In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.
The cube is dual to the octahedron. It has cubical or octahedral symmetry.
The cube is the only convex polyhedron whose faces are all squares.
Homework Statement
Find the moment of Inertia of a cube (mass M, length L) around an axis going through one of the edges.
Homework Equations
I=Ʃmr2
The Attempt at a Solution
Well I imagined the cube is formed of infinitely many square plates. The width of the square plate is dL...
Homework Statement
Twelve resistors, each one with a resistance of R ohms, form a cube (see attached figure). Find R17, the equivalent resistance of a diagonal of the cube.
(The first attached picture was scanned from the book "Physics" by Halliday, Resnick and Krane, 4th edition.)...
Homework Statement
An insulating cube of edge a has a uniform charge density p. The charge is zero everywhere outside the cube. The potential at an infinite distance from the cube is taken to be zero. If the potential at the center of the cube is Vo, find the potential at a corner of the cube...
Looking around at all the cheap surplus beam splitter cubes out there. I've found no description of how things would be expected to behave outside of the spectral bands for which they're designed.
Leaving out the transmissivity of the glass itself, should I assume that when relative...
Homework Statement
Find the Green's Function for the Helmholtz Eqn in the cube 0≤x,y,z≤L by solving the equation:
\nabla 2 u+k 2 u=δ(x-x')
with u=0 on the surface of the cube
This is problem 9-4 in Mathews and Walker Mathematical Methods of Physics
Homework Equations
Sines, they have the...
Homework Statement
A cube of aluminum is 20 cm on edge. Aluminum has a density 2.7 times that of water (1 g/cm3) and a specific heat 0.217 times that of water (1 cal/g·C). The heat in calories needed to raise the temperature of the cube from 20°C to 30°C is about:
Homework Equations...
a,b,c are integers not all equal and w is the cube root of unity then minimum value of |a+bw+cw2|(w is not equals one).
My answer
|a+bw+cw2|<=|a|+|bw|+|cw2|
|a|+|bw|+|cw2|=a+b+c.
so at lest one value of |a+bw+cw2| will smaller than the minimum value of a+b+c. for integers this minimum...
Homework Statement
I'm trying to calculate the kinetic energy of a rotating cube about one of its face diagonals, using the moment of inertia tensor for the cube rotating around one of its corners.Homework Equations
T=\frac{1}{2}\omega\cdotL
L=I\omega
(I'm not sure how to signify vectors in...
Hi,
I want to charectize the function whose cube is smooth from R to R. For example x^1/3 is smooth and olsa any polynomial but how can i charectrize it?
Thanks
A cube of polished steel sits on top of a highly polished and waxed hemisphere of polycarbonate (radius 92 cm). For these two surfaces interacting, the coefficient of kinetic friction is the same as the coefficient of static friction. The cube is given a very small 'nudge' perpendicular to the...
Can you solve the volume of "a cube" with unequal heights?
I have a challenge for someone (which I plan on working on this weekend myself when I have free time from my homework).
Can you calculate the volume of a cube-like shape with four different heights and with perfect square base if you...
Homework Statement
The electric flux through each face of a 4.50m x 4.50m x 4.50m cube is 130Nm^2/C .
How much charge is inside the cube?
Homework Equations
Electric Flux = E*A = Qin/ε
The Attempt at a Solution
I know electric flux is given, 130Nm^2/C and I'm trying to solve for...
Hi,
I'm new on this forum. We have some science days in our school, and there is a big 1.5x1.5x1.5m ice cube melting. There is a contest who will guess the aprox. time that it takes to melt.
I think it will be more than two days, but I would like to get a more concrete answer somehow... :)...
1. The electric field in the region of space shown is given by E=(8i + 2yj) N/C where y is in m. A) What is the magnitude of the electric flux through each face of the cube. (3.0 M sides, 2.0m from yz axis)? B) Is there any charge in the cube?
2. E * da
3. To be honest I have...
Suppose 27 identical cubes are glued together to form a cubical stack. If one of the small cubes is omitted, four distinct shapes are possible; one in which the omitted cube is at a corner of the stack, one in which it is at the middle of an edge of the stack, one in which it is at the middle of...
Homework Statement
Suppose we there is a cube (a x a x a) made up of 8 protons. 1 at each point
What is the Electric Potential Energy
Homework Equations
U=q1*q1/4*pi*epsilon_0*r
The Attempt at a Solution
*U12 = Potential Energy to bring 2 to 1*
I'm aware of how to do the...
Homework Statement
An E-field is given as \vec{E}y = b\sqrt{y}\hat{j} V/m. Find the net flux through a cube with vertex at (0, a, 0) and side lengths a. (A picture is attached, but it is essentially the cube that would typically be at the origin, shifted along the y-axis by a units) (You can...
Homework Statement
So I need to find the total voltage across the current source.
Looking at the attachment, I took
front square: B_______C
......|.....|
......|.....|
......A_______D
back square: E_______H
......|.....|
......|.....|
......F_______G
Homework Equations
node analysisThe...
Hi,
I have no knowledge of Calculus. I am actually studying Computer Science. One of the exercises in the textbook I am using ("Python Programming" by John Zelle) suggests that the answer to the problem can be solved either through a simple simulation program or through calculus. I am still...
Homework Statement
Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not ). The number density is about and the temperature is about 3 K.
What is the edge length L of an LxLxL cube of gas with 1.0 J of thermal energy?
I found:
P =...
Homework Statement
I attached a picture to make it easier...
Homework Equations
Coulomb's Law: F=k(q1*q2)/(r)^2
a^2+b^2=c^2
Charge properties
The Attempt at a Solution
I uploaded a picture of one of the cleaner sheets of work I used so far...Basically, I suppose I'm at a...
Hi,
Is there any way to analytically calculate the perturbation of a uniform electrostatic field by a dielectric cube.
I know a solution exists for dielectric spheres but I haven't been able to come across the solution, when dealing with a cube.
Ohh.. and I'm assuming the simplest case...
What are the benefits of solving a rubiks cube?
I know chess is good for Logic, Concentration, Focus, Visualization and all that. However I don't have a chess board but do have a rubiks cube. Does the rubiks cube also help in those areas? More so or less so?
I would like to compile a short list of inverse-exponent force magnitude fall-off laws for several simple geometries for material made of monopoles and for material made of parallel dipoles (of negligible length).
Far field force for any two objects is, of course, proportional to 1/r^2 for...
Imagine a cube wrapped in Latin squares and try to solve the following puzzles. Please be aware the symbols at the borders are shared between neighboring cube's sides.
Let me know if you like it or not.
This is rather straightforward:
This is a bit harder
Lets us say I have a cube and I apply to a face of the cube a heat flux of 100 watt/m^2.
Lets us say i divide the face of the cube into say 10 elements (area of each face of the element is 1 m^2).
What will be the flux on each element , will it also be 100 watt/m^2?
Sorry for a...
Homework Statement
A cube of gold (resistivity ?R = 2.44 10-8 O m, density ?D = 1.93 104 kg / m3, and specific heat c = 129 J / kg °C) that is 3.5 mm on a side is connected across the terminals of a 40-µF capacitor that initially has a potential difference of 340.0 V between its plates...
A wire is broken down into 12 pieces so that each piece is of resistance 1R. The pieces are joined together to form a cube. What would be the resistance at the diagnols of the 4 faces of the cube?
Homework Statement
The mass of the piece of ice is 0.25kg.
Heated by an electric heater (assume there is no loss of energy to the surroundings)
Started at -30°C at 0seconds
After 150s the ice cube is -10°C
Homework Equations
Q=mL_{f}
\Deltat=Q/P
The Attempt at a Solution...
I'm only interested in the 2d representation of this, as I will be applying whatever I learn to a physics engine
Anyways, I know that a block resting on a flat surface will have a normal force acting on it equal to its weight
However, I'm not interested in gravity
But, say a block comes...
I put 1 litre of ice cube to the micro-oven which is age is about 30 years. The shape of the ice cube was a little bit circular. I set the power of the micro to the maximum. There were continuous white electric shocks inside the micro. The ice cube contained a little fish which contained some...
Hi.
I am trying to calculate the thermal stresses in a steel cube which is placed inside another steel cube of bigger dimensions, supported by steel bars at the base and sides.
Both the cubes are in contact with fluids at different temperatures.
Can someone please suggest the methodology as i...
Parallel axis theorem, cube! (Confirm)
// Idisp = Icenter + mass[ (RdotR)*I - RcrossR ]
So to test it out, I create a long box at the origin, and then a smaller
box, half its width, so I can offset it along the x axis, and times it by
2, so it should equal the inertia tensor of the long...
My answer is 12.9 grams, and the correct answer is supposed to be 11.9 grams. I cannot figure out why? Note. the answer i got is 12.9, and not 11.06. I know for this situation, the heat absorbed by the ice equals the heat lost by the water and aluminum, and since there is a phase change from a...
I'm trying to find out what the rotation group of a cube is. It seems natural to view it as a subgroup of S_{6}, because any rotation is just a permutation of the faces of the cube. The sources I've seen say that the rotation group of a cube is isomorphic to S_{4}, because rotations can be...
Homework Statement
A block of wood, of side 2a and mass M is on an horizontal plane. When it turns, it does it over the edge AB. A bullet of mass m<<M and velocity v hits on the opposite face to ABCD, at a height of 4/3*a. The bullets gets stuck on the block. Find the minimum value of v so...
Homework Statement
Evaluate the surface integral. For closed surfaces, use a positive orientation.
\mathbf{F} = <x,2y,3z>
S is a cube with vertices <\pm1, \pm1,\pm1>
Solution
[PLAIN]http://img34.imageshack.us/img34/9730/unledjfx.jpg The Attempt at a Solution
I understand that my book...
Hi there,
If A is unitary I understand that it obeys AA+=1 because A-1=A+.
Why does A3=1?
The explanation simply says that "A just permutes the basis vectors"..
It then goes on to say that since A3=1, then eigenvalue a3=1 also, which are 1, ei.2pi.theta/3, and ei.4pi.theta/3. This...
I'm not sure this question goes here, but I'll post anyway.
Is it possible to express the problem of solving Rubik's cube in mathematical terms? Furthermore, is there a definite strategy to solve it?
Homework Statement
Dear All,
I am having problems understanding how to deal with related rates. The problem is the following:
A solid 400gm metal cube of size length 10cm expands uniformly when heated. If the length of its side expand at 0.5cm(hr), find the rate at which, after 5...
Homework Statement
Given that the equation x^{3} + ax^{2} + bx + c = 0 has the roots r_{1}, r_{2}, r_{3}, develop formulae for r_{1} + r_{2} + r_{3}, r_{1}r_{2}+r_{1}r_{3}+r_{2}r_{3}, r_{1}r_{2}r_{3}
Homework Equations
The Attempt at a Solution
Not really sure where to...
Homework Statement
Hello! I am going to do a demonstration involving the Leslie's cube to demonstrate the emissivity of a thermal radiation from different surfaces. I have been reading some about black body radiation which has emissivity = 1 but this is not the case. Leslie's cube has 4...
Homework Statement
an ice cube is melted in water which is continuously stirred to be at a constant temperature of 0 degrees. the stirring is gentle enough so the work done is negligible.
my question is why in this case does the heat come from the air to melt the ice cube and not the...
I came up with a math research topic dealing with fluid dynamics, but I do not understand fluid dynamics much, so I would like to know what happens in the following situation:
A cube is on the bottom surface of a room. The cube is to be filled with a certain amount of fluid, and the room is...
1. Find the cube roots of the complex number 8+8i and plot them on an Argand
diagram
Thats the problem, I've had a go at the solution and came up with 3 solutions using the \sqrt[n]{r}*(cos(\frac{\theta+2\pi*k}{n})+isin(\frac{\theta+2\pi*k}{n})), but the answers (roots) I get, I can't plot it...
Homework Statement
A wood cube .30m on each side has a density of 700 kg/m^3 and floats levelly in water. (a) What is the distance from the top of the wood to the water surface? (b) What mass has to be placed on top of the wood so that its top is just at the water level.
Homework...
Homework Statement
Find the moment of inertia of a cube, all edges length A, with mass M through the centre ( through mid point of 2 opposite sides)
Homework Equations
I = integral( r^2 dm
dm = density x volume where volume of a slice ( thin) square = AxAxdx = A^2 dx
= p A^2...
Homework Statement
Let f(x)=x^{1/3} show that it is uniform continuous on the Real metric space.
Homework Equations
By def. of uniform continuity \forall\epsilon>0 \exists\delta>0 s.t for \forall x,y\in\Re where |x-y|<\delta implies |f(x)-f(y)|< \epsilon
The Attempt at a Solution...
Does the magnetic field increase linearly with the number of magnets? For example, will 8 1/2 inch neodynium cubes have the same strength as a 1 inch cube?
Thanks in advance