Cube Definition and 613 Threads

Homework Statement Let X = ##\mathbb{R^m}## and ||.|| be a Norm on X. The dual norm is defined as ##||y||_*:=sup({\langle\,x,y\rangle :||x|| \leq 1})## a) Show that ##||.||_*## is also a norm b) Construct two norms ##||.||^O## and ##||.||^C## so that: {##x:||x||^O=1##} is a regular octahedron...

Homework Statement I have a value of $$ U=U_0+x (∂U/∂x)+y(∂U/∂y)+z (∂U/∂z)+1/2x^2(∂^2U/∂x^2)+1/2y^(2∂^2U/∂y^2)+...$$ We need to find the mean value of the U. So the answer is $$\overline{\rm U}\approx U_0+a^2/24(∇^2U)$$Homework Equations $$\overline{\rm U}=1/a^3 \int \int\int Udxdydz$$ The...

Homework Statement The figure shows a closed Gaussian surface in the shape of a cube of edge length 3.20 m. It lies in a region where the electric field is given by E=(1.65x+2.86)i + 4.39j + 5.47k N/C, with x in meters. What is the net charge contained by the cube? Homework Equations net...

Homework Statement A point charge q is placed inside a cube of side 2a. What will be the flux associated with the lower surface ABCD? Homework Equations I think I can apply Gauss Law here, but can't think of something connecting it with the lower surface. ∫B.dl = 1/ε° X Charge Enclosed The...

Homework Statement is cast irion body and face centenerd cube structure? wasnt quiet sure, i thought it was both because it can solidify different temperatures one of them Homework Equations mululpe different cast irons The Attempt at a Solution

Homework Statement There's a metal cunducting cube with edge length ##a##. Three of its walls: ##x=y=z=0## are grounded and the other three walls: ##x=y=z=a## are held at a constant potential ##\phi_{0}## . Find potential inside the cube. Homework Equations The potential must satisfy Laplace...

Homework Statement A rigid cube in the figure moves in space. At a certain time ##t## its front face ##ABCD## is vertical and the velocity of vertex ##A## is vertical down ##v## while the velocity of its vertex ##D## makes an angle with the vertical and has magnitude ##v_{2}## while lying on...

http://meetings.aps.org/Meeting/DFD18/Session/E19.1 link to presentation https://gizmodo.com/we-finally-know-how-wombats-produce-their-distinctly-cu-1830414749 This may belong in Fluid dynamics. It is begin presented at an APS Fluid Dynamics seminar. @boneh3ad might know more. Wombats...

What's the minimal angle of a ramp such that a cube with side 10 cm placed on it will tip over? The coefficient of friction between the cube and the ramp is 0.6. I have given it some thought and I have come to certain conclusions: I think that the cube will tip over once the force of gravity...

We have a glass containing 0.5 liter (0.5 kg) of water whose temperature 100 degrees Celsius. We also have an ice cube with mass 0.01 kg and temperature -10 degrees Celsius. The cube is put into the glass. The glass is then insulated from the outside world, until the cube has melted. What will...

Homework Statement A solid non-conducting cube of side l and uniformly distributed charge q, has electric field E and potential V at one of its vertex, imagine this cube to be made of 8 smaller cubes of side l/2. if one such cube is removed, find the new field and potential at the point where...

Proof by contradiction that cube root of 2 is irrational: Assume cube root of 2 is equal to a/b where a, b are integers of an improper fraction in its lowest terns. So the can be even/odd, odd/even or odd/odd. The only one that can make mathematical sense is even/odd. That is...

Homework Statement Griffiths' Introduction to Electrodynamics problem 2.10, Homework Equations Gauss' Law, ##\int_{S} \textbf{E}\cdot \textbf{dS} = \frac{Q_{\text{enc}}}{\epsilon_0}##[/B]The Attempt at a Solution It seems reasonable that the flux through the shaded surface and the front...

Homework Statement A metal cube is placed in an empty vessel. When water is filled in the vessel so that the cube is completely immersed in the water,the force on the bottom of the vessel in contact with the cube (A) will increase (B)will decrease (C)will remain same (D) will become zero...

Homework Statement A large sealed container full of air falls into the ocean. It has internal dimensions of 6.06 2.59 2.43 m, with walls made of steel (8050 kg m3 ) which is 2.00 cm thick. Does it float? Homework Equations FBuoyancy = density*volume*g weight = mg m = density*volume density of...

Hi, Sorry for this weird question. My computer crashed and also the notes in it. I had a book wherein I'd written all the formulae. There is one formula in notes of Power System. X = cube root of R. I remember there was a website that even had its derivation, but I don't have the bookmarks...

1. Homework Statement The 4.00 kg cube in the figure has edge lengths d = 8.00 cm and is mounted on an axle through its center. A spring ( k = 1400 N/m ) connects the cube's upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated 4.00° and released, what...

In an ABCD.EFGH cube whose side length is 8, the distance between the point G and the line BH is ... A. 4 cm B. 4\sqrt2 cm C. 4\sqrt3 cm D. 8\sqrt2 cm E. 8\sqrt3 cm I got \frac{8}{3}\sqrt6 cm. Do you guys get the same answer?

Given an ABCD.EFGH cube whose its side length is 8 cm. The point P is within AB so that AP = 3PH. The distance between P to AC is ... A. 2\sqrt3 cm B. 3\sqrt3 cm C. 2\sqrt6 cm D. 3\sqrt6 cm E. 4\sqrt6 cm So AH is 8\sqrt2 cm and PH = 6\sqrt2. What do I do now? Is the triangle HPC a right triangle?

Homework Statement Homework Equations Volue of a sphere: ##~\displaystyle V=\frac{4}{3}\pi r^3## Area of a sphere: ##~\displaystyle A=4\pi r^2## Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution The fixed area is k, the edge is a: $$6a+4\pi...

In plane geometry it is impossible to construct a line equal to the (cube root of 2) times the length of a side of a cube, making it impossible to double a cube with a compass and straight edge. Maybe plane geometry needs one more dimension. What happens if we extend the geometry to 3D(solid...

Homework Statement A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in _______ equilibrium with respect to rotation about the edge and in _________ equilibrium with respect to rotation about a horizontal axis that is...

Homework Statement Homework Equations Gauss's Law The Attempt at a Solution I simply used logic and observed the symmetry of the cube. If the charge is placed on the middle of the cube, the flux would simply be Q/∈0. The face of the cube itself can be split into 4 squares, with the charge at...

Hey guys, can't seem to make sense of this question from phys. It goes.. "A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure a. The atoms reside at the corners of cubes of side L = 0.200 nm. One piece of evidence for the...

Homework Statement Find the electrix flux through the top side of a cube. The cube's corner is on the origin, and is 'a' units on length. The charge 'q' is located at the origin, with the corner of the cube. Homework Equations Gauss's law and symmetry The Attempt at a Solution I take 8 cubes...

Homework Statement Conside the fig below. A tank of water (height of water column b) is kept on a electronic weighing scale . a metal cube (side a and density D) is hung from a spring balance and the spring balance is slowly lowered into the tank till the cube reaches the bottom of tank. The...

I'm using a non-polarizing beamsplitter cube in an experiment, but it's behaving in an unexpected way. I expected that, if a laser beam enters the cube from one side, ~50% of the beam passes through the cube in the same direction, while ~50% of the beam is reflected and exits the cube at a...

How can I calculate the length L of each side of a cubic simulation box with 500 molecules (in Ångstrøm) when I want molar volumes of V1 = 0.6 l/mol?

I did a PF search to try to see if this was discussed before, and didn't find what I was wanting to ask about (I could have missed it). :smile: I'm writing a Rubik's Cube game C/C# program for fun (starting with a console app and working up through various GUI options). I'd like to use a...

Hi, Just wondering if I'm going about solving this problem correctly: "A block of iron quickly sinks in water, but ships constructed of iron float. A solid cube of iron 1.6 m on each side is made into sheets. From these sheets, to make a hollow cube that will not sink, what should the minimum...

Homework Statement I'm given a force law is F = \frac{-k}{r^3} and that initially, the particle is in a circular orbit the particle is given an impulse parallel and in the opposite direction to its velocity find the distance from the center for the particle as a function of time. Homework...

Hello. I have some problems with making Lagrangian. I need your advice. 1. Homework Statement I have this situation: Consider the circular path is intangible and without friction. I have to find Lagrangian for coordinates x and θ. Homework Equations [/B] L = U - V The Attempt at a...

There are $9$ points in the interior of a cube of side $1$. a) Show that at least two of them are less than $\frac{1}{2}\sqrt{3}$ apart. b) Can $\frac{1}{2}\sqrt{3}$ be replaced by a smaller number?

Homework Statement A uniform charge density of 700 nC/m3 is distributed throughout a spherical volume of radius 6.00 cm. Consider a cubical Gaussian surface with its center at the center of the sphere. [reference picture] What is the electric flux through this cubical surface if its edge...

I've uploaded a picture instead of writing the whole problem. So the forces to consider here are - the weight of the cube, the normal force exerted on it by the funnel surface in contact, the centripetal force, and the frictional force. If there is no relative motion between the cube and the...

Homework Statement The electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude ##3 \frac{N}{C}## and directed outward from the axis of the rod. (a) How much charge per unit length exists on the copper rod? (b) What would be the electric flux through a cube of...

As per my understanding, a linear equation with two variables form a line segment (ax=by+c or ax+by=c) and linear equation with three variables form a plane (ax=by+cz+d or ax+by+cz=d). Am I right? And if I am right, does an equation with four variables form a cube?

Okay, I have a very simple question that...Suppose we have a very wide cube(dense and hard)...We place two persons at each of its ends...One the persons strikes its surface at one end. Now this person A will hear the sound due to vibrations of that end's surface (which further vibrate the air...

Homework Statement The volume of a cube is 'v' cubic yards, and its surface area is 'a' square feet. If 'v' = 'a' what is the length in inches of each edge?Homework Equations volume of a cube = e^3 surface area of cube = 6e^2The Attempt at a Solution volume of a cube = 'v' cubic yards...

Homework Statement A cube of side L=2m is made of a cooper cable with 2mm^2 of cross section area. 1) Find the electric resistance of one side of the cube. 2) Find the equivalent resistance in between the points A and B.

Good day members of physics forums . I am a university student currently studying thermodynamics and I just am a bit confused about a heat transfer problem. If you have the following items: 1 metal container which is well insulated from the outside ; ; 1 quantity of water and an icecube ...

During a random conversation with a friend, we got onto the subject of dropping a 6ft cubed cube of Hardened-Steel from the height of 100 meters. I ended up getting really curious about the energy it would cause, as well as the potential impact/destruction it would cause on the area...

Imagine I have a 10x10x10cm cube filled with a scintillating material (material capable of generating light when energized). Three cameras are looking at this cube from three orthogonal directions (x, y, and z). Light is generated inside the cube and is refracted as it leaves the cube and...

Homework Statement The force required to immerse a wooden cube of side 4 cm and relative density RD 0.5 completely in water is 1) 16x10-3 kgwt 2) 32x10-3 kgwt 3) 64x10-3 kgwt 4) 128x10-3 kgwt Homework EquationsThe Attempt at a Solution Density of the cube = 0.5 gcm-3 Volume of cube = 64 cm3...

I wonder if it is possible to at least estimate the stress (or the impact force) that the cube in question will experience due to the collision with the concrete floor. Assumptions: 1. The cube is dropped from height h 2. The cube is relatively small, thus we can neglect air resistance...

Homework Statement Vapors of 100 C is added to an ice cube of 0 C. How much of the ice cube has melted and what's the final temperature if the masses of the steam and the ice cube are 10.0 g & 50.0 g respectively? Homework Equations Lw = 3.33 x 105 J/kg cw = 4186 J/kg*C Q = m*c*ΔΤ Q =...

Homework Statement Consider a uniformly charged cube with uniform charge density ρ.The ratio of electrostatic potential at the centre of the cube to that of one of the corners of the cube is? A hint on how to approach the problem's solution would be appreciated.(whether to use gauss law or not...

]Homework Statement Solving the cubic equation x^3 + 6x = 20 by using formula gives (10+ sqrt(108))^1/3 - (-10 + sqrt(108))^1/3 How do you show that this comes out exactly 2? No calculators allowed.Homework EquationsThe Attempt at a Solution Tried cubing the expression and tried using the...

Homework Statement An ice cube of mass 0.01.kg at a temperature of 0 degrees Celsius is dropped into a cup containing 0.10kg of water at a temperature of 15 degrees Celsius. What is the max estimated change in temperature of the contents of the cup? SHC of water = 4200J per kg per kelvin...

EDIT ... ... SOLVED ...Can anyone help me with displaying the cube root of 2 as shown in the example below taken from Dummit and Foote, Section 13.4 ...https://www.physicsforums.com/attachments/6605Help will be appreciated, Peter*** EDIT *** Just found what I think is the solution ... it's...