What is Conservation: Definition and 999 Discussions

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. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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...
  6. 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} -...
  7. 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...
  8. H

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

    ddd
  9. 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)?
  10. 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.
  11. 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]
  12. 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...
  13. 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 =...
  14. 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?
  15. 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: $$ 3\vec v_0 = \vec v_1 +2\vec v_2 $$...
  16. T

    Current conservation for SU (N)

    Here is my solution
  17. 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}} +...
  18. 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)}\...
  19. 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...
  20. 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...
  21. T

    MTW Exercise 22.7 -- Calculate the law of local energy conservation for a viscous fluid with heat flow

    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...
  22. 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 +...
  23. 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...
  24. 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...
  25. 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...
  26. 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
  27. 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...
  28. P

    Momentum conservation question

  29. 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...
  30. 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...
  31. 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 +...
  32. 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...
  33. 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...
  34. 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...
  35. 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 :')
  36. 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##...
  37. 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?
  38. 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...
  39. 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...
  40. O

    Law of Conservation of Energy Problem (kicking a soccer ball)

    a) So far, I have equated Ek to Eg to solve for h. 1/2(m)(27)^2 = m(9.8)h. I haven't taken the angle into consideration. I'm not sure if I have to use the x or y component. I got my answer to be 37m but again I don't believe this is correct. b) I did Ek = Eg + Ek. 1/2(m)(27)^2 = m(9.8)(3.5) +...
  41. Qwet

    I Conservation of energy in general relativity

    Hello. I have a question about the law of energy conservation in GR. As time is inhmogeneous, we don't have energy-momentum 4-vector which would be preserved during system's dynamical change. It is only possible to define 4-vector locally. And next, the problem regarding how to sum this vectors...
  42. Ayandas1246

    Conceptual questions about Angular Momentum Conservation and torque

    List of relevant equations: Angular Momentum = L (vector) = r(vector) x p(vector) Angular velocity of rotating object = w(vector), direction found using right hand rule. Torque = T(vector) = dL(vector)/dt I have a few questions about torque and angular momentum direction and...
  43. lomidrevo

    I Is Energy an Illusion in the Many-Worlds Interpretation?

    I think I have a rough idea about it, but I am not sure whether it is correct. At least I feel that my understanding is a bit vague. Here it is: Globally (I mean across all worlds), the energy is conserved because the universal wavefunction evolves strictly according to Schrodinger equation...
  44. J

    Conservation: Mass Dropped onto a Spring, Find the Compression

    First I wanted to find the kinetic energy the mass had when it hit the spring (converted from the potential Energy it had) thus Ek=mgh=9.8*2.6*3.5=89.18 Now I know as this Ek changes to 0 the potential energy of the spring as its being compressed will be at its maximum so, Ek=Ep...
  45. Nick tringali

    How does capillary action of a liquid not violate energy conservation?

    I am learning about capillary action of water. As water moves up paper. How is that not violating energy conservation as it is going against the force of gravity. This obviously can't be infinite energy.
  46. M

    Conservation of Angular Momentum -- Child jumping onto a Merry-Go-Round

    So we know that the initial intertia of the merry go round is 250 kg m^2 and its angular speed is 10 rpm. MGRs angular momentum would be L=Iw=250(10)=2500kg m^2 rpm. We know the mass if the child is 25kg, and the child's linear velocity is 6m/s. We convert linear to angular w= v/r = 6/2 =...
  47. WonderKitten

    Conservation of angular momentum

    Hi, I have the following problem: A homogeneous disc with M = 1.78 kg and R = 0.547 m is lying down at rest on a perfectly polished surface. The disc is kept in place by an axis O although it can turn freely around it. A particle with m = 0.311 kg and v = 103 m/s, normal to the disc's surface at...
  48. wcjy

    Conservation of energy, centripetal acceleration, kinematics

    (a) Using COE, $$mgh = 0.5mv^2 + 0.5I\omega^2$$ I solved it, where $$\omega = 112 rad/s$$ (b) This is the part where I have question or problem. I saw my course mate working and he start of with finding centripetal acceleration. $$a_c = \frac{v^2}{r} = \frac{(r_0\omega)^2}{R_0}$$ Why isn't it...
  49. Saptarshi Sarkar

    Conservation of angular momentum under central forces

    I know that the force must be a central force and that under central forces, angular momentum is conserved. But I am unable to mathematically show if the angular and linear momentum are constants. Radial Momentum ##p=m\dot r = ma\dot \theta=ma\omega## Angular Momentum ##L=mr^2\dot\theta =...
  50. H

    Plane pendulum: Lagrangian, Hamiltonian and energy conservation

    Hello! I need some help with this problem. I've solved most of it, but I need some help with the Hamiltonian. I will run through the problem as I've solved it, but it's the Hamiltonian at the end that gives me trouble. To find the Lagrangian, start by finding the x- and y-positions of the...
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