so we started out this next section of our floating and sinking unit by thinking about this little thought experiment where this Olympic um athlete is underwater lifting up two different people on a bar and we were thinking about you know why is it that we are able to do this when we're playing around at the swimming pool where when we try to lift somebody up they feel a lot lighter than they do if we're out on land and so we asked the question you know what would a scale actually read when weighing an object in and out of the water and so I had to do some predictions we actually weighed some things in water to see what would happen using our spring scale and we found out that when you do weigh something in water it turns out that it actually does appear to weigh less than it did when you were weighing it in air and we said that the reason behind this had to do with the fact that something must be pushing upward on the object to make it appear to weigh less and it turns out that that thing is an upward Force called the buoyant force um the weight of the object is acting downward in a downward Direction and as any of you know who have taken um physics class for every action there is an equal and opposite reaction this is one of Newton's Laws so when that object pushes downward with its weight there is a force pushing back upward from the water and so we often represent forces using arrows to show both their Direction and the magnitude of the force now when we are representing buoyant force what we want to do is actually use a convention called a free body diagram where we show the arrows um rather than doing it like this picture here what we actually want to do is show the arrows coming off of what we would consider to be approximately the center of mass of the object something like these diagrams here so basically I typically just draw a circle where I think the center of mass would be approximately and then draw the vector arrows that represent forces acting on the object coming from that Circle all right so let's talk a little bit more in depth now about the boyant four so we've done some Upper Middle School level AC activities I would say possibly getting into the level of about 9th grade but I am going to give you a little bit of college math to go with this phenomenon as well and so what we want to do here is think about buoyancy in a quantitative fashion so when we think about um the weight of the object hanging from the screen the spring scale we can represent that Vector um as the weight of the object the force due to the weight um which is equal to the mass of the object times the acceleration due to gravity and so we call this Force the real weight of the object um we can add that Vector to both of these scenarios because um the gravity um acting on the mass of the object does not change whether you're in air or on water in water as long as you're on planet Earth um so the real weight of the object is going to be the same in both scenarios on the other hand up at the top here we have what we would call the apparent weight of the object as opposed to the real weight which we can represent with fime w and the apparent weight of the object is equal to the apparent mass of the object times gravity now we've already stated that there is some Force pushing upward on the object to create this reduced apparent weight and that Force which I represent here with the yellow arrow in an upward direction is the buoyant force of the object so how much is quantitatively the buoyant force well one of the things that we can say about the buoyant force is represented by this first equation here so the buoyant force is equal to the real weight of the object minus its apparent weight so in the case here on the right um if we know that the real weight of the object is 5 kilg and the apparent weight of the object seems to be 3 kilg when it's in water what is the magnitude of the buoyant force in this situation well it's clearly must be 2 kilg now let's say when we put this object into the water we use a special Beaker that has a little overflow spout so that when we put the object in the water we can actually capture the water that was displaced or pushed away when the object went down into the water and if we put that little um Bowl here on a scale and weigh it what we are getting here is the weight of the water that was displaced by the object and so one of the things that's kind of interesting is it turns out that the water the weight of the water that was displaced by the object hanging from the spring scale is also equal to to the weight of the object minus its apparent weight if this is true then we can create an equivalency here which brings us to our third equation which is the buoyant force is not only equal to the real weight of the object minus its apparent weight the buoyant force is also equal to the weight of the water that is displaced by the object so if this is true let us think about the conditions that mathematically would allow for an object to float and for an object to sink so why don't you kind of think about this for just a minute so what conditions of comparing the buoyant force um um and things like that will lead to an object floating and what conditions will lead to the object sinking how large does the buoyant force need to be for the object to float or sink well how about this what if the buoyant force is greater than the weight of the object in that case the object is going to be floating if the the upward force is greater than the force the downward force from the weight of the object then clearly that object is going to float in addition if the weight of the water displaced by the object is greater than the weight of the object the object will also float on the other hand if the buoyant force is less than the weight of the object so that the downward arrow is greater then clearly the object will sink and similarly if the weight of the water displaced by the object is less than the object's weight then again the object will sink hopefully you also have watched the Con Academy video um about Archimedes principle and buoyant force to help reinforce all of this so that pretty much brings us to the end of this unit floating and sinking um thanks for listening to today and um if you have any questions please let me know take care and have a good night