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A cube 5.0 $\mathrm{cm}$ on each side is made of a metal alloy. After you drill a cylindrical hole 2.0 $\mathrm{cm}$ in diameter all the way through and perpendicular to one face, you find that the cube weighs 7.50 $\mathrm{N}$ (a) What is the density of this metal? (b) What did the cube weigh before you drilled the hole in it?

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Physics 101 Mechanics

Chapter 13

Fluid Mechanics

Temperature and Heat

Cornell University

Rutgers, The State University of New Jersey

University of Washington

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.

09:49

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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thing. Okay. And this problem, we're given a cube with side length point. 05 meters. Ah, I believe in the question it sze given in centimeters, but we're going to wantto converted two meters. That'll be more convenient. Um, And in this cube, a cylindrical bore eyes punched through it. And the radius of the cylindrical bore is point no. One meters. So the first thing they were asked for in this question, part is what the density of the material that the Cube is made out of is. And to do that, we simply take the mass of the of the object and divided by its volume. The mass is a pretty straightforward calculation were given that it's way is on 7.5 Newtons and so to convert its weight to its mass, we simply divide by the gravitational acceleration which is nine point E meters per second squared. This will give us the mass in units of kilograms. Now, um, the next thing that we need is an expression for the volume. So, of course, the volume of a cube is its side ling cubes and we need to subtract from that volume The volume of the cylindrical boar that was punched through the cube. And, um, the volume of a cylinder is pi r squared l. So we simply on subtract higher squared l from the total volume, which is all cute. And now it's just a matter of plugging the numbers. And we take this calculation we substituted in for M, and we substitute in this for l and this for our no give a certain city now in part B were asked what the mass of the Cube was prior to having the the board punched through it. And now, since we have the density, that's a pretty straightforward calculation. So the mass will be given by its density times its volume and without the cylinder punched in it, the volume is simply l acute. And the road that we want to use in this calculation is the same road that we got in our party. Lastly, if we want to convert this to away, we simply we simply multiplier and G, which is 9.8 and so all together, what this is gonna look like symbolically is row l cute tree and from part, eh row is actually I want to be a little bit careful now to distinguish the M before and after the hole is punched. So it's called us and after. And this is also M after and so substituting in our expression for robe before all together it will be given by this. And so now it's just a matter of plugging in the various numbers.

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