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A piece of wood is 0.600 $\mathrm{m}$ long, 0.250 $\mathrm{m}$ wide, and0.080 $\mathrm{m}$ thick. Its density is 600 $\mathrm{kg} / \mathrm{m}^{3} .$ What volume of lead must be fastened underneath it to sink the wood in calm water so that its top is just even with the water level? What is the mass of this volume of lead?

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5.266 $\mathrm{kg}$

Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

University of Michigan - Ann Arbor

Simon Fraser University

University of Sheffield

McMaster University

Lectures

03:45

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

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A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases and plasmas. Fluids display properties such as flow, pressure, and tension, which can be described with a fluid model. For example, liquids form a surface which exerts a force on other objects in contact with it, and is the basis for the forces of capillarity and cohesion. Fluids are a continuum (or "continuous" in some sense) which means that they cannot be strictly separated into separate pieces. However, there are theoretical limits to the divisibility of fluids. Fluids are in contrast to solids, which are able to sustain a shear stress with no tendency to continue deforming.

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Okay, So in this problem, uh, we have a piece of wood. So let's draw here. We have the peace off would. And above this piece of wood we have, we have lead. So that's what here, size amount off lead on. We know that this would is completely underneath the water, but not the leads. Okay, so that is this system. So what is the forces involved in this problem? First of all, we have the weight off the would so and we actually have the weight off the lead. So let's call this huge weight off capital M G, where this is just a mess off the lead, plus the mass off the wood multiply body gravity's acceleration and the other force involved in this problem is just a buoyant force f b. Okay, so now that establish our system, what we must remember is what is buoyant force. So buoyant force is just the density off the liquid which in this case, is going to be the water. Ah, that's not mistake. He's w with peace. W So that's what I'm gonna call That's called these Pepto W. So this is okay. Now let's move off at the buoyant force, as we as we saying, is the density of the liquid, which in this case is the water multiply by the volume submerge multiply by the gravity acceleration. And according to the Newton Second Low, we know that the buoyant force should be equal capital. OMG Therefore, we can cross the gravity here A simplified the equation so we can have density of the water. Times of autumn submerge equals the capital in which is the great mass mess above a wood and elite. No, let's see, we do not have the mess that is correct. You do not have the mess, neither the woods or the lead. So that's why they're gonna do Let's move on and continue the problem here. We know that the volume submerge this is the density off the water. We know that the volume submerge is just a volume off the would because the lead is not submerge. So the equation is it s a water volume of the woods. The move supplies the mess off the lead so we can describe this us The density off lead times followed, um, off lead, plus the density off. I would times Let's see the volume off. What? So the problem. The question wants to know What is the mess in the volume off lead? So, first of all this, calculate what is the volume of lead? Because if we discover the volume off lead, we can, Then Coakley the mess. So let's do it. The volume off lead. If we rearrange desecration going to be density off water times the volume off would minus density off. Woods multiplies the volume off would all days divided by the density off lead minus in density off water. Okay, that is too many doubles here getting confused. So that's put the vat is here. So the density of water 1000 multiplies the volume off would. So the volume off would will be just the multiplication between the wide diff EQ and IHS length. So this is promoted by all this. We're going to find out that the volume is 0.0 to elf, Okay? Minus Ah, the mass of the woods. We don't Yeah, we actually have the message, would. So we do not need to use the then city off the woods times the volume of the wooden here we can use directly d mess. So the mess is just 7.2 kilograms. All this divided by the density of the leads, which is 11 0.3 times 10 to the tree minus one 1000 which is the density of water. So calculating this Finally, we get that volume off lead is just four point 66 times 10 to the minus four meters cubic six. No, that we have volume off lead. We can calculate his mess so the mass of lead is going to be equal. His density times he's following. So this is just 5.66 At 11.3 times. Stand to the tree multiplies 4.66 I'm Stan to the minors, for which gives us a final result Mass off the lead equals five points 27 kilograms and that's your final answer. You're just problem

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