Conservation Definition and 999 Threads

Conservation biology is the study of the conservation of nature and of Earth's biodiversity with the aim of protecting species, their habitats, and ecosystems from excessive rates of extinction and the erosion of biotic interactions. It is an interdisciplinary subject drawing on natural and social sciences, and the practice of natural resource management.The conservation ethic is based on the findings of conservation biology.

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  1. Andrew1235

    Mass conservation in a sphere to find radial velocity of a flame

    I am not sure what form of mass conservation to use to solve the above problem from An Introduction to Combustion by Stephen Turns. Can anyone explain what form of mass conservation applies to a sphere in this context?
  2. casualguitar

    Modelling of two phase flow in packed bed using conservation equations

    Previously, I have seen the derivation of the energy conservation equations for simulation of single phase flow in a porous media (a packed bed). These are the energy equations for the solid and fluid respectively: I understand the derivation, however, these equations will only work when the...
  3. K

    Find the Conserved Quantity of a Lagrangian Using Noether's Theorem

    So Noether's Theorem states that for any invarience that there is an associated conserved quantity being: $$ \frac {\partial L}{\partial \dot{Q}} \frac {\partial Q}{\partial s}$$ Let $$ X \to sx $$ $$\frac {\partial Q}{\partial s} = \frac {\partial X}{\partial s} = \frac {\partial...
  4. Nick tringali

    How Does Energy Conservation Apply to MCAT Physics Problems?

  5. stephenklein

    Conservation of the Laplace-Runge-Lenz vector in a Central Field

    I actually have worked through the solution just fine by taking the derivative of \vec{L}: \frac{d \vec{L}}{dt} = \dot{\vec{v}} \times \vec{M} - \alpha \left(\frac{\vec{v}}{r} - \frac{\left(\vec{v} \cdot \vec{r}\right)\vec{r}}{r^{3}}\right) I permuted the double cross product: \dot{\vec{v}}...
  6. amjad-sh

    I Single-slit diffraction experiment and the conservation of energy

    In a single-slit diffraction experiment, a monochromatic light of wavelength ##\lambda## is passed through one slit of finite width ##D## and a diffraction pattern is observed on screen. For a screen located very far away from the slit, the intensity of light ##I## observed on the screen in...
  7. R

    B Why exactly do Virtual Particles not violate Conservation of energy?

    Recently I've read more about virtual particles and at first I tought that there were only doubts that virtual particles are not interpretable with the help of uncertainty principle. Furthermore it can't be used an an "excuse" for the temporary violation of the conservation of energy. Can...
  8. Andrew1235

    Conservation of energy for a series of elastic collisions

    The speed of the block after the nth collision is $$ V_n=(2e)^n*v_0 $$ By conservation of energy the block travels a distance $$V_n^2/(2ug)$$ on the nth bounce. So the total distance is $$ d=1/(2ug)∗(v_0^2+(2ev_0)^2...) $$ $$ d=1/(2ug)∗(v_0^2/(1−4e^2)) $$ $$ d=1/(2ug)∗(v_0^2∗M^2/(M^2−4m^2))...
  9. elcaro

    I Energy conservation in an expanding universe

    The total amount of energy is still a conserved quantity, even in an expanding universe based on a positive and constant energy density, and even under the rapid exponential expansion during inflation, total amount of energy is conserved. For how this works, see this lecture by Alan Guth, the...
  10. U

    Some help in understanding energy conservation

    While I am working through proving the homework statement, I encountered a problem. The problem is as follows: From the energy equation above, one can see that the minimum value of ##p## is ##m_T##. However, how does one explain why when ##p=m_T##, ##\sqrt{m^2_B+m^2_T}>m_A##?
  11. G

    I Conservation of momentum in a collision

    Now, deriving relativistic momentum isn't terribly difficult, but that's not the same as understanding it. I'm trying to figure out why conservation of momentum in special relativity requires the gamma factor. When I looked at conservation of momentum in elementary physics, we basically just...
  12. C

    B Conservation of energy and magnetism

    Please redirect me to the correct part of thr forum if this is the wrong place When we lift up an object n then let it fall back, then potential energy - > kinetic energy If I drop a magnet onto another magnet with like pole facing each other (that sits on the floor), the falling one maybe...
  13. F

    I Conservation of finite difference for vibration equations

    Let's discuss whether the energy under a finite difference (FD) scheme is conserved. Take the simplest vibration eq mx''+kx=0, which one will use a FD scheme to solve. The energy is mx'^2/2+kx^2/2. Whether the energy is conserved doesn't depend on the FD scheme for the ODE but upon the FD scheme...
  14. Ebi Rogha

    I Vacuum energy and Energy conservation

    Also, I have heard from physicists that vacuum energy fluctuation (creation and destruction of virtual particles) violates energy conservation. The reason, they justify, is based on uncertainty principle (energy-time form of uncertainty principle), energy can exist and disappear for a very short...
  15. baby_1

    Violate current conservation in Perfect Magnetic Conductor (PMC)

    Hello, I need to know why having an electric current in Prefect Magnetic Conductor(PMC) violate current conservation. Based on the boundary conditions or lorentz force or ..., I couldn't be successful to prove that surface current can violate current conservation. In the textbooks, they...
  16. Paulpaulpa

    I A ray crossing 2 media of different indices and energy conservation

    The ##I_i## are the intensity of the rays, in other words energy per surface units per radians by seconds. The d##\Omega## are the solid angles The equation p75 isis what I don't understand. I suppose that each side represent the energy going and out of the surface dS but I don't understand...
  17. F

    Conservation of charge with Dirac delta

    Hello, I was reviewing a part related to electromagnetism in which the charge and current densities are defined by the Dirac delta: ##\rho(\underline{x}, t)=\sum_n e_n \delta^3(\underline{x} - \underline{x}_n(t))## ##\underline{J}(\underline{x}, t)=\sum_n e_n \delta^3(\underline{x} -...
  18. Vandenburg

    B How does conservation of energy apply at the nuclear level?

    Electrons rotate around a nucleus for long periods of time. Where does the energy for this motion come from? Ok, I realize that electrons don't actually rotate around the nucleus, like a tiny solar system. But if the electron is wave function, it's still constantly vibrating, constant...
  19. H

    Can I use the principle of conservation of energy for this problem?

    ddd
  20. S

    I Special Theory of Relativity & Conservation of Mass

    Does the law of conservation of mass fail to meet the first postulate of the special theory of relativity(the laws of physics are the same in all inertial frames of reference)?
  21. S

    B Conservation Laws & General Relativity: Understanding Energy

    How does general relativity shows the conservation of energy. Because I was reading and listening to something today that touched on this subject. It almost seems as though if you scale GR to larger sizes it stops working and turns into an incomplete law of nature like Newton's laws of gravitation.
  22. T

    The back way for deriving Maxwell's Equations: from charge conservation?

    I found one article in 1993 talking about it.[Unacceptable reference deleted by the Mentors]
  23. Uchida

    Conservation of Linear Momentum of Rigid Body

    I solved it by two methods: ----------------------------------------------------- First, by conservation of linear momentum, using the vector velocities of each particle: In the imminence of the impact, the velocity of all the three particles are the same, \vec v_0 = - \sqrt{2gh} \hat j...
  24. Z

    Proving Energy Conservation in a Gravitational System with Multiple Bodies

    Hi all. I'm trying to prove energy conservation in a (maybe) uncommon way. I know there are different ways to do this, but it is asked me to prove it this way and I'm stucked at the end of the proof. I'm considering ##N## bodies moving in a gravitational potential, such that the energy is ##E =...
  25. H

    Confirming Conservation of Kinetic Energy: An Explanation

    D is correct, the reasoning is as follows: 1/2*(M1V1)^2 + 1/2*(M2V2)^2 = 1/2 * (M1 + M2) (Vcm)^2, since V1 =V2 =Vcm KE retained = KE final = 1/2 *M(Vcm)^2 Let me know if reasoning is okay? However, why A isn't correct?
  26. TheGreatDeadOne

    Conservation of momentum in an oblique launch and projectile explosion

    This problem I already solved using another resource (just get the coordinate of the center of mass reach and from it, get to the larger mass. R = (3v02) / (4g)). But I'm having some trouble calculating using moment conservation. Here what I've done so far: $$ 3\vec v_0 = \vec v_1 +2\vec v_2 $$...
  27. T

    How to Implement Current Conservation for SU(N) in the Adjoint Representation?

    Here is my solution
  28. E

    A Conservation of energy for stationary particle attached to string

    I was going to put this in the homework forums, but on second thoughts it's more conceptual so perhaps here is better. It's about problem 4, chapter 6 of Wald. Part (a) is fine, $$u^a \nabla_a u^b = \frac{\xi^a}{(-\xi^c \xi_c)^{1/2}} \left( \frac{\nabla_a \xi^b}{(-\xi^c \xi_c)^{1/2}} +...
  29. TheGreatDeadOne

    Speed of a hanging rope sliding on a nail (using energy conservation)

    I solved this problem easily using Newton's second law, but I had problems trying to use mechanical energy conservation to solve it. How I solved using Newton's second law: ##\text{(part of the rope that is on the left)}\, m_1=x\rho g,\, \text{(part of the rope that is on the right)}\...
  30. George26

    Conservation of mass: control volume approach question

    Summary:: Control volume question that has a brine solution entering a tank and mass accumulates over time. Hello, I'm currently struggling with a control volume approach question that has a brine solution entering a tank. I get to a point where I have a first order differential equation. I...
  31. guyvsdcsniper

    Law of Conservation of energy and Wnc

    This is my understanding of the law of conservation of energy and the role non conservative forces factor into it. Could someone confirm if I have this right or explain where I am going wrong if I am? I would appreciate it. With the law of conservation of mechanical energy, ΔKE+ΔPE=0. This...
  32. T

    Is My Calculation of Local Energy Conservation in a Viscous Fluid Correct?

    I've come to a grinding halt with this and I can't see a way forward. Can someone please take a look at what I've done so far and let me know if what I have done is OK and then if it is, give me a hint on how to proceed. First up, Is ## u \cdot \nabla \cdot T = u_\alpha...
  33. P

    Is the Book Right? Examining Conservation of Momentum

    My proposed solution: When the student stops at the end, suppose the carriage is moving at speed u. 0 = (M+2m)u - m(v - u) ==> u = mv/ M+3m After jumping out, the total momentum of the Carriage + collector system is 0 - mu = -m^2v/ M+3m. By conservation of momentum for the Carriage +...
  34. P

    Conservation of energy in rotating bodies

    The conservation of energy equation is basically GPE is converted to KE of block and KE of cylinder. To get the correct answer, the KE of the cylinder is 1/2mv^2, where m is its mass and v is the velocity of its COM (which is the centre of cylinder). However, I viewed the cylinder as rotating...
  35. P

    Conservation of energy in Gravitation

    Suppose a rocket is moving at radial velocity vr and tangential velocity vt in the Sun's gravitational field. At some time, the rocket enters the gravitational field of Mars (with the above mentioned velocities), and gravitation effects due to the Sun can be ignored. After more time, the rocket...
  36. A

    Symmetry associated with current conservation

    As I understand it for every symmetry there is associated a conserved quantity - so for time symmetry there is energy conservation. I understand as well that charge conservation is associated with a 'mathematical' local symmetry - something turning in a mathematical space at a point so to...
  37. S

    Momentum Conservation: How to Reconcile a Negative Value?

    Maybe a silly question but on the above question using the conservation of momentum: momentum before firing (0) = momentum after firing (55*35)+(M*2.5) If I re-range the above it's M = -(55*35)/2.5 = -770kg. I can I reconcile that minus sign (basically get rid of it)? Thanks
  38. Y

    Conservation of Energy on Current-Carrying Wire in Magnetic Field

    So force on a current carrying wire = ILxB. If I have a bunch of bar magnets making a uniform magnetic field of strength B, then a 1 meter long wire of 0 ohms carrying 1 Amp, the force on that wire is (1)(1)xB = 1B. If I let that force move the wire for a time T, let's assume the wire moved a...
  39. P

    Is the latter part of the momentum conservation question correct?

  40. J

    I Quantum Tunneling in the Sun and Conservation of Energy

    Hi, In my textbook it says that if you consider the electrostatic repulsive barrier that protons in the Sun need to overcome in order to get into the range of the strong nuclear force to fuse together then it fails to fully account for the measured power output of the Sun. It says that the...
  41. Leo Liu

    Conservation of energy in a CM system moving at constant velocity

    My book uses ##1/2m_1v_{1c}^2+1/2m_2v_{2c}^2=1/2m_1v_{1c}'^2+1/2m_2v_{2c}'^2## to show that the angles of deflection of the collision between two particles are the same in the centre of mass frame. However, I am doubtful that one can apply the conservation of energy to a "moving" system because...
  42. C

    Solving for $$\omega_2$$ using Conservation of Angular Momentum

    Unfortunately, I couldn't arrive to the correct answer ($$=0.28mL^2 \omega^2$$ ) and will be happy to understand what am I doing wrong. **My attempt:** Using $$ E_k = \frac{1}{2} I \omega^2 $$ I obtain that the difference I need to calculate is $$ \frac{1}{2} (2mL^2)(0.8\omega)^2 +...
  43. F

    B Energy Conservation in Relativity: Perpetual Motion?

    This is very much, a ... what's wrong with this approach... Consider a large mass with no atmosphere, i.e. the moon. On it, construct a tower of arbitrary height. On the tower build an energy to mass machine, to convert energy to mass via E=mc^2. Once the mass is created, drop it from the...
  44. F

    Annihilation: calculation of photon energies

    I set up this problem this way: ##p_a^{\mu}=(E, \sqrt{E^2-m^2}, 0, 0)## ##p_b^{\mu}=(m, 0, 0, 0)## ##p_c^{\mu}=(2E_\gamma, 2E_\gamma, 0, 0)## I have chosen to consider the two photons as a single particle of energy equal to ##2E_\gamma##. At this point I applied conservation of the...
  45. JGHunter

    Lavoisier's Law of conservation of mass

    Hi, I'm writing a short story which addresses an issue in time travel that I don't really see getting addressed, and I was wondering where I could find the original quote where it is written that mass or energy can neither be created nor destroyed? I'm aware the original won't be in English...
  46. O

    Law of Conservation of Energy Problem: Trampoline

    For a) I did Eg = Ee + Eg and tried to solve for x. I got 5.4 m but I think this is wrong. I have no idea how to do the rest, please help :')
  47. F

    Minimum energy of a photon to produce ##\pi^+##

    I have a doubt about the first request: I suppose to find the minimum energy of ##\gamma## in the situation where ##p## is stationary, there is no reason to say that the proton is stationary if I were to calculate it in the CM, right?. So I have to consider che LAB-frame to find ##E_\gamma##...
  48. mattlfang

    Find the velocity and acceleration of a pulley in a mass-spring system

    This looks like a classical setup but I can't find a solution. We can calculate the energy of the system by looking at the work done by the gravity and the spring. But how do we divide the energy between the kinetic energy of the pulley and the rotation of the pulley?
  49. E

    Show charge conservation in a curved spacetime

    For the flat spacetime we could just use that partial derivatives commute as well as the antisymmetry of ##F^{ab}##, i.e. ##\partial_b \partial_a F^{ab} = -\partial_b \partial_a F^{ba} = -\partial_a \partial_b F^{ba} = -\partial_b \partial_a F^{ab} \implies \partial_b \partial_a F^{ab} = - 4\pi...
  50. E

    I Recovering Newton's energy conservation law for an Earth's lab

    I'm looking at Schutz 7.4 where first he obtains the following expression for a geodesic: $$ m \frac {dp_\beta} {d\tau} = \frac 1 2 g_{\nu\alpha,\beta } p^\nu p^\alpha $$ This means that if all the components of ##g_{\nu\alpha }## are constant for a given ##\beta##, then ##p_\beta## is also...
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