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...