It is important to remember that force is a vector and that pressure force in liquid is perpendicular to the surface. If the liquid container does not have the shape of a vertical prism, then the force on the bottom surface is not equal to the weight of the liquid, because weight of the liquid...
The last equation holds for any vertical column with constant cross-section (prism). If the liquid has any other shape, you can still derive the same equation for imaginary vertical column in the liquid. "vertical" means directed in direction of gravitational acceleration. This way the pressure...
Hi,
I already posted this in solid state physics forum, but no one answered, so I guess this topic might belong to Mathematics.
I read a text about crystallography where matrices were designated in the form:
(S2 O S1)
where S1 is input coordinate system, S2 is output coordinate...
Dot product and cross product are simply definitions of functions that depend on two vector variables. Definitions need no proof, however their potential usefullness should be justified.
Here are two simple applications of dot product and cross:
1. Calculation of work done by a force. If...
Hi,
I read a text about crystallography where matrices were designated in the form:
(S2 O S1)
Where S1 is input coordinate system, S2 is output coordinate system and O is the operator
corresponding to the matrix. I found this designation is often more useful than the
usual...
Can anyone explain how Lorentz factor is defined (the one from theory of diffraction,
not special relativity)? I read that intensity of diffracted beam is proportional to
Lorentz factor, but I could not find its definition.
On what parameters does the Lorentz factor depend? How does the...
I think I understand the units now.
The unit of distance/the difference between two lowest energy states of hydrogen atoms is:
E0=5.9*10^-6 eV
A quantum particle with this energy has a frequency:
f0=E/h=1.4*10^9 Hz
The unit of time corresponds to this frequency...
I would like to understand how units of distance, time and mass are defined on
the golden record on Voyager spacecraft .
I suppose the units are similar to natural units (speed of light=Planck constant=1), except that the basic unit is not GeV:
The unit of energy is the energy...
Thanks for the replies.
I have another question:
Is it obvious that any object which causes an oscillating
electromagnetic field in it's neighbourhood will emit
electromagnetic power? Or does such object exist which has a
zero time average of emitted power?
For example, to prove...
1. Can a solenoid connected to alternating current generator be used as transmitter of electromagnetic radiation?
2. Can a solenoid be used as a receiver of electromagnetic waves?
I think point 2. is possible, since alternating magnetic field will induce voltage in the loops of solenoid...
Problem: We want to calculate a polynomial of degree N-1 that crosses N known points in the plane.
Solution A: solving a NxN system of linear equation (Gauss elimination)
Solution B: construction from Lagrange basis polynomials.
One of my professors said that the first solution is...
This is a known old experiment for measuring G. I have seen the instrument at my college.
check http://en.wikipedia.org/wiki/Cavendish_experiment
However it is difficult to perform properly, because gravitation forces are so small.
You have made a mistake with the assumption that there...
You are right, I derived with respect to the wrong variable. I wanted to calculate the derivative of gamma at least at integer parameter values, but it seems I won't be able to do this, since I can't calculate the resulting integral.
I have tried to calculate the derivative of Gamma function and got a strange result, which
is obviously wrong. Can someone find the mistake?
Definition:
Gamma[z]=Integral[t^(z-1)exp(-t)dt]
Derivative:
(d/dz)Gamma[z]=Integral[(d/dz)t^(z-1)exp(-t)dt]=Integral[(z-1)t^(z-2)exp(-t)dt]=...
First I thought that the computer model was just wrong. But it is also possible that the plunger is supposed to shift to a new position instantly, so that the molecules could not push it back (like in Hirn's experiment). In this case the molecules simply fly over the free space without doing any...
I have some questions about thermodynamic potentials (internal energy U, enthalpy H, Helmholz free energy F, Gibbs free energy G):
1. The differentials of potentials:
dU<=TdS-pdV
dH<=TdS+Vdp
dF<=-SdT-pdV
dH<=-SdT+Vdp
Do this equations apply only for a single homogeneous system or can...
The simplest example is a cylinder full of gas, closed by a piston, where you can add energy by two ways:
1. Compressing the gas with pushing the piston (this is adding work)
2. Putting the cylinder into contact with a body with higher temperature (this is adding heat)
In the first case...
I agree, it is possible to convert some of the horizontal kinetic energy into vertical kinetic energy by placing the leg (or two legs) at an angle (lower than 90 degrees) to the ground, absorbing the radial kinetic energy and keeping tangential kinetic energy (which has a positive vertical...
I read an introductory text about diffraction of X-rays in crystals and I am not sure why the wavelength in the crystal is assumed to be identical to the wavelength outside the crystal. I think that the speed of electromagnetic waves can depend on the type of matter, so wavelenghts can be...
That is not completely true. In theory a particle can have a well defined position (if wave function is delta) or momentum (straight wave), just not both at the same time.
How to open a file with a name that is not defined in advance, but
is entered after the program is executed?
I am using fopen function, but it seems that it's argument must be
a fixed string, not a variable.
If you are solving geometry problems with both distances and velocities involved, then you
are probably making a mistake: remember that they have different units! (unless you study relativistic theory)
For the mentioned problem you should use formulas:
s=R*fi (fi is angle of the part of...
I think I got the solution now. The unknown pressures on element surfaces should be left as unknown variables in the Lagrange equations together with unknown displacements and a sistem of linear equations can be obtained, where the unknown vector contains both unknown displacements and...
1. I read that each gene has a 50% chance to be transferred to a single gamete.
Does the distance between two genes on the same chromosome influence the conditional probability for the second gene to be transferred to the same gamete as the first one?
2. Can the process of reproduction...
Probably the safety distance propotional to the velocity (constant safety time) is most reasonable. If this time is higher than your reaction time (usually about 1 s), then this will allow you to start braking before the car in front, so you can't crash if both can the same deceleration...
I am trying to make a program that solves elasticity problems with finite element method and
I don't understand how to bring in boundary conditions.
Constant displacement boundary conditions seem simple: replace variables that represent the displacements at surface nodes with the prescribed...
1 vs. 1 trading of human energy for industrial energy was not practival even in the second half of the 18. century, when Watt invented the first usefull steam engine. And of course is even less practical now. However it may seem reasonable to buy that bike if you like a lot of (indoor) physical...
So steel can be found in different phases, based on the temperature. Let's say that we determine the phase and the temperature. Is it possible to determine atom structure mathematicaly then?
How are atoms inside a steel arranged?
Ussually we can get the data about the mass share of different elements of steel and the lattice type. But the lattice only tells us where an atom is situated, not the type of the atom. Can we tell anything about the type of the atom at a certain...
I have some questions about CSL (coincidence site lattice) boundaries between crystal grains.
1. What is the relation between twin boundaries and CSL boundaries? Is it true that all twin boundaries are CSL boundaries, but not vice versa? Is the energy of twin boundaries even lower that the...
The only unknown thing is the function f: one must measure it experimentaly. If you only care about one particular real life problem, then you only need the value of f for that problem: you get this value by one experiment on the model that gives the same argument for f as the real life problem.
To be more precise, I would like to know the positions of atoms to determine stress tensor in any point in the material (not necessary near the surface).
It seems straightforward to calculate strain tensor from the deformation of base vectors of Bravais lattice, but I'm not sure if they can...
The formula is correct, but the projectile velocity is probably much lower (maybe 400 km/h?). I assume the game does not consider air resistance (you can check this by observing the symmetry of the trajectory). You should use your formula for range(angle) to calculate theoretical range (with...
I heard that it is possible to measure positions of individual atoms in a crystal. Is this true?
I understand the principle of measuring crystal orientation and base vectors of Bravais lattice with X-ray, but I have no idea how positions of individual atoms can be obtained. I suppose it is...
I am trying to understand how to solve a certain type of elasticity problems.
Let's say that we have an isotropic material (2 elastic constants are known) in zero gravity with a shape of a half space
(limited by the boundary plane and infinite on one side of the plane).
Boundary conditions...
You must distinguish between the power lost in the transmitting wire and power lost in the whole circuit (wire+load).
we want to minimize power lost in the wire at the fixed power at load P(load):
P(wire)=I*V(wire)=I^2*R(wire)
Obviously we must minimize I. Since the same I also runs...
I think the original poster is trying to overgeneralize a formula that connects air pressure with the weight of the air column.
Formula p=rho*g*h
or more accurately dp=rho*g*dh
can only tell us the difference in pressure in a gas or fluid. It is of no use when one puts
a substance into...
When the soup is heated close to the boiling point and one puts noodles inside, it boils over (even if it is put away from the fire). Does anyone know why?
You can determine a pressure in a material by:
A) determining the outside pressure
In this case the material will compress until its internal pressure will balance outside pressure.
B) determining the volume.
In this case you just force the material into a certain volume and it will...
After measurement of momentum the wavefunction colapses into an eigenstate of momentum operator. After measurement of position the wavefunction colapses into an eigenstate of position operator. Those two eigenstates are always diferent. So even if we had a time machine, it would be imposible to...
I would like to explain the theoretical "100 % efficiency gun" a little better:
let's say that we have a very long (but finite) frictionless tube with length L and cross-section S, closed at one end. The tube contains ideal gas at a very high temperature T on a small volume S*dL near the...
I don't think a water gun or pneumatic gun can be considered a heat engine, since they are
not powered by heat: they are powered by work of the pump that maintains pressure. Water or air is just used to transfer force or temporary store energy. Converting heat to work is a much more difficult...
Theoreticly a gun could have 100% efficiency: if the barrel were very long and frictionless, the bullet very heavy and we would fire it in space, then nearly all of the thermal energy of the gas would be transferred to kinetic energy of the bullet. The efficiency would approach 100% when the...
I am learning for our second full year quantum mechanics subject (last year of undergraduate education). The topics include group theory, first and second quantization, Heisenberg and interaction picture, system of N particles, standard model, Klein-Gordon and Dirac equation...
Does anyone...