Relationship Definition and 999 Threads

Homework Statement Prove the relationship $$\left(\frac{\partial H}{\partial\lambda}\right)_{nn} = \frac{\partial E_{nn}}{\partial\lambda},$$ where ##\lambda## is a parameter in the Hamiltonian. Using this relationship, show that the average force exerted by a particle in an infinitely deep...

Homework Statement in the first photo , the direction of x-ray and the atomic plane are shown. whereas for the 2nd photo , the the direction of x-ray and the atomic plane are not shown... so i would assume the glancing angle = 0 . beacuse the atomic plane is [FONT=Georgia]parallel to the x-ray...

What is the relationship between heat and thermal energy?

Homework Statement Find the relationship of acceleration between the masses, m1, m2 and m3 where m1>m2>m3. The question has a free pulley in the left attached to mass m1. then goes through a fixed pulley , through a free pulley that is attached to m2 and then through a fixed pulley, with the...

Homework Statement As shown in the plot above, terminal velocity is shown to increase linearly with the number of coffee filters dropped in a turbulent (air) medium. Therefore, terminal velocity depends on mass. Give an explanation for this starting from Newton's laws.Homework Equations \vec{F}...

Homework Statement When lights falls on metal suface , electrons are emitted if the wavelength of light is less than or equal to λ , .If lights of 0.5λ is used , then maximum kinetic energy of electrons is E . if lights of 0.25λ is used , what's the maximum kinetic energy of the electron...

I am doing a ER Diagram for a class and having a lot of trouble with a specific piece of the sentence. Anyway, here is the business requirements we are diagramming: The video rental company has several branches throughout the USA. The data held on each branch is the branch address made up of...

Hello there, so today I started doing my research on oscillations in a course on advanced mechanics. The experiment was to mathematically model the speed of sound in air and experimentally prove the usability of the model. To keep it simple and pose my question as directly as possible, my...

So pretty frequently I encounter questions like a) Are these vectors linearly independent? b) Do they span all of R? Why? As I understand linear dependency, the linear combination of the vectors in question exists as the Null vector for some set of coefficients.

Homework Statement Why does 25 atomic ppm oxygen mean 25 moles of oxygen in 1e6 mole Fe? Homework Equations # = mol*Avo The Attempt at a Solution I understand the ppm (parts per million) part. Hence why 25 ppm means 25:1e6. What I do not understand is how they go from atomic to...

Full title: Relationship between the constructibility of regular polygons and the reducability of trigonometric functions into expressions of square roots. I stumbled upon this after I derived the formula for the area of a triangle given it's side length x as a trigonometry exercise. ## A =...

Homework Statement An electrical engineer in your semiconductor company is working on a design of an electrical contact with a Si wafer. The electrical contact is in the form of a thin Cu “finger” touching the back side of a wafer as shown below. The electrical engineer claims that he is...

Hi, PF: I'm currently about to graduate from my Ph. D. program in Physics and I want to focus my research in theoretical physics. I feel very excited by topics such as Astrophysics and GR, but also low temperature physics, such as superconductivity, bose-einstein condensation, superfluidity...

I am conducting an experiment on the parabolic trough that concentrates the solar light and heats up water. I am using different metal sheets (zinc, aluminium, copper, tin...) for the parabolic trough to see the differences in temperature change. I researched on a few things and I understand...

As many people know, you can use electrical energy to create magnetism (electromagnets) and you can use permanent magnets to create electrical energy through induction (generators, the rotor inducing the stator). So what is the relationship here? Magnetism is not a form of energy or an energy...

Does light energy(waves) affect sound waves...? i read in one post that light affects sound indirectly.If yes how do we relate and calculate that..?

1. I have a question regarding the equation ΔG° = -RT lnK. When solving for the equilibrium constant K, what is the relationship between the vapor pressure of each molecular compound in a reaction? ΔG° = Free energy change R = Universal gas constant T = Temperature K = equilibrium...

Homework Statement Consider a solid disk of mass m and radius R rolling along a horizontal surface with the center of the disk moving horizontally with a speed v. The total kinetic energy of the disk is a combination of translational kinetic energy , KEt and rotational kinetic energy, KEr...

Hello Guys, From the torque curves of most of the ic engines it can be seen that torque is maximum at a particular rpm range then it starts dropping. It is said that the torque is maximum when the volumetric efficiency is maximum , i just can't understand the relationship between the both...

hi guys, I have been doing a research on white dwarf stars and chanrashekhar limit. I need to plot a graph for the mass-radius relationship of the dwarfs. from the equalization of the hydrostatic equilibrium pressure and the electron degeneracy pressure I found out the radius -mass relationship...

This is about attempting to solve ##\left( y'\right)^2 = y^2 - 1 ##. \int\frac{dy}{\sqrt{y^2 -1}} = \pm \int dx using a trig. substitution and another trick, \int\frac{dy}{\sqrt{y^2 -1}} = \ln\left(y \pm \sqrt{y^2 - 1} \right) + C I'm not sure about that \pm sign. It came in when doing \tan...

Hi, I have a question I'd like some help with which is related to my job working with drill rigs. Where you have a cylinder such as a drill string where the forces of the ground pressing in from all sides how much influence does the surface area have on the rotational force required to...

Homework Statement State the mathematical relationship (Linear,Quadratic,Exponential) and determine the regression equation for this relationship. Homework Equations X| 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | Y| 50 | 14 | 2 | 14 | 50| 50 |194|302| The Attempt at a Solution ?.? i...

There is this girl that I am interested in. We have talked at school over the last couple of months. Should i ask her to hang out first. Or should i ask her on a date. And this should probably be in person. I'm worried about moving to fast. What kind of things can I say to her to see if she...

Hi, folks I have had a hard time to find out whether or not there is a theorem in Linear Algebra or Spectral Theory that makes any strong statement about the relationship between the entries of a Matrix and its Eigenvalues and Eigenvectors. Indeed, I would like to know how is the...

E=mc² shows the relationship between matter (mass) and energy, but another elementary information in the atomic physics is the electrical charge. So exist some relationship between energy and electrical charge?

Question:- A block of mass 10 kg moving with a velocity of 1 m/s collides with a spring of force constant 1000 N/m. Calculate the compression of the spring at the moment when kinetic energy of the block is equal to one-fourth of the elastic potential energy of the spring. Attempt:- Step 1...

Hi, I am a bit confused with the relationship between gravitational field strength and gravitational potential. As far as I know, gravitational field strength is defined as: g=\frac{F}{m}=\frac{GM}{R^{2}} and gravitational potential is defined as: V=\frac{-GM}{R} Now if I...

Homework Statement I'm trying to find a relationship between spring and torsion constants for an experiment but am not sure what it is and am struggling to find it. Homework Equations Torque = Torsion Constant * Angle of Twist Force = Spring Constant * Extension Shear Modulus...

I've been wondering for a while why force is the negative derivative of potential energy. In our books, they write that F=-dU/dx, and U=-W I don't really understand why it should be negative. Doesn't the force need to be positive in order to increase the potential energy? For example, when you...

Why is e^-1 the inverse of natural log e? Thank you

I am having trouble with this number density astrophysics question. Any help is greatly appreciated: Consider a galactic disk with radius much larger than its thickness. Let R be the radius and the thickness be 2H where H is the ‘scale height’ of the disk. For a population of objects with...

I am very familiar with the equation: $$f(t)=Asin(ωt+ϕ)$$ Used to describe the instantaneous value f(t) of a wave with amplitude A, frequency ω, and phase shift ϕ at time t. This equation is very intuitive to understand: As t increases the value within the sin operator will increase from ϕ...

Hello. I need some help with one question about relationship of two matrices. The task: Suppose that I is identity matrix, u - is vector, u' is transposed vector, α - real number. It can be prove that inverse matrix of I+α*u*u' has similar form I+x*u*u'. The task is to find x. I tried to...

I carried out an experiment in a wind tunnel and it shows that as I increase the air velocity the water temperature drop is bigger but the rise in air temperature going through the radiator becomes lesser. Am I wrong to understand that its due to the fact that the air mass flow rate has...

So K = kcm + kint Since kcm relates to the center of mass, am I correct in my understanding to state kcm = 0.5mv2cm? What about kint? What does this variable refers to conceptually?

Homework Statement Moist air at 32 degrees C has a dew point of 26 degrees C. The total or atmospheric pressure is 100.7kPa. find the: Molal Humidity Relative Humidity Homework Equations Molal Humidity = \frac{P_{i}}{P_{tot} - P_{i}} Relative Humidity = \frac{P_{i}}{P_{vap}}...

Homework Statement Prove the formula xcscx=2B(ix)-B(2ix)Homework Equations B(x)=x/((ex)-1) sinx= (eix-e-ix)/2i The Attempt at a Solution I know that it makes sense to use the formula for B(x) with x=ix and x=2ix, and rewrite xcsc(x) as x/sin(x), plugging the above relevant equation in for...

Hello everybody. This is my first post here and I hope I'm not asking a question that's been addressed already (I did try to use the search function, but couldn't find what I'm looking for). Both the Bayes theorem and the law of large numbers are mathematical theorems derived from...

Homework Statement "Suppose x[n] is a DT (discrete time) periodic signal with fundamental period N. Let us define x_{n}[n] to be x[n] for n ε {0, 1,2, ... , N-1} and zero elsewhere. Denote the Fourier transform of x_{n}[n] with X_{n}[e^jω]. How can one find the Fourier Series coefficients...

When I look up curriculums at school, I always find the main sequence of Calc 1-3(single variable to multivariable) then differential equations. But when I look up the definitions, diff equations are just called "equations and how they relate to their derivatives." I'm assuming there's more to...

I have a question about a spring gun. Suppose the barrel of a spring gun is placed horizontally at the edge of a horizontal table. You put say a marble in the barrel and compress the spring x cm and after releasing the marble it travels a horizontal distance of y cm before hitting the floor (so...

Decoherence relationship to the "measurement problem" I have heard the argument that "decoherence" in quantum states causes the quantum collapse to occur, and that this solves the "measurement problem". But I'm still left with a nagging question... Does decoherence only produce quantum collapse...

Homework Statement Given an electric field: E=Ex*ex+Ey*ey with Ex=cos(kx-wt) Ey=cos(kx-wt+e) where e is the phase difference Show that Ex^2 + Ey^2 - 2*Ex*Ey*cos(e) = ( sin(e) )^2 Homework Equations Ex=cos(kx-wt) Ey=cos(kx-wt+e) The Attempt at a Solution Was...

I just listened to a lecture on this, and I'm not sure I quite get the point. What the lecturer did was examine coherent states in the simple harmonic oscillator then linked excitations of an oscillator to the number of field quanta. The goal of the lecture was to show how Maxwell's...

cyclotron -- relationship between velocity and radius in a cyclotron the radius of the path of electron increases.but how if the velocity of the electron is accelerated its kinetic energy should only increase but why is it's radius increasing despite the fact that it's moving to the dee with...

Homework Statement Consider two unshaded circles ##C_r## and ##C_s## with radii ##r>s## that touch at the origin of the complex plane. The shaded circles ##C_1,C_2...C_7## (labeled in counterclockwise direction sequentially) all touch ##C_r## internally and ##C_s## externally. ##C_1## also...

Homework Statement Prove that the group velocity of a wave packet is equal to the particle’s velocity for a relativistic free particle. Homework Equations vgroup = Δω/Δk = dω/dk E = (h/2π)*ω = √(p2c2 + m2c4) The Attempt at a Solution I'll be honest..I have no idea where to...

Homework Statement We calculated times of the periods of varying pendulum lengths. (20cm, 40cm, 60cm, 80cm). Then the frequency was calculated for each length and then a frequency-length graph was made. Since the graph is an exponential relationship we graphed our values on a log-log chart...

Hi all, After reading Feynman's Lectures I see that his way to understand energy is as a conserved quantity. On the last days then I've seem Susskind's lectures on classical mechanics and he also defines energy like that. He says that energy is a conserved quantity, being able to characterize...