Derive Definition and 591 Threads

Homework Statement 14.6 The coefficient of kinetic friction between the slider and the rod is μ, and the free length of the spring is ##L_0 = b##. Derive the expression for the work done by the friction force on the slider as it moves from A to B. Neglect the weight of the slider. Homework...

Homework Statement Derive the expression for the work done by the ideal spring on the slider when the slider moves from A to B. Assume that the free length of the spring is (a) ##L_0 = b##; and (b) ##L_0 = 0.75b## Homework EquationsThe Attempt at a Solution Can you check if my solution...

On the Simpson's Rule wikipedia page they mention in their derivation that the calculation can be simplified if one notices that there is no loss in generality in setting ##a=-1## and ##b=1## for the integral ##\int_{a}^{b}P(x)\cdot dx## as a result of scaling. I'm not entirely sure what...

Homework Statement I need to find the intial velocity of a ball, given the angle the pendulum bob swings through. I need to derive this equation. [/B] V0=4.43mtotalL1/2{1-cosΔθ}1/2/mball Homework EquationsThe Attempt at a Solution I have barely any attempts since I can't even think where to...

I understand that there are roughly ##N=10^{79}## nucleons in the visible Universe. This number comes from adding up the nucleons of ##100## billion stars in ##100## billion galaxies in the visible Universe i.e. $$N=\frac{10^{30}}{10^{-27}}. 10^{11}.10^{11}=10^{79}$$ where mass of sun is...

Homework Statement A particle of mass m is dropped from a height h, which is not necessarily small compared with the radius of the earth. Show that if air resistance is neglected, the speed of the particle when it reaches the surface of the Earth is given by ##\sqrt {2gh}## ##\sqrt {\frac {R_E}...

Let $S_n(k)$ be defined by: $S_n(k) = 1 + 2k+3k^2+...+(n+1)k^n$, where $|k| < 1$ and $n \in \Bbb{N}$. Derive a closed form for $S_n(k)$ and find the limit: $$\lim_{{n}\to{\infty}}S_n(k)$$.

1. The problem statement, all variables, and given/known data Homework Equations The Attempt at a Solution So basically I took vertical direction formula and I solved for "t". I then took the horizontal direction formula and solved for "x" or we can also call x the "Range" since that's...

Einstein's field equations (EFEs) describe the pointwise relation between the geometry of the spacetime and possible sources described by an energy-momentum tensor ##T^{ab}##. As well known, such equations can be derived from a variational principle applied to the following action: $$S=\int\...

<Moderator's note: Moved from a technical forum and thus no template.> 1st time posting, be gentle. Physics with calc 1 Im reviewing my exam which i did poorly on and can't understand why things are done, i have many questions but ill start with one, and since I am new maybe someone can tell...

Homework Statement Hi again, I will re-write this on behalf of a request. I am struggling trying to derive these equations for a physics lab. The equations asked to derive are the equations that describe a perfectly elastic collision between objects of identical mass. These are given to me...

All, I need help deriving the Transfer Function of this circuit from first principles. http://i66.tinypic.com/24v3z9s.jpg

I just watched this video that perfectly explains how to derive the equations for the slip angle of a car: However, how could this be done for a three axle system (car-trailer)? Would you have to express distance a (in the video) in terms of b (distance from centre of gravity to the second...

Homework Statement Action attached: To find the EoM of ##\phi ## / ##\phi^* ## Homework Equations The Attempt at a Solution [/B] Without deriving from first principles, using E-L equations I have: ## \partial_{u}\frac{\partial L}{\partial_u \phi} - \frac{\partial L}{\partial \phi} =0 ##...

Homework Statement Use ##~\cos\alpha-\cos\beta~## to develop the formula for the derivative of cos(x) from the definition: $$\frac{d(\cos x)}{dx}=\lim\frac{\cos(x+\Delta x)-\cos x}{\Delta x}$$ Homework Equations $$\cos\alpha-\cos\beta=(-2)\sin\left( \frac{\alpha+\beta}{2} \right)\cdot...

Homework Statement In the chapter about differentiation there is this question: Homework Equations Cosine rule: $$a^2=b^2+c^2-2bc\cos\alpha$$ $$\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$$ The Attempt at a Solution $$a^2=b^2+c^2-2bc\cos\alpha$$ $$d^2=e^2+c^2-2ec\cos\beta$$...

Question Background: I'm considering the Eddington-Robertson-Schiff line element which is given by (ds)^2 = \left( 1 - 2 \left(\frac{\mu}{r}\right) + 2 \left(\frac{\mu^2}{r^2}\right) \right) dt^2 - \left( 1 + 2 \left( \frac{\mu}{r} \right) \right) (dr^2 + r^2 d\theta^2 + r^2 \sin^2{\theta}...

Homework Statement Derive the mirror equation for a convex mirror (Si*So=f^2). Do not use a Ray heading toward the center of curvature point (C). Si - distance between the object's image and the focal point. So- distance between the object and the focal point. Do- distance between the mirror...

<Mentor's note: Moved from a technical forum and thus no template.> A ring's kinetic energy is integral of 0.5v2 dm. Distance X is rΘ, and Θ is defined as distance traveled/radius, so X is r*distance traveled / r. Velocity V is X divided by time, so V is r*distance traveled / rt, and I define...

I am trying to derive weak-field Schwarzschild metric using Linearized Einstein's field equations of gravity: []hμν – 1/2 ημν []hγγ = -16πG/ c4 Tμν For static, spherically symmetrical case, the Energy- momentum tensor: Tμν = diag { ρc2 , 0, 0, 0 } Corresponding metric perturbations for...

Hello, so my question is, if for some metric, we have found (somehow) Fμν, and we know that: Fμν=∂μAν-∂νAμ, how do we find Aν? I tried solving the differential system after imposing the Lorentz gauge ∂μAμ=0 but still, without some initial guess about which components of A are zero, the system...

The question is about to derive an approximate expression by regular solution theory, It is difficult for me to find relevant source on this question. However, the question to me is so vague that I do not know how to answer. What I have tried is to search what the interaction parameter is...

Homework Statement Playing in the street, a child accidentally tosses a ball (mass m) with a speed of v=23 m/s toward the front of a car (mass M) that is moving directly toward him with a speed of V=20 m/s . Treat this collision as a 1-dimensional elastic collision. After the collision, the...

I thought this mental experiment: consider an inertial frame of reference solidal to a particle moving with velocity v respect to another inertial frame of reference, i got to find the momentum in the second frame of reference (in the first is 0 since is solidal with the particle) p= m* dx/dt...

Homework Statement "By choosing the lower limit of integration in Eq. (28) in the text as the initial point ##t_0##, show that ##Y(t)## becomes ##Y(t)=\int_{t_0}^t(\frac{y_1(s)y_2(t)-y_t(t)y_2(s)}{y_1(s)y_2'(s)-y_1'(s)y_2(s)})g(s)ds## Show that ##Y(t)## is a solution of the initial value...

I'm studying for my electrodynamics exam and one of the past exam questions is: From the scalar and vector potentials, derive the homogenous wave equations for E and B fields in vacuum. I did derive the wave equation for the B field by simply taking the curl of the homogenous wave equation for...

Homework Statement derive the equation of motion of a mass-spring-pulley system using lagrange's equations. A mass m is connected to a spring of stiffness k, through a string wrapped around a rigid pulley of radius R and mass moment of inertia, I. Homework Equations kinetic energey T = 1/2...

Problem attached. I would appreciate anyone's help. I am an alloy chemist working on an MS degree in materials engineering and have come to the mechanical engineering part of the program and am feeling a bit behind. Deriving an equation for this case is proving to be difficult for me although...

Homework Statement "Derive the equations for position (in terms of acceleration, initial position, initial velocity, and time) and velocity (in terms of constant acceleration, a, initial velocity, v0, and time, t) from the definitions of position, velocity, and acceleration (derivative...

Homework Statement Spherical,homogeneous star with radius R orbiting black hole at distance ## r_p >>R ## .Derive the tidal force acting upon the star by dividing the star into two equal parts and making the necessary approximations. Homework Equations The tidal force equation of ## a \propto...

Homework Statement I am given this equation: where m and M are masses. I have to obtain the following as a final result: Homework EquationsThe Attempt at a Solution so far, I have done this (This may not be the most efficient or the easiest way, but it is how my professor wants it to be...

I have seen that the energy of the band structure is defined in the following form. How do you obtain this form of the equation? Additionally, how can you obtain the effect mass of the electron? Do you just manipulate algebraically the equation of the energy of the band structure and solve it...

Derive a reduction formula for the integral: $\int \sec^nx dx, \;\;\; n \ge 2.$ - without any help from an online integrator.

Homework Statement A wooden toy mouse of mass (m) is attached to a spring with constant (k) and suspended vertically as shown below. The toy is released at the point the spring is unstretched at position x = +A, passes through equilibrium at x = 0 and the spring’s maximum extension occurs at x...

I'm studying for my introduction to modern physics exam, and reading about the ultraviolet catastrophe and why equipartition theorem stops working to explain blackbody emissions for high frequencies I was thinking if we could use the theorem to arrive at the quantification of energy (probably...

Homework Statement Two rods of the same material, of equal length l, and of cross section A and 2A respectively, are mounted between two rigid (i.e., nondeformable) cross frames. The frames are pulled by a pair of forces P, located at distance x from the thin bar. Derive an expression for the...

I've already read the derivation in which we use the light pulse clock kept in a spacecraft such that the light pulse follows a zig-zag motion due to motion of the spacecraft being perpendicular to motion of the light pulse. Then, we apply Pythagoras theorem to derive the formula. BUT this...

Homework Statement Show that the energy, E, that needs to be supplied to an ideal refrigerator to cool a mass M with specific heat C by \DeltaT from an initial temperature T_i is: E\sim \frac{MC\Delta T^2}{2T_i} Homework Equations Carnot efficiency where T_i is the starting higher temperature...

There's one equation that I've seen being used already, which by itself is quite simple, but I can't understand where it comes from. The context is as follows: suppose we have one heat engine operating between systems A and B whose temperatures are T_A>T_B. Let's suppose further that the...

I'm really lost on this one. I'm really not sure how to get started on this. I started it out as a force problem and solved for ax = g*cos(theta). I then integrated that (treating it like a constant) from zero to D to find my initial velocity at the time the block reaches the edge of the...

I understand that the fusion of hydrogen to helium in our sun's core generates gamma rays. My question is how are these gamma rays transformed to the full spectrum of photons that we that we observe from earth?

Consider this equation: f(x(t),y(t))=2(x(t))^2+x(t)y(t)+y(t) One way to calculate df/dt is directly using the chain rule: \frac{df}{dt}=4x(t)\frac{dx}{dt}+\frac{dx}{dt}y(t)+\frac{dy}{dt}x(t)+\frac{dy}{dt} \frac{df}{dt}=(4x(t)+y(t))\frac{dx}{dt}+(x(t)+1)\frac{dy}{dt} Another way is by using...

Everybody knows what is the Wave Function is. $$\Psi=\space e^{i(kx-\omega t)}$$ or $$\Psi=\space cos{(kx-\omega t)} \space - \space isin{(kx-\omega t)}$$ But can anyone tell me how it is derived. Since Schrodinger Equation is derived so easily using this Wave Function. I think it is necessary...

Homework Statement I'm watching this lecture and wanted to attempt to derive the expression for ΔTo/ΔTs Homework Equations ΔTo = ΔTs + VΔTo / U The Attempt at a Solution I have worked out that ΔTs = 1-V / U, however I'm stuck trying to get ΔTs / ΔTo because of the ΔTo on both sides of the...

Homework Statement Consider two points located at ##\vec{r}_1## and ##\vec{r}_2##, and separated by distance ##r = |\vec{r}_1 - \vec{r}_2|##. Find a time-dependent vector ##\vec{A} (t)## from the origin that is at ##\vec{r}_1## at time ##t_1## and at ##\vec{r}_2## at time ##t_2 = t_1 + T##...

[Mentor note: Thread moved from technical forums so no formatting template shown] Unfortunately, I'm completely lost with this question: 1. A particle is moving along the x-axis. Its position as a function of time is given as x=bt-ct^2 Derive an expression for the x- component of velocity...

i get stuck in how to find the magnitude of rotating vector . why say that |dA/dt|=A(dθ/dt) but who we can derive it or interpret this fact

Hello! I'm trying to derive the linear velocity vector from the position vector and the angular momentum vector. I've seen on the internet that V = W x R (V,W and R are all vectors and x is the cross product) but I cannot for the life of me derive it! I've tried doing it by writing out the...

Homework Statement I want to derive these equations Homework EquationsThe Attempt at a Solution But I don't have any idea how can extend cos(summation) and sin(summation) in form of Bessel function or product of Sin(wmt+phim)

Homework Statement D1=6cm D2=2cm ( i have to prove that 2nd moment of area (J) of a circulal plate abouts its polax axis(zz) is equal to piD^4/32 ) Homework EquationsThe Attempt at a Solution J=pi6^4/32 - pi2^4/32 = 125.66 J=r1^2x2pirdr J=Integral 2pir^3d2 = 2pi integral(high 3 , low 1)...