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The object from the previous question is now placed in oil, which has a density 1/2 that of water. What happens? The block sinks to the bottomThe block floats lower...

Question

The object from the previous question is now placed in oil, which has a density 1/2 that of water. What happens? The block sinks to the bottomThe block floats lower.The block floats as before:The block floats higher CURA

The object from the previous question is now placed in oil, which has a density 1/2 that of water. What happens? The block sinks to the bottom The block floats lower. The block floats as before: The block floats higher CURA



Answers

A material will float on the surface of a liquid if the material has a density less than that of the liquid. Given that the density of water is approximately $1.0 \mathrm{g} / \mathrm{mL},$ will a block of material having a volume of $1.2 \times 10^{4} \mathrm{in.}^{3}$ and weighing 3.5 $\mathrm{lb}$ float or sink when placed in a reservoir of water?

So a book off would is floating on water. Onda. A layer of oil is now poured on top of the water. Too adept that more than covers the block. So quick set up here shows us we've got something that looks like this. You have a block, floating water, some of its utmost and then oil covers. Look, so we have a little Okay, So part berry say's is the volume of wood submerged in the water greater them less. They're all the same as before, and this is a really fundamental issue here. This should be very easy for us to answer, because whenever you submerge anything in a fluid, that fluid provides a level of buoyancy and a forced upwards to whatever object it is that we're looking at. And so even you when you're in the earth's atmosphere, if that's a fluid, has a density. There was a slight buoyancy force provided by the atmosphere course that buoyancy force in comparison to the wait. It's absolutely minute because the earth's atmosphere as a fluid has such a small density. Before that reason, when you cover this block with oil, it provides a greater buoyancy force onto the block. And so the answer should be very easy here, just through common sense. The volume submerged in water, the in water is ness. Do you see you? The buoyancy force, which is just another F B. The next part of the question asks if 90% of the wood is submerged in the water before the oil is that find the fraction submerged when the oil of density 875 kilograms. For me too cute covers the book. So making note of that 875 kilograms, that means cute. And now that it's just worth you this question so what do we know? Waiting. The block is equal to density of water volume submerged most black Barty and how much is submerged? The question tells us this by saying 90% instead, most in the water before the orders at So the way to the block really can be calculated is sort of territory. V. We don't know, but we're more supply by no 0.9 as 90% of the block is there, handle at G to make our equation correct. So what do we do next? I'll concede that density of water times the volume in water. You're very careful here. I would like my G And to that the density in oil. It's a bad way of writing all hope. But I think it's just about Richard. Volume in oil is justice multiplied by G. He's going to equal no 0.9 for you, Dempsey off water most part by chief. So what have we done here? We've worked out the way to the block. And so what we're effectively saying is the way to the block is equal to the sum of the two buoyancy force is provided by the two different liquids. This is very important because we've got a lot of things here that we could work with. Okay, so we're gonna quickly expand a little bit more on this and say, Gents, team water terms the volume in the water, Most part Barchi plus volume in oil. The dentist, Ian Doyle. Secrets is a total volume, minus the volume in water. Most black Margie once again has to equal the weight of the block. So what are we doing? Yeah, let's just consider for a second that we've just fact arised out. We've worked out that the volumes of most in oil is going to equal the check your body minus volume in water, and we're eliminating the volume in oil and solved the problem to the portion of the volume of the block that's in the water so effectively, What we're doing is we're trying to eliminate the for you, my foil it effects exhibition. So what does that mean? Well, let's go into another page and just rewrite what we've got here so we can hear you see how we can mathematically manipulate this. That's a bit higher on the page is gone off a little bit. So what I've just previously stated is the volume is the density in the water is equal to the volume in the water multiplied by G plus the density in oil multiplied by the total value minus the volume in water. Naturally, most black by G is equal to the weight of the block. No fortnight you were right. And now for the maths factories out the volume in water, leaving a swift identity of water minus the density of oil, most like by chief and of course, the rest. We've just taken to the other side using a value of the turkey. No 0.9 turns the density of water minus the density of oil. Most black by G on very quickly things start to get a lot mathematically nicer because we can cancel out those G's. And we could get a ratio for the volume in water over the talking for you, which is really what we're working for. A war alone. Take it. There's no 0.9 exploited by the density of water. Subtract from that intensity of oil and take the ratio of that with the density of water. Subtract the density of oil when we have numbers for all of this on we put those into a calculator. Now the density of water. His 1000 kilograms hit me just cute against your oil is baked 175 kilograms for me Too cute. That stays in by the question putting all those into a calculator. Get an answer. No 0.2. I'm not question what fraction is submerged when the oil covers the block without fraction is the volume in water divided by the total volume, which is no 0.2. You can also write this 20%

All right. So nice city water is one grandpa really that the block has born in about one point to 10. 10 to the fourth cubic inch mass up £350. And so we can look up. That one cubic inch is equal because you're 16.387 Well, centime cubic centimeter. That is because to 16.387 million later, £350 because £1 because 453.59 to graph. So, um, we need to find the density will be equal to mass over volume. He called to 350 on fall 53 592 over one point to tend to the 4 16.387 grand over Real Leader. And that 0.8 grand The leader that is lesser than one. So the clockwork float

The answer to this question is obvious if you ever seen a piece off board in water, but let's do it starting from it. Now let's say our container is full of water outside, full of some fluid whose density is greater than the density. Often object. Now, as the object is lowered into the water, the buy and force on it increases the weight off. The object is obviously MG. It is volume times, g times its density. Let's call it roll object and the boy and forces. Obviously, volumes have merged times G times density off. What the fluid. So obviously the density of fluid is larger than 10 city of objects, which means these two. When these two are equal, these are most value will be smaller than the total value. Well, let's write it again. The submerged volume small we times throw off the fluid is it will do the total volume times they're off the object. So much volume by total volume is roll off the object, but often fluid. Because the fluid has a large intensity, this will be less than what it means. The buoyant force will be equal to the weight before the object for you so much is let's say at this point, the buoyant force and the wait will be equal in the cancel out. So the object will simply stay there. It won't go down, are up. This is floating basically when an object because it'd which has density smaller than that off Floyd, he is.

Let's first cell for the density of the block of material, we have £3.5. We need to convert this to grounds. So our conversion here is £1 is equal to 453 0.59 grams of working this oats. Give me, um 1500 in 87.565 grams will keep all of our sig figs here. And we're told that it has a volume of 1.2 times 10 to the four inches cubed. So one inch is equal to 2.54 centimeters and we're gonna cube that. So this would be equal to, uh, 2.5 for times 1.21 for this would be equal to, um, one point 966 times 10 to the five centimeters cubes. Let's calculate the density of the block of material. We don't know what the material is. Sequel to em over V, which is equal to 1587.565 grams over 1.966 times 10 to the fifth centimeters cubed, so work. So for a density here, their density would be equal to 8.7 times 10 to the negative, three grams per centimeters cubed. So since the density of the block, which is 8.7 times 10 to the negative three grams per milliliters programs per, um, grabs from milliliters. Centimeter cubed doesn't matter. Um, these units are interchangeable. It could be crabs from a leader. Um, is less then the density, um, of water, which is one gram per mil leader. Um, the block will float when placed in the reservoir of water.


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