deriving Definition and 962 Threads

I'm in third year undergraduate physics, and more and more I'm seeing problems in homework and assignments that say "Prove that" and "Show that", basically just deriving equations. There's just one problem, I can't do it for the life of me. I had a thermodynamics test recently, and despite...

A body of mass m is in a gravitational field of strength g. The body is moved through a distance h at constant speed v in the opposite direction to the field. Derive an expression in terms of m, h and h, for the work done on the body. Im bad with derivations, I need to get better. So...

I could use some help with this question: Derive the geometric series representation of 1/(1-x) by finding a0, a1, a2,... such that (1-x)(a0+a1x+a2x^2+a3X^3+...)=1 Thank you.

So the problem I am working on is: In the figure, find an expression for the acceleration of (assume that the table is frictionless). I have attached the figure of reference. I have so far tried to solve by first looking at m2 to get: 2T-m_2*g=m_2*a so T= (m_2*(a+g))/2...

Yeah this one is good... Derive the following: int(1/(x^2 + a^2)dx = 1/a*arctan(x/a) + C any idea how I would derive this thing? Cause I'm totally lost...

Hi everyone, Right now, I am working on a homework problem asking me to derive the Compton effect, which is given by \lambda\prime-\lambda=\frac{h}{m_ec}(1-cos\theta) A diagram of the situation can be found here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/compton.html#c1...

I've been given a small project to ease me into life as a PhD student and part of it involves working out Feynman rules for scalar bosons coupling to gauge bosons. I've been reading through Peskin and Schroder Chapter 9 and want to clarify if I've got my understanding right of how to do it...

Does anyone know how to derive the spherical unit vectors in the cartesian basis? Or a good link that might show how its done? I would also like to see it done for the cylindrical coordinates. I have tried to do it, especially for the spherical case, but i can only get r-hat. It would be...

I have a question from Strang's Linear Algebra on page 230. Does anyone know how to derive the attached statement?

Can anyone tell me how to derive the sin(x+y) and cos(x+y) expansions? The ones that are like cos x sin y or sin y cos x + other stuff? Preferrably, could this be derived with Euler's formula alone? Or something not too geometric? (All those OAs and OBs and XBs and XYs on geometric diagrams...

Newton's Law of Gravitation Derivative Hi, I was wondering if anyone could help me find the derivative of Newton's Law of gravitation [F=(GmM)/r^2] and what it means? What does the minus sign indicate? I'm kind of confused on the subject at hand and hopefully someone can help out. Thanks

y = ln[\sqrt(x^2+2)] I changed it to y = ln[(x^2+2)^{1/2}] I know the derivative of ln = \frac {1}{x} I'm not sure how to proceed.

I want to derive the theory of finite element using my own understanding. With this derivation i want to understand the fea theory of rod element I call the nodes as "points" in a structure. This scenario is for a simple one dimensional displacement of points(that is the single degree of...

A question asks for me to show that the minimum pressure of a star is given by: P_{min}=\frac{GM^2}{8\pi R^4} where M and R are the mass and radius of the star. My answer goes like this: Gravitational force towards center = \frac{GM(r)\delta M(r)}{r^2} Pressure force outwards =...

Well we start out with -\frac {d} {dt} \int_{V}^{} \sigma dV = \int_{\Pi}^{} \vec{J} \cdot d\vec{\Pi} Using the Gauss theorem \int_{V}^{} (\frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J}) dV = 0 so \frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J} = 0 and written in 4D...

I'm trying to linearize Klein-Gordon equation, following Dirac's nobel lecture: (E^2 - (pc)^2 - (mc^2)^2) \psi = 0 (E + \alpha pc + \beta mc^2) (E + \alpha pc - \beta mc^2) \psi = 0 Expanding the equations yields: -\alpha and \beta commutes with E and p -\alpha^2 = \beta^2 = 1 -\alpha...

I have to show that for a van der Waals gas the critical temperature, volume and pressure are given by: T_c= \frac{8a}{27bR} V_c= 3nb p_c= \frac{a}{27b^2} I started off this way: Van der Waals states that for a non ideal gas the pressure is: P = \frac{nRT}{V-nb} - a...

It's a really easy question, I know, but I must be doing something stupid. Can someone please spell out how to get the right hand side matrix form out of the individual equations? http://img234.imageshack.us/img234/8497/lorentz25wv.jpg

As a refresher exercise in modern physics, I want to derive Wien's displacement law: \lambda_{max}T=2.898x10^{-3}mK from Planck's formula: R(\lambda)=(\frac{c}{4})(\frac{8\pi}{\lambda^4})(\frac{hc}{\lambda})(\frac{1}{\exp^(\frac{hc}{\lambda\kT})-1}) by differentiating R(\lambda) and...

Hello. I need some help with the following problem. There is a cart on an incline and a pulley with a suspended block. Assuming that (the force of friction)= (mu)(N) symbolically show that the coefficient of rolling friction for the car moving down the incline plane with a constant...

I am trying to derive the geometric series for the following given identities, \begin{array}{l} \frac{1}{{0.99}} = 1.0101010101... \; \; \; {\rm{ (1)}} \\ \frac{1}{{0.98}} = 1.0204081632... \; \; \; {\rm{ (2)}} \\ \end{array} Here is my answer for (1), \sum\limits_{n = 1}^\infty...

For a van der Waals gas experiencing an adiabatic process derive the following expression: T(V-nb)^(R/Cv) = Constant I tried using PV^gamma = Constant with gamma = Cp/Cv and Cp - Cv = nR with PV = nRT but could not get it. Any hints? I would have to use Boyle's law to account for...

Using Newton's 2nd Law for a damped oscillator: ma = -kx - \alpha x which is a second order linear DE. To solve it we use the trial integrating factor e^{\lambda x} [/tex] to come to the root equation mx^2 + \alpha x + k = 0 where we can find our two solutions to be r_{1} \ and...

Ok these are the equations I am allowed to use. Ep=mg(delta)h w=fd v_av=(delta)d/(delta)t (delta)d=v1(delta)t^2 + 1/2a(delta)t^2 V2=V1^2 + 2a(delta)d w=work done(j) f=force(Newtons) d=distance(m) v_av=average velocity t=time(secs) v2=final velocity v1=initial velocity a=acceleration...

So, the average rate for a reaction of type A --> product is given by \text{rate} = -\frac{\Delta A}{\Delta t}. Also, \text{rate} = k \cdot \text{A}. The instantaneous rate for a reaction of that type is \lim_{\Delta t\rightarrow\0} -\frac{\Delta A}{\Delta t} = -\frac{dA}{dt}. Setting the...

Given the sum {_\lim {i} \rightarrow 0} \sum_{k=0}^{\frac{x}{i} - 1} i\sqrt{1 + i^{2n-2}((k+1)^{n} - k^{n})^{2}} I want to know how to derive to the value of this sum exactly. This is actually the value of the lenghts of a curve from a point to the origin of the form f(x) = x^n... I thought...

Two gravitaionally bound stars with equal masses m, separated by a distance d, revolve about their cneter of mass in circular orbites. Show that the period is proportional to d^3/2 and find the proportionality constant. I know that in this case, F = mv^2/r and that F=Gm^2/d^2. But where...

Most textbooks derive this formula by taking the derivative of the Lorentz position transformation. However, I've been presented the problem of deriving it using four velocities and the Lorentz transformation matrix. Unfortunately I've been looking at it for hours and still don't know how to...

Deriving a Launch Angle Equation -- Projectile Motion -- Please Help This is physics in the area of projectile motion. My class and I are doing a lab where we have to calculate the launch angle in order to perform a successful lab. The experiment is as follows: the projectile launcher releases...

Hiya, I have been looking at a problem, and just can’t get my head round the right way to tackle it. I have a whole heap of data for an airline showing the taxy duration of each of their flights (this is the time taken to go from the gate to actual lift off). As I see it, there are 3...

I was given the following problem for a homework assignment: Given F(x,v) = kvx where k is positive and the velocity is v-nought at x = 0, t = 0, what is x as a function of time? First I derived v as a function of position: v = v-nought + kx^2/2m Then, I derived x as a function of...

I have a question of the form, "how did they go from this step to that step?" I am following a paper from R. Kubo, called "The fluctuation-dissipation theorem". I suspect variable substitution and a simple assumption are used, but I don't know how. Here is the basic expression from which...

Hi there, I was wondering if anyone would be willing and able to help me with this question. Q. Derive the boundary condition satisfied by D at the interface between 2 media. I know that the D field is continuous at the suface, but I need to be able to derive this. If anyone can...

A spheroid is defined by: x2/a2 + y2/b2 + z2/a2 - 1 = 0 (equation 1) where a and b are the semi-major and semi-minor axes, respectively. If you have any two of x,y,z-values, you can solve for the third, simply by rearranging the above equation: x = +/- sqrt(1 - y2/b2 -...

The requirements, posed on a system given by the configuration coordinates q(t) = (q^1(t), q^2(t), ...) that (1) they be subject to 2nd-order equations of motion: q'(t) = v(t), v'(t) = a(q(t),v(t)) and (2) have a classical configuration space at each time: [q^i(t), q^j(t)] = is nearly...

Hey could anyone help me out there to know how you get to the formula of free fall displacement. D= 1/2 x g x t^2? I really have no clue of how to get it using other formulas. I started using the D=Vi x T + 1/2 x A x T^2 but then I got stuck I didnt know which other formula to bring into cancel...

In this problem, you will use your prior knowledge to derive one of the most important relationships in mechanics: the work-energy theorem. We will start with a special case: a particle of mass m moving in the x direction at constant acceleration a. During a certain interval of time, the...

I just have a quick question. I know that in physics and any other math, you can short cut your way if you know various relationships and thus you can derive various forumlas from a few simple ones. Is there any trick to doing this or an easier way, because i have never really been exceptionally...

For an undergraduate electrodynamics homework problem we were asked to derive the following: (griffiths 6.21) show that the energy of a magnetic dipole in a magnetic field B is given by - U = -m.B where B is the magnetic field and m is the dipole moment. I went about this...

How would you go about deriving the volume of a prolate spheroid using calculus? Would I use the method of shells? I am not sure where to begin. Any help and tips are greatly appreciated! Thanks :smile:

Please Help Me ! Hello, I REALLY need help deriving a function if f(x) = \frac{-x-2}{(x-2)^3} what would its derivative be? Here's what I did so far:: Using the quotient rule, f'(x) = \frac{(x-2)^3(-1) - (-x-2)(3(x-2)^2(1))}{((x-2)^3)^2)} = \frac{-(x-2)^3 +...

I haven't made any real calculations on this, just thought a bit in my head... Assume a square with side 1, meaning the diagonal would be 1.41. The distance between 2 corners if moving along the edges is of course 2. Now starting in upper left corner let's move 0.5 in x -0.5 in y 0.5...

I've been trying to derive general solutions for cubic roots, i.e. the general solutions of (will Latex just work?) $ax^3+bx^2+cx+d=0$ I do not want to be shown the solutions - but does anyone know what direction to go into achieve this? I thought I'd found solutions at one point but...

I've recently attempted the following problem, http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/June2001.html with the following solution http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/solutions/June2001.html I've managed to form the meaningful derivatives (as...

I am trying to derive an equation for the oscillation of a conical float. There is a conical float with a density of delta 2 and its floating on water with density 1. Find the oscillation of the floating conical float. The final solution should be: d^2y/dt^2=-g+(g((L-y)/L)^3)/p where y(t) is...

I can't figure out how to derive this. This is the formula for the volume of a cone. R is a constant and the side of the cone. Can be any real number. If anyone could take a crack at deriving this id be very greatful! V = \pi/3 * (R(1 - x/2\pi))^2 * \sqrt{(R^2 - (R(1 - x/2\pi))^2}

Ok so I understand how we derive Planck Length using the natural constants G,h, and c. However, how do we know this indeed represents the smallest possible length an object in the universe? Or does Planck length just represent the smallest possible length under which gravity is still influential?

How do you find the identity for sin(a+b) using algebra or calculus? I already know how to do it with geometry and by using imaginary numbers.

a uniform thin rod of length L and mass m is pivoted at one end the point is attached to the top of a car accelerating at a rate A. a) what is the equilibrium angle between the rod and the top of the car? b) suppose that the rod is displaced a small angle phi from the equilibrium derive the...

for shallow waves (where \lambda \leq 1/2 depth) in a tub, can anyone tell me why... speed\ of\ wave = \sqrt{gravity * depth} i mean, is there a way to get this formula by deriving from others?