What is Conservation of energy: Definition and 999 Discussions

In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. This law, first proposed and tested by Émilie du Châtelet, means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite. Classically, conservation of energy was distinct from conservation of mass; however, special relativity showed that mass is related to energy and vice versa by E = mc2, and science now takes the view that mass-energy as a whole is conserved. Theoretically, this implies that any object with mass can itself be converted to pure energy, and vice versa, though this is believed to be possible only under the most extreme of physical conditions, such as likely existed in the universe very shortly after the Big Bang or when black holes emit Hawking radiation.
Conservation of energy can be rigorously proven by Noether's theorem as a consequence of continuous time translation symmetry; that is, from the fact that the laws of physics do not change over time.
A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind cannot exist, that is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings. For systems which do not have time translation symmetry, it may not be possible to define conservation of energy. Examples include curved spacetimes in general relativity or time crystals in condensed matter physics.

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  1. K

    I Energy conservation in general relativity

    Is energy conserved in general relativity? I have read most of the posts here that address this. But it isn't clear to me, what most people say is that energy is conserved locally but it can't be defined globally, some people say this means that energy is not conserved in GE while others argue...
  2. H

    How to assign signs to energy?

    The gravitational potential leads to velocity in downward direction, but spring potential does in upward direction. So should these energies have different signs (plus and minus or vice-versa)?
  3. J

    I Car, gas and total energy calculation

    Hi, What I understood about the principle of conservation of energy: Et = Ep + Ec = constant. For example: Et = 1/2mv^2 + mgh (h = height). Consider a car moving at speed v. For example: Et = 1/2mv^2 + E(gas + exhausts). Indeed, I include the exhausts, otherwise with the drop in the quantity...
  4. BikGer2

    Confused about a conservation of energy problem

    Hi, I assumed I was supposed to find the amount of kinetic energy body 2 receives after contact, assuming the collision is central, body 1 will be at rest after the collision. I started by using the equation for conservation of momentum: \begin{align} m_1v_1 = m_1v_1' + m_2v_2' \\ 50 * 20 =...
  5. Argonaut

    Spring Problem Involving Variables and Constants Only

    Here is my attempt at the solution: a) The apparatus may only experience acceleration ##a > g## while in contact with the spring. Since the spring exerts the greatest force when it is the most compressed, the apparatus will undergo the greatest acceleration at that point. So Newton's second...
  6. MatinSAR

    Spring with mass hangs from the ceiling

    I know that we can answer it using conservation of energy or using N's 2nd law. Using N's 2nd Law: ##F = mv \frac {dv}{dx}## ##Fdx = mvdv## For spring we have : ##F=-kx## ##(mg-kx)dx=mvdv## We'll get same result using above equation. My question: Average spring force from 0 to x is ##-\frac...
  7. P

    Challenging problem about an impact with a smooth frictionless surface

    The system of two material points of identical mass connected by a rigid rod of negligible mass and length ##L## is an example of a conservation of energy problem. The initial energy of the system is the sum of the kinetic energy of the two points and the potential energy of the rod, which is...
  8. F

    Flywheel inertia problem

    I am stuck on what to do to calculate the inertia of a flywheel using the method described. I am supposed to use conservation of energy equations to calculate the inertia. I have a picture of the experiment and also the measurements I have taken. It seems each method I try I get a different...
  9. P

    Problem with when to use Force and Energy. What compresses spring/

    This is how I tried to do it, which is the most direct. The force that the mass exerts on the spring is mgsin(53). and I equated that to kx. and found x. but apparently, this is wrong and the teacher told me a different method. (ME)1=(ME)2 due to conservation of mechanical energy...
  10. zachary570

    Conservation of Energy with Gravitational Potential Energy

    I was working on this problem but after getting to the answer I questioned the methods that I used for previous problems that I had solved. I understand that the total energy of the system remains constant and that we use the conservation of momentum to relate the two velocities. This gives two...
  11. kmm

    I Stress-energy tensor and energy/momentum conservation clarification

    I've been working through Bernard Schutz's book on GR and have run into some confusion in chapter 4 problem 20 part b. In this chapter, the stress-energy tensor for a general fluid was introduced and was used to derive the general conservation law for energy/momentum, where we found that...
  12. nav888

    Conservation of Energy when lifting a box up off the floor

    So, I cannot for the life of me write a conservation of energy statement, when an object is lifted up by a force. So in my example there is a box on the floor with v = 0, and then a force of magnitude F, where F > mg, acts on the ball, now the net force is F-mg, and hence the work done is (F -...
  13. A

    Do different length ramps violate conservation of energy?

    mgh=(1/2)(m)(v^2) gh=(1/2)v^2 sqrt(2gh)=v Should have the same v, but this is not the case based on the answer and real-life experiments.
  14. milkism

    Conservation of relativistic energy, collision of particles

    Question: With maximum do they mean that the speed of the pions is the same as the proton and an antiproton? Otherwise there will be two unknowns, and if I use both relativistic-energy and momentum conservation equations I get difficult equations.
  15. C

    Discovering Vector Direction in Conservation of Energy Problems

    For this problem, Is the length vector into or out of the page and how do you tell? EDIT: Why must we use conservation of energy for this problem? I tried solving it like this: ##IdB\sin90 = ma ## ##IdB = ma ## ##v_f = (2aL)^{1/2} ## ##v_f = (\frac {2dIBL} {m})^{1/2} ## Which is incorrect...
  16. Superposed_Cat

    I Conservation of Energy in GR: A-B System Analysis

    Assume you have a two particle system, A, which has a mass and gravitational pull of g, and B, an object with low mass, The system starts at time 0 with the distance between A and B being 0, A being at rest and B having enough kinetic energy to move it a distance r away from A, until time t all...
  17. L

    Two charged spheres hitting each other

    Since the forces involved (gravity and electric force) are conservative we can use conservation of energy. The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get...
  18. A

    The Work of Friction: Explained in .32m

    The answer is .32m. I set the elastic potential energy as equal to the work, but at first I put the force in the work equation as (F elastic - F kinetic friction) times distance and rearranged. 1/2kx^2 = (kx-Ff) d (0.5) (22) (0.035)^2 = (22 x 0.035-0.042) d 0.013475= 0.728 d 0.013475/0.728 = d...
  19. S

    I Conservation of energy in quasar outflows?

    I found this article* about the behavior of quasar outflows in cosmology and how they can create a magnetic field. In section 2.1.4., the authors say that when a quasar produces a "wave" or an outflow, the material will be emitted with energy coming from both the quasar itself and the Hubble...
  20. D

    A dial can spin on a fixed rotational axis

    What I have done is on my Ipad that I cant upload or at least don't know how to... :/ With hope of help DJ
  21. C

    Conservation of Energy with Mass on Hemisphere

    I tried approaching this question like this: F_N - mgcos(theta) = -mR(theta_dot)^2 and theta_dot = v/R since R is constant F_N = m(gcos(theta) - (v - v_0)^2/R) (with v being final velocity and v_0 being the initial velocity from the impulse) and then using energy conservation: at t = 0: E =...
  22. H

    How is converted the energy of a E.M. wave in a conductor

    I'm thinking about how the energy is conserved when a E.M. wave pass through a conductor. If a E.M. pass through a conductor, the electrons must move "oscillated", thus the energy from the E.M. wave is converted to kinematic energy. Another way I see that is the E.M wave must generate a current...
  23. C

    Why doesn't this solution work? (Springs and Conservation of Energy)

    I already know the solution to this, all you do is set the height of the top of the trampoline to 0 and solve for initial velocity so the equation for the conservation of energy $$mgh_0 + \frac{1}{2}mv_0^2 + \frac{1}{2}kx_0^2 = mgh_1 + \frac{1}{2}mv_1^2 + \frac{1}{2}kx_1^2$$ becomes...
  24. S

    Apparent weight problem (kinematics + conservation of Energy + Newton's laws)

    Hello there, I have tried the problem but don't get a different of 6g's as I am supposed to. I am not sure whether I interpreted the problem in the correct way, but I would love some feedback/hints on what went wrong in my solution, thanks in advance. Solution: SITUATION DRAWINGS + FBDS so...
  25. S

    Conservation of energy problem with friction included

    so I haven't looked at the solution yet, but I know that a 100% the velocity needs to be bigger, but analytically, I get a - sign instead of a + sign as you'll see at the final square root. So for the first 15meters of the motion all you should know is that ##v_1 = 10.458 m/s##. for the 2nd...
  26. A

    B Conservation of momentum and conservation of energy details

    If we have a ball with mass m dropped from a height h down to the ground, how come we can't set the conservation of energy equation just as the velocity of the ball turns 0. mgh = 0 If instead the ball were moving with an initial velocity v, would the equation be ##mgh + \frac{1}{2}mv^2 = 0##...
  27. M

    Conservation of Energy in Trampoline Bounce

    I was able to calculate the correct answer (given by a solution sheet), V=5.364 m/s, using the momentum impulse equation, P0+J=Pf. If this value is correct, however, I don't understand how energy is being conserved. The speed increases after the person bounces off the trampoline while the mass...
  28. C

    A rocket on a spring, related to potential/kinetic energy

    Part A) So from a force diagram we can see that the only two forces acting in our system are the spring force(positive y axis) and the weight of the rocket(negative y axis), which means the spring force is equal and opposite to the weight force. The weight is simple enough ##12* 9.8=117.6N##...
  29. J

    B Conservation of Energy and Momentum in an Explosion

    Hey, I have a question about explosions and how kinetic energy works during them. I have outlined my question on the attached image. Please let me know if something is wrong or needs clarifying. Thank you.
  30. T

    Conservation of energy -- Using a spring to launch a ball up an incline

    Ei = 1/2 K (x)^ 2 K = .0152N/m x = .0375 m Ei = 1.06x10^-5 Ef= 1/2mv2 + mgh m = .164kg, v is unknown, h is .0375sin(8.3)=.00541, Ef set equal to Ei 1.06x10^-5=1/2(.164kg)(v^2)+ (.164kg)(9.8)(.00541) v = .3254m/s I have gotten this answer multiple times but it is not correct. I am going...
  31. K

    B "Prove" that LPG burns with a blue flame ....

    The household LPG burns with a blue flame. There's nothing to prove! But what if we attempt to do that? How do we go about it? I started with the assumption that it is a complete combustion of the LPG. A Google search tells me that the calorific value (the amount of heat a substance gives off...
  32. mohamed_a

    I Problem with understanding angular momentum

    I have a problem in understanding angular momentum equation (mrv), especially the part where radius is involved. imagine an elastic collision occurred between sphere of mass (M) attached to a string forming a circle of radius (R) and moving with velocity (V) and another stationary sphere having...
  33. RogerWaters

    B Why doesn't cosmic inflation violate conservation of energy?

    Hi all, I'm not a physics student (although I have a PhD in a different field) and so don't have the math, but I'm trying to interpret a key passage from Krauss' book 'A Universe from Nothing' where he is (trying?) to explain, in 'layman's terms', what Alan Guth termed 'the ultimate free lunch'...
  34. S

    Problem of spring block system: force vs conservation of energy

    I have used the work energy theorem like all source have shown me an have arrived at the right answer where work one by all the forces is the change in kinetic energy -1/2kx^2 - umgcosΘx +mgsinΘx = 0 is the equation which becomes -1/2kx -umgcosΘ+ mgsinΘ = 0 where k= spring constant u=...
  35. J

    I Interference and conservation of energy in a resonator

    It is known that constructive interference in one place must be compensated for by destructive interference in another. Take a simple Fabry Perot resonator for example. The interference occurring at both sides of the first mirror (assuming one incident electric field) compensate each other out...
  36. tiago000000

    Exploring the Law of Conservation of Energy with a 5kg Weight and 10L Bucket

    Hi everyone! I regularly use the forum to learn but never registered to post anything, as I have nothing to teach really… But today I have a question regarding the law of conservation of energy that I can’t find the answer to, and maybe someone will help me understand: (I’ve attached a drawing)...
  37. J

    I Fresnel equations and conservation of energy (phase shifts)

    Quantum mechanically speaking when we split a wave in two the resulting waves must have a 90 degrees phase difference for energy to be conserved. Take the beamsplitter depicted in [1] for example. But the Fresnel equations state that the reflected wave should experience a phase shift of π when...
  38. C

    B E.P.E. -> ? when 2 masses are attached to a spring

    Two masses m and M are attached to a compressed spring. When the spring decompresses, the masses won't be pushed off the spring. What will happen to the masses and the entire system? By conservation of energy, the elastic potential energy of the spring will convert into kinetic energy, but which...
  39. 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...
  40. 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...
  41. 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))...
  42. L

    Amplitude of oscillation of a mass which is the pivot of a pendulum

    1) By conservation of mechanical energy we have ##m_2gl(1-\cos(\alpha))+m_1gl=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2+m_1gl## and by conservation of linear momentum along the x-axis we have ##m_1v_1+m_2v_2=0## which gives us ##v_2=\sqrt{\frac{2m_1gl(1-\cos(\theta))}{m_1+m_2}}## and...
  43. 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...
  44. 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...
  45. F

    De-excitation of a moving atom with photon emission

    The information I have are the following: ##p^\mu=(E, p, 0, 0)## ##p'^\mu=(E', p'\cos\beta, -p'\sin\beta,0)## ##k^\mu=\tilde{E}(1, \cos\alpha, \sin\alpha, 0)## Where: ##E=\sqrt{M^2+p^2}## ##E'=\sqrt{m^2+p'^2}## Using the conservation of the four-momentum ##p^\mu=p'^\mu+k^\mu##...
  46. Z

    Conservation of energy proof

    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 =...
  47. 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}} +...
  48. 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)}\...
  49. 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...
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