Derive Definition and 591 Threads

Hi, I was wondering how to derive relationship between radiocative constant and half life, which is t1/2=ln2/b, where b=decay constant. It seemed like the it was just replaced into the equation A=A0(1/2)t/t1/2. Thanks in advance

How to derive "dark energy" density from Jorrie's Hubble radius limit (c^4/(8 pi G))*3*(17.3e9 light years)^(-2) Paste that in the google window, and see what you get. When I paste that into google I get 0.5393 nanopascal, which is equivalent to 0.5393 nanojoule per cubic meter. If the...

Hello everyone! I'm trying to learn the derivation the covariant derivative for a covector, but I can't seem to find it. I am trying to derive this: \nabla_{α} V_{μ} = \partial_{α} V_{μ} - \Gamma^{β}_{αμ} V_{β} If this is a definition, I want to know why it works with the definition...

Homework Statement Use \frac{\partial z}{\partial r}=\cos\theta\frac{\partial z}{\partial x}+\sin\theta\frac{\partial z}{\partial y} and \frac{\partial z}{\partial\theta}=-r\sin\theta\frac{\partial z}{\partial x}+r\cos\theta\frac{\partial z}{\partial y} to show that...

Homework Statement For an electrochemical cell Gibbs free energy is is given by G=-nFE Gibbs free energy for a reaction at any moment in time and standard state free energy is given by G=Go + RT lnQ Derive an expression relating standard state cell potential and equilibrium constant for...

Q. Use the addition formula cos(u+v) = cos(u)cos(v) - sin(u)sin(v) to derive the following identity for the average rate of change of the cosine function: (cos(x + h) - cos x) / h = cos x ((cos h - 1) / h) - sin x ((sin h) / h) A. cos(x+h) = cosxcosh - sinxsinh subtitute this to...

Homework Statement Obtain deflection curve in terms of q, L, and EI Homework Equations Use the second order differential equation of the deflection curve to solve. Meaning that the M(x) is the second derivative and you integrate twice to get V1 and V2 The Attempt at a Solution From the...

Hi Folks,I have come across some text where f(x,y)=c_1+c_2x+c_3y+c_4xy is used to define the corner pointsf_1=f(0,0)=c_1 f_2=f(a,0)=c_1+c_2a f_3=f(a,b)=c_1+c_2a+c_3b+c_4ab f_4=f(0,b)=c_1+c_3bHow are these equations determined? F_1 to F_4 starts at bottom left hand corner and rotates counter...

I am new to this site. I have a problem with the derivations of second order equations for SHM. F= -kx F+kx+0;ma+kx=0 m(second time derivative of x)+k(first time derivative of x)=0 As my textbook says above equation implies that x(t)=Acos(ωt+∅) But I can't understand why. From where did...

Homework Statement Derive the relation: E' = \gamma (E + \beta p c)Homework Equations p' = \gamma p \\ E^{2} = p^{2} c^{2} + M^{2}c^{4}The Attempt at a Solution start off with stationary frame S E=mc^{2} then in moving frame S' E'^{2} = p'^{2} c^{2} + E^{2}: lorent transform momentum: E'^{2} =...

In a Griffith's book (page 15-16) an author derives a momentum operator. In the derivation he states that he used a integration by parts two times. He starts with this equation which i do understand how to get to. $$ \begin{split} \frac{d \langle x \rangle}{dt} = -\frac{i\hbar}{2m}...

Homework Statement Derive the formula for final velocity, v_2, without time included in said formula. \overrightarrow{a}: Known \overrightarrow{s}: Known v_1: Known \Delta t: Unknown (can be calculated, but defeats the purpose) \overrightarrow{v_2}: Unknown and to be calculatedHomework...

Homework Statement The relationship between pressure and volume of an ideal gas is expressed as pv=constant in a reversable isothermal condition. Show that the relationship between pressure and volume of the same gas is expressed as pV^gamma=constant in a reversible adiabatic condition where...

At our QM intro our professor said that we derive uncertainty principle using the integral of plane waves ##\psi = \psi_0(k) e^{i(kx - \omega t)}## over wave numbers ##k##. We do it at ##t=0## hence ##\psi = \psi_0(k) e^{ikx}## \psi = \int\limits_{-\infty}^{+\infty} \psi_0\!(k) \cdot...

Homework Statement (a) A ring with charge Q and radius R is in the yz-plane and centered on the origin. What is the electric potential a distance x above the center of the ring? (Use any variable or symbol stated above along with the following as necessary: k.) (b) Derive the electric...

Hello ! I have an upper triangular matrix for an operator T in which an eigen value has been repeated s times in total. Derive an expression for s . My thoughts : ( Let * imply contained in ) then :I know that : (a) Null T0 * Null T1 *...*Null Tdim V = Null Tdim V + 1 = ... (b) Will i...

Assume you have no knowledge about the microscopic information, all you know about the system of pure material is it's equation of state and number of particles. Why can't we get Cv=(∂U/∂T)V from here(if this is wrong how do we solve it?)? Why can we obtained some other quantities just from...

Homework Statement A jaguar(A) leaps from the origin at a speed of v0 = 6 m/s and an angle β = 35° relative to the incline to try and intercept the panther(B) at point C. Determine the distance R that the jaguar jumps from the origin to point C. given the the angle of the incline is θ = 25°...

Say I have a mass m on a non linear spring k with some damping b. I start with the restoring force of the spring F=-kx+x^3... the x^3 is the non linearity. Set that equal to Newtons second law F=mx'' = -kx+x^3 Add in the damping which is dependent of velocity bx' ......mx'' = -kx +...

Hi everyone, I'm trying to follow how Dirac went about deriving his wave equation. I know there's a couple of different ways to "derive" this, but I'm trying to follow the original method that Dirac used. There's a lot of good stuff online for this, but there's a step that I get stuck at and...

Homework Statement a) Use Planck’s radiation law to derive the Stefan-Boltzmann law for the case of zero background temperature (i.e., T0 = 0). Homework Equations http://csep10.phys.utk.edu/astr162/lect/light/plancklaw.gif The Attempt at a Solution So I know we are suppose to...

derive the density of an ideal gas as a function of temperature?? Homework Statement Derive the density of an ideal gas when it is allowed to expand as a function of temperature when pressure is kept constant/ Homework Equations The Attempt at a Solution density= PM/(RT) , where...

Hi I am a new member and put illustrated diagram and my answer for Ra and Re but stuggling with how to calculate the other reactions of the beam, one other thing on the illustrated diagram it show w1, w2, w3 the weight is 0.2 kg on each load case, i think this needs to be converted 0.2 x 9.81 =...

I am reading Resnick and Halliday's "Basic Concepts in Relativity" (ISBN: 0023993456) and have come to an impass about deriving equation 3-4a \begin{equation}m = \gamma m_0\end{equation} in the text. The authors wrote that the equation can be derived from the following equations...

Homework Statement { y }_{ f }={ y }_{ i }+{ v }_{ yi }t+\frac { 1 }{ 2 } { a }_{ y }{ t }^{ 2 }\\ { v }_{ yf }={ v }_{ yi }+{ a }_{ y }t Derive { { v }_{ yf } }^{ 2 }={ { v }_{ yi } }^{ 2 }+2{ a }_{ y }({ y }_{ f }-{ y }_{ i }) 2. The attempt at a solution This isn't an actual...

How did scientists derive the formula -GMm/r=Ep in order to calculate the amount of work required to move an object from an infinitely large point (or an extremely large distance as my textbook says) ?

Homework Statement Apply the physical pendulum equation to a ring pivoted on its edge to derive the equation for the period of a ring pendulum for small oscillations about the pivot point. Include a diagram showing the restoring torque acting on a ring pendulum displaced from equilibrium...

1. Hello there, I am a first year undergraduate mechanical engineering student, looking for help on a question. "Figure Q2 shoes a schematic diagram for an aircraft catapult system. The aircraft is represented by the mass A (Ma), and μ is the coefficient of friction between the aircraft and...

\Gamma(n) = int(0 to infinity)[(x^(n-1))*e^-x]dx Show that it can also be written as: \Gamma(n) = 2int(0 to infinity)[(x^(2n-1))*e^(-x^2)]dxI have no idea how to go about this. I have tried integration by parts of each to see if anything relates, but how can you get from an exp(-x) to and...

I am trying to find out how to derive the cyclotron and synchrotron frequency, but everywhere I look it is derived by saying that the force of the magnetic field is not qvB, but (v/c)qB. What on Earth is this c? I am guessing it means speed of light but then it is not the case that (v/c)qB =...

Homework Statement We did a lab in my PHYS with Caclulus I class involving a collision of cart A (given an initial push) and cart B (initially at rest) on a relatively smooth surface. *At the moment of the collision, the two carts become attached, providing a completely inelastic collision*...

As per: https://en.wikipedia.org/wiki/Elementary_charge Charge is quantum. As per https://en.wikipedia.org/wiki/Magnetic_flux_quantum Magnetic flux is quantum. Magnetic flux is measured as follows: Magnetic flux = \frac{Energy * Time}{Charge} Thus: \frac{Charge}{Magnetic flux} is...

Starting with: x'=\gamma(x-vt) & x=\gamma(x'+vt') I know that I can derive t'=\gamma(t-vx/c^2)... however I can't seem to make it fall out mathematically. The suggested method is to cancel x'. Can anyone help me out on the steps? Much appreciated! :)

Homework Statement Derive the formula v= (v'+u)/(1+v'u/c^2) the velcoty addition formula using the below formulas? Homework Equations 1. vt1=L+ut1 2. (proper time)=(proper length)/v'+(proper length)/c 3. ct2=L-ut2 4. (dilated time)= (proper time)/(sqrt(1-v^2/c^2)) 5. L=(proper...

I was just curious, sorry if it is already asked, I was going through a book on photonics and came across the relation coherence time, t = λ*λ/Δλ I did not find any proof of this. Can anyone explain me how this relation is found?

My question is how to get from equation A to B. By using partial fractions? differential? any methods?

Starting with the expressions for average acceleration (Change in Velocity over Change in time), average velocity at constant acceleration; algebraically (NO CALCULUS) derive the equation for one-dimensional motion that relates displacement to the acceleration, assuming acceleration is constant.

1. Derive Wien's displacement law from the Planck Spectrum. 2. Planck's Law: \frac{2hv3}{c2(e\frac{hv}{kt}-1)} Where v = frequency; c = speed of light; h = Plank's constant k = Boltzmann's constant The Attempt at a Solution Well, the first thing I wanted to confirm was that this was in fact...

Hi, dear all, hope your guys allow me to ask this tricky question. Refer to the attachment, i would like to derive the principal radii of an ellipse, the final equation and figure is provided in Stephen Timoshenko Theory of plates and shells 2nd edition. consider the ellipse has form...

Homework Statement Derive the expression v = lnfn where ln is the shortest distance between nodes for the nth harmonic. Homework Equations v = wave speed ln = shortest distance between nodes for the nthharmonic fn = frequency of the nth harmonic The Attempt at a Solution Is it...

So i am having a slight problem deriving this equation. there is a simple way which is v=u+at -> t = v-u/a s = (v+u)t/2 so s = (v+u)*(v-u)/2a 2as = (v+u)(v-u) 2as = v2-u2 v2=u2+2as but i am having trouble understanding this way V2=(u+at)2 V2=(u+at)(u+at) V2=u2+a2t2+2uat - i can't...

"why does the professor derive the equation?" I often hear people of other majors (engineering) ask me why the professor derives the equation to be used in some situation (like a continuous charge distribution electric field from coulomb's law divided by the test charge) instead of just giving...

I have a function, x(t), where x and t are real scalars. I have been trying to derive an analytical expression for the nth derivative of x with respect to t:x^{(n)}(t) \triangleq \frac{d^n}{dt^n}x(t)= \ \ ?However, getting a general expression is proving tricky. Meanwhile, I have managed to...

I am aware that physicists are trying to derive born rule from unitary evolution. Has there been any success? What is the current status of that program?

Homework Statement I should derive \vec{F_{q}} = \frac{-q'^{2}}{4∏ \epsilon_{0}} \frac{r'/a}{(r'^{2} - a^{2})} \hat{r} from \vec{F_{q''q'}} = k\frac{q' q''}{\left|\vec{x'} - \vec{x''}\right|^{2}} Homework Equations The Attempt at a Solution I know that q'' = -q'...

1. (x=X1+vt1, x1=x-vt ) 2.(t=t1+vx1/c2, t1=t-vx/c2 ) I know that 1. is x in terms x1 and x1 in terms of x. I understand it very well, the adding and substracting of velocity. But i am unable to understand the 2.how these equation are derived and what does they mean. The mane...

I am a third year undergrad in the UK and I have been looking over my first year notes on special relativity. I found this passage talking about predictions we can derive if light is corpuscular. "If light is corpuscular (emitted like bullets) one expects the speed of light to depend on the...

Homework Statement A subway train travels over a distance s in t seconds. it starts from rest and ends at rest. In the first part of its journey it moves with constant acceleration f and in the second part with constant deceleration r \, . Show that s \, = \, \frac {[\frac {fr} {f \...

Homework Statement Hey, For an assignment I need to derive the optimal angle for maximum range (derive Equation 2 below). I know how to derive equation 1 but I need to derive the second equation so I can substitute h = 0, and h = 1, into it, to show the optimal angle for maximum range for...

Homework Statement There is a fixed spherical body of mass M whose center is to be taken as origin. Another body of mass m whose initial position vector \vec{r} is given. This body is projected with initial velocity \vec{v}. Find the equation of trajectory of body with mass m around the body...