Conservation Definition and 999 Threads

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I want to derive from ##T^{\mu \nu}_{,\nu}=0## the equation: ##\int T_{0\mu}d^3 y=constant##, I don't see how exactly. From the derivative I know that ##T^{0\mu}_{,\mu}=0##, but I don't see how to integrate this equation, it's ##T^{00}_0+T^{0i}_i=0##. But how to proceed from here? Thanks in...

The solution is an application of the law of conservation of energy. Start with equation (1). The masses are in equilibrium and are not accelerating. This implies that ΔK = 0, because the kinetic energy will not change without acceleration. Thus, we are left to find equation (2) in terms of θ...

I can't seem to wrap my head around the notion of conservation of quantum information. One thing that might help that is if someone can tell me what the associated symmetry is. For example, phase symmetry leads to conservation of electric charge according to Noether's theorem; a fact that...

If we have a two dimensional measurementbasis, then we have two possible outcomes of the measurement. Now I figured: considering the law of conservation of energy, if one particle goes in, one and only one can come out. So outcome "both results simultaneously" cannot happen, for that would...

Hi, Since this is a question about COAM (Conservation of Angular Momentum), I will assume I can leave out the part on translation and just use the formula below: ##Initial Angular Momentum= Final Angular Momentum## whereby ##I = \frac {1}{12}ML^2## (of rod) So, ##\frac {1}{12}ML^2(1.5)=\frac...

I encountered a weird conflict between my thought process and that of author's solution in book: The common viewpoint of both of us were invoking conservation of energy of this SHM system But the author proceeds to solve it using conservation of momentum, taking the new mass added to system as...

The vacuum density, or the zero point energy, of a field, doesn't change as space expands, it remains constant. But, aren't particles and virtual particles just fluctuations of these fields? Meaning as space expands, more and more particles are being created, violating conservation of energy?

I have tried using Conservation of Energy but I'm getting incorrect answer.

I want to ask why is it that we use gauge pressure instead of absolute pressure in CV analysis for momentum conservation of fluids. I did read that because P(atm) would be present everywhere so it won't have a net effect on the CV but it's highly non intuitive as I can't apply force balance on...

So to start off, the piece that hits the ground first is the smaller piece. So I can form the equations where: where ##8(u_{8kg})= m_{1}v_{1}+m_{2}v_{2}## ##m_{1}+m_{2}= 8## After 2 seconds, ##30 = v_{1}(2)+\frac{1}{2}at^{2}## ##v_{1}= 5.2m/s## ##(30-16) = v_{2}(2)+\frac{1}{2}at^{2}## ##v_{2}=...

Hola! So my first approach to this is use both the conservation of energy and momentum equations since collision between the first two objects are elastic. Let the 3 blocks be a,b and c (from left to right) Does this means the following: whereby ##v_{a} ##= speed of block a after collision...

I just have a basic physics question about bicycles that has been confusing me. Consider three situations. In the first situation a person, of mass m, is running down a street at constant velocity v1. In this case the person is converting energy stored in their body into translational kinetic...

In Newtonian mechanics, conservation laws of momentum and angular momentum for an isolated system follow from Newton's laws plus the assumption that all forces are central. This picture tells nothing about symmetries. In contrast, in Hamiltonian mechanics, conservation laws are tightly...

In my most recent thread, I discussed the conservation law involving the 4-velocity vector: gab(dxa/dτ)(dxb/dτ) = -c2 Now, I've read that you can apply this law to the Euler-Lagrange equation in order to get some equations that are apparently equivalent to the geodesic equations. Now here is...

In my quest to learn how to solve the geodesic equation, I came across this law which apparently holds true for all metrics (according to what I read): gab(dxa/dτ)(dxb/dτ) = -1 Well, I tested this formula out with Minkowski space (- + + + signature): If I understand correctly, then in...

It is said that for a particle in a box the energy is in a superposition. If indeed that is the case what happens when a measurement is made where does the excess energy go. Of course, that is based on my understanding is that superposition is a real physical and not platonic.

If someone could advise what I've done wrong it would be much appreciated. How have they eliminated the initial and final for y, and simplify only to y? Also, how did they simplify to a positive 2? What algebraic steps have I missed? Thanks for your help.

I suppose that the principle of conservation of angular momentum holds also for a cloud of particles weekly interacting at low pressure, density and temperature. And it should be still applicable when the particles or the atoms would start condensing and forming fusion products or simply solid...

Hi, I understand and I'm sorry that there are going to be many loopholes in what I'm trying to put together and that too without any mathematical formulation but I don't even know where and what to start with. Suppose we have a finite length insulated hollow cylinder filled with with air at 1...

Problem Statement: Are this 3 topics comes under laws of conservation of momentum? Relevant Equations: Are this 3 topics comes under laws of conservation of momentum? Are this 3 topics comes under laws of conservation of momentum: energy lost due to impact, inelastic impact, purely elastic...

2 bodies that have distance d between them are distancing from each other because Hubbles law. at time t=0 distance between them was d(0) and speed between them was 0. If no force interacts with them then distance is increasing by rate ##\frac{\partial d}{\partial t}=H_0*d## Is it correct...

Problem Statement: Hello! I'm trying to learn how to know if a particular interaction is allowed or forbidden. I found 3 decays which i can't understand. Relevant Equations: The decays are: 1) \eta \rightarrow \pi ^{0}+\gamma 2) \phi \rightarrow \rho^{0}+\gamma 3) \eta \rightarrow \pi...

I write Conservation of Energy: Potential Energy loss(change): U = m g ##\Delta##h = m g (R+r) (1-cos##\alpha##) kinetic Energy gain(change): K = (##\frac {m v^2} 2## + ##\frac {I \omega^2} 2##) + (##\frac {M v_2^2} 2## + ##\frac {I_2 \omega_2^2} 2##) U = K m g (R+r) (1-cos##\alpha##) =...

A cyclist coasts along a road, he drives across a small puddle of water, after which the wheels leave wet lines on the road. Now we concentrate our attention to the linear momentum of the water on a wheel. It decreases. Momentum is conserved, so what got the momentum that the water had?

Part (iii) is the part I am stuck on and is a 5 mark question. I have some idea of how to attempt it shown below momentum is conserved so mux = mvy + mvz (where ux is the initial velocity before the collision of ball x, vy is the velocity after the collision of ball y and vz is the velocity...

So, I was reading my textbook in the section regarding net torque, and they gave an example of a seesaw with one person at each end, and they said that there is a net external torque due to the force of gravity on each person. I completely understand that; however, when I was reading another...

Let v be the speed of the block and x elongation of the spring beyond the equilibrium point. Initially, v = 0 and x = 0. At the maximum elongation, the block also has v = 0, it has moved a distance equal to x (parallel to the plane) and the variation of height is equal to -x⋅sin(53°). W(FNC) =...

I'm thinking through a few basic things - hopefully in a new way. One thing that struck me is that momentum (mv) and energy (e.g. 0.5mv^2) can be conserved but velocity is not. For one thing, velocity is relative, of course. I'm wondering whether there's a quantity a bit like velocity but not...

Hi all, I struggle to understand how energy is conserved I fission. If the binding energy per nucleon increases, surely the mass defect simply accounts for that difference to conserve energy before and after. How does the mass defect account for the kinetic energy of the fission fragments as well?

I am confused about the cosmological constant and dark energy. In the most accepted theory, energy is created as the vacuum of space expands. This contravenes the conservation of energy. The law of conservation of energy does not hold in curved spacetime but isn't our universe flat spacetime ...

If we have an object in space (deep space where it is under no other gravitational influence) and we push it a little so that it gains some velocity and after some time comes into the influence of a planet's gravitational field and crashes on it. Where is that energy from the crash coming from...

Here are the two questions I want to compare: 1. A student of mass 62 kg stands on an upholstered chair containing springs, each of force constant 2.4 × 103 N/m. If the student is supported equally by six springs, what is the compression of each spring? 2. A 0.20-kg ball attached to a vertical...

A while back I thought of an issue with parallel charged plates. Imagine this: a set of opposite charged resistive plates with holes in the center. In theory, there is a finite amount of energy required to push a positive charged particle through the hole in the positive plate (in theory it...

I understand that ##\dot m=\rho Q## and ##{\dot m}_{in}= {\dot m}_{out}## . So one can say that ##\rho Q_1 = \rho Q_2##. But I'm not sure if that equation is correct. I don't know if the density remains constant, or the volume flow rate. And then how I'm also supposed to tie a state equation in...

Why is angular momentum conserved for a charge in an electric field?

Hello, I am an undergrad and am in an introductory level astrophysics course. I have a bit of confusion that I didn't know where to get help from so I made an account here. Please let me know if I miss some common etiquette or something... I don't understand how the slingshot maneuver...

My only issue is what this would look like. I can't draw a respective picture.

Hi, once again I'm probably asking a question that is more about human physiology than physics (I recently asked a question that had to do with hearing). I found a (definitely too hasty) reference to a ballistocardiograph in a high school textbook. So I got curious about the way this apparatus...

Suppose we have a quantum object in superposition to some measurement basis, given by: ##\frac{\sqrt{2}}{\sqrt{3}}|a \rangle + \frac{1}{\sqrt{3}}|b \rangle##. (1) Suppose the measurement is made, and the system evolves, according to MWI, into ##\frac{\sqrt{2}}{\sqrt{3}}|a \rangle|W_a \rangle +...

Homework Statement Homework Equations $$F = \nabla \phi$$ The Attempt at a Solution Let's focus on determining why this vector field is conservative. The answer is the following: [/B] I get everything till it starts playing with the constant of integration once the straightforward...

I have a problem in mechanics. On the wedge and block only the gravisational force (mg) is exerted (and there is no friction in this system). What is asked in the question is the final velocities of the wedge and the block (vB, vK). The velocity of the block is conserved when it reaches at the...

Homework Statement A person is bungee jumping from the top of a cliff with height H. The un-stretched length of the bungee rope is L. The person comes to a stop just before hitting the ground. The length of the cord is equal to H(amax-g)/(amax+g), where amax is the maximum acceleration upward...

Given the figure, how can i arrive to this formula knowing that angular momentum is conserved? I know that p = mv and L = p x r. So the initial momentum will be L1 = mV x R and the final momentum will be L2 = mv x r. I am not sure how R will equal to b since the distance between the...

Homework Statement A ski starts from rest and slides down a 22 o incline 75m long. Coefficient of friction is 0.090. What is the skiers speed at the base of the inlcline? Use energy methods Homework Equations PE=mgh KE=mv2/2 W=Fd The Attempt at a Solution Since mass was not given I did PE=KE...

Homework Statement This question was on a recent AP Physics 1 exam as a multiple choice; "Three air track gliders, shown to the right all have the same mass M. Gliders 2 and 3 are initially at rest. Glider 1 is moving to the right with speed v. Glider 1 collides with glider 2 and sticks to it...

For a curve parametrised by ##\lambda## where ##\lambda## is along length of the curve and is 0 at one end point. At each ##\lambda## say tangent vector V and A be the two possible vectors of the tangent space. where ##V=V^\mu e_\mu## and ##A=A^\nu e_\nu##, {e} are the basis vectors. Now ##...

Hello forum. I have a HW question that I don't fully grasp just yet. It was multiple choice and somehow I guessed the right answer based on the work I did complete, but I want to know how to get to the solution and which steps I'm leaving out. I'll follow the format to write out the...

Homework Statement Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are identical. They push against one another, as in Figure 7.11, and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces...

Homework Statement A fireworks rocket is moving at a speed of 45.0 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities v1 and v2. What are the magnitudes of v1 and v2? Homework Equations Conservation of Momentum m1v1 + m2v2 = m1vo1 + m2vo2 The...