What is Energy: Definition and 999 Discussions

In physics, energy is the quantitative property that must be transferred to a body or physical system to perform work on the body, or to heat it. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement in the International System of Units (SI) of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of one metre against a force of one newton.
Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature.
Mass and energy are closely related. Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.
Living organisms require energy to stay alive, such as the energy humans get from food. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy. The processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the Sun and the geothermal energy contained within the earth.

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  1. M

    I Energy and sand batteries (thermal energy storage)

    Hi, I'm new here, so apologies if this is covered somewhere else. I'm just playing with the notion of building a sand battery. Sand has a spec heat cap. of 830j/kg degrees K. If I want to heat 1000kg of sand up to 400 deg c, by my rough calculations that will require 332 000 Kj of energy, or...
  2. uxioq99

    The Energy Expectation Value for a Moving Hydrogen Atom

    ##\begin{align} \langle E \rangle &= \int_{\mathbb R^3} \int_{\mathbb R^3} \int_{\mathbb R^3} \int_{\mathbb R^3} g^\dagger (\tilde K) g(K) |\psi_0(x)|^2 \left(E_0 +\frac{\hbar^2 |K|^2}{2m}\right) e^{i(K-\tilde K)\cdot X -\frac{i}{\hbar} \left(\frac{\hbar^2 |K|^2}{2m}-\frac{\hbar^2...
  3. C

    Differentiating the equation for the mechanical energy of a spring

    Why when we differentiate ## E = \frac {1}{2}mv^2 + \frac {1}{2}kx^2 ## with respect to time the answer is ## \frac {dE}{dt} = mva + kxv ##? I though it would be ##\frac {dE}{dt} = ma + kv ##. Many thanks!
  4. L

    B Where does the energy of gravity come from?

    Since gravity accelerate things (even with some people saying that it's not a force) there must be a consense that it adds energy to things. There are even hydroeletric power plants generating energy everywhere. So where does the energy of gravity come from? Is it spontaneous generation of energy?
  5. Astronuc

    Modeling and Simulation in Nuclear Energy

    Modeling and simulation, or computational physics/chemistry, is a large and important part of engineering. In nuclear energy, there are applications of finite element methods (and occasionally finite different or finite volume depending on the problem) applied to nuclear plants, nuclear...
  6. L

    A Going from Cauchy Stress Tensor to GR's Energy Momentum Tensor

    Why do the Cauchy Stress Tensor & the Energy Momentum Tensor have the same SI units? Shouldn't adding time as a dimension changes the Energy Momentum Tensor's units? Did Einstein start with the Cauchy Tensor when he started working on the right hand side of the field equations of GR? If so, What...
  7. xpell

    B Energy needed to stop the Earth's inner core ---and its effects?

    This is not for any kind of homework ---the last time that I went to school was 30+ years ago. However, I am a curious person, I've been asked by other people who know that I love science and I need to calculate this: As you will most possibly know, a misreading of this paper by the media...
  8. A

    Finding the final speed of a space probe using work and kinetic energy

    First I found work: W=(3.85x10^5)(2.45x10^8) W= 9.43x10^13 Then used that for difference of kinetic energy: 9.43x10^13 = (1/2) (4.55x10^4)v2^2 - (1/2)(4.55x10^4)(1.22x10^4)^2 9.43x10^13 = (22750)v2^2 - 3.386x10^12 9.43x10^13 + 3.386x10^12 = (22750)v2^2 9.77x10^13 = 22750v2^2 9.77x10^13/22750...
  9. S

    B Compressed R134A refrigerant as a store of energy?

    How much energy is used to compress e.g. 0.8 Kg (typical mass in a typical fridge freezer; edit: I've just seen that 0.8 kg is not normal at all; it's more like 150 g - this means my idea should be quite cheap and compete well with rechareable batteries) R134A refrigerant and could it be...
  10. A

    Net work and kinetic energy (pushing a wagon to accelerate it)

    I'm a little confused because my teacher used Bill's 500J of work for the kinetic energy equation and I don't understand why. I used the net work, so 300J, to find the speed and I'm not sure why that's wrong. Wouldn't friction make the wagon move slower than if there was no friction? So why...
  11. J

    Engineering Calculate the bonding energy of two ions

    1.) So first I differentiate and set it equal to 0 and get: $$\frac{A}{r^2} -\frac{Bn}{r^{n-1}} = 0$$ 2.) When solving for r, I'm not quite sure how to take away the exponent so I get up to the second to last step: $$r^{n-3} = \frac{Bn}{A}$$ Would it be: $$r = \sqrt[n-3]{\frac{Bn}{A}}$$ ...
  12. 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...
  13. abrogard

    B Atomic Energy Levels: Simplified Explanations for the Curious

    I find this very interesting. But it is above my head. Is there a simpler explanation/volume perhaps that I could get, consult? https://www.sciencedirect.com/topics/earth-and-planetary-sciences/atomic-energy-levels
  14. G

    Chemistry How to compute specific surface energy for cubes of varying sizes?

    I got these values but I wanted to make sure I was doing it the correct way a) 0.548 J/g for system of 1 µm cubes b) 9.131 x 10^19 J/g for system of 1 nm cubes c) 273.890 J/g for system of 1 nm radius spheres
  15. A

    I Why is the minimum energy equal to the energy uncertainty?

    I was watching this video on Youtube, however, I don't get the step at 14:50 where he says that ΔE≥½hf means that E0=½hf. Could someone explain why the minimum energy is equal to the energy uncertainty?
  16. B

    A Energy levels shifts in a time-varying electric field

    Hello! I have 2 levels of the same parity with energies ##E_1 < E_2##, and another level of opposite parity a distance ##E## from the ##E_2##. I also have that ##E_2 - E_1 << E##. I have a laser on resonance (I am trying to scan along the resonance and find it) with the transition from ##E_2##...
  17. Lotto

    B The energy of a molecule has what sign?

    And have all molecules or even atoms negative energies? So when a molecule have energy let's say -70 Ha and the other -75 Ha, does it mean that the second molecule has a lower energy?
  18. 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...
  19. H

    I Global evolution of a Bell pair of photons

    Hi Pfs, consider a pair of maximally entangled photons where the total momentum is null and the same thing for the total angular momentum. I suppose that this pair is like an universe: nothing outside the pair acts on it except maybe a device for the measurement of these two properties (no local...
  20. tallwallyb

    Why Does Hooke's Law Seem Contradictory in Calculating Spring Energy?

    On the energy part, I keep getting mg=(1/2)*x*k, which is contradictory to Hooke's law F=mg=kx. What is going on?
  21. lxhull

    Doubling the Thermal Energy of a Frozen Chocolate Bar

    The farthest I got was double thermal energy equals mass times specific heat capacity times change in temperature (115+34) 2Eth=(mc149) To Eth=mc74.5 I'm not sure where to go from here. It seems like I don't have enough information.
  22. uSee2

    Pan suspended by a spring (Energy + SHM)

    I have successfully completed parts A, and B, however, I am confused on Part C. Here was my attempt and the answer key's attempt: My attempt: Since I correctly knew the speed after the collision, and the gravitational potential energy after the collision if I set h=0 at when it was at rest...
  23. S

    I Exploring the Potential of Vacuum Energy & Gravity

    I was reading this, but am confused: https://nautil.us/the-remarkable-emptiness-of-existence-256323/
  24. paulimerci

    Find elastic energy in the compressed spring.

    a) Elastic potential energy stored in the compressed spring is written by, where k =400N/m, compressed spring distance x = 0.5m $$ U_g = \frac {1}{2}kx^2$$ $$ U_g = 50J$$ b) When block C is compressed, it has stored spring PE and when it is released, the block accelerates to the right, where it...
  25. I

    Calculating the energy savings of an insulated cavity in home wall construction

    I am a client who bought a new house and the cavity in the wall was not insulated. I can calculate the U value of the uninsulated wall and the U Value of the wall if it were insulated correctly. front the two different U values I want to calculate how much extra energy is being lost through a...
  26. S

    Why is the elastic potential energy in position 2 zero?

    Hello, so we have two potitions right, if we take ##\theta = 90## as the first position (i.e. both rods are flat) and then the second position at ##\theta = 0##. I totally understand the exercise, not difficult. The only issue I am having is the torsional spring... it says that it is uncoiled...
  27. S

    Rotating Rod in Plane: Kinetic Energy & Moment of Inertia

    hello guys, I wanted to ask whether I can just consider/think about this as being rotation around a fixed axis in a plane representing it as if it was 'just' a rod. This is mainly so that for the kinetic energy in the second position is where if we think about it in just a plane. Is this...
  28. haha0p1

    Kinetic energy of an alpha particle

    Kindly help me solve this question. The only thing so far that I know in this question is that energy is conserved and the momentum of Alpha particle will equal momentum of Thorium.
  29. mathbrain9

    Link between increase in Potential energy and the thermal energy lost

    "Heat is the transfer of kinetic energy between molecules. If the velocity is more, the kinetic energy will be more so that the heat is more." "As an object's speed increases, the drag force from the fluid increases exponentially. For example, when you drive at high speeds, the frictional force...
  30. uSee2

    Experimental Design: Pulley and Mass Hangers

    ^ This is my personal drawing of the diagram, I couldn't take a picture of the actual one. The setup is a pulley wrapped with a cord and mass hangers attached to each end. My first thought when approaching this problem was to first determine the rotational inertia of the pulley, then use some...
  31. S

    I Hubble flow kinetic energy into other types of energy?

    Spacetime expands at an accelerated rate and the particles with movement associated to this expansion are coupled to the Hubble flow. In many papers that I've read, objects coupled to the Hubble flow are treated as if they have some velocity and kinetic energy associated with it.However, can...
  32. MajorJinxs

    I Question: To use or not to use? (heating bricks for energy storage)

    I have a Hicks hot water stove that has a Cast Iron fire box. I am looking for Clay bricks or Something like it to retain more heat to hold over night inside the fire box. But i am need help with the difference in materials as far as heat retention per brick for longer holding time. Hicks hot...
  33. chwala

    Use the energy method to find the distance moved by particle

    This is from an examination paper -A level. My interest is on part (ii). Ok my take; i. ##KE_{initial} = \dfrac {1}{2} mu^2= \dfrac {1}{2}× 0.4 ×12^2=28.8## Joules. ii. ##\dfrac {1}{2} mv^2=\dfrac {1}{2} mu^2-mgh## ##0=28.8-(0.4×10×h)## where h is the vertical perpendiculor distance...
  34. S

    I Can gravitational waves gain energy in an expanding FRW spacetime?

    I was reading this paper (*Green's functions for gravitational waves in FRW spacetimes:* [https://arxiv.org/abs/gr-qc/9309025](https://arxiv.org/abs/gr-qc/9309025)) and I had a specific question about one statement in the paper that I would like to ask: At page 6, the author says that...
  35. tracker890 Source h

    Q：Hydrostatic Pressure vs. Energy Conservation Equation

    Please help me to understand which ans is correct. To determine the ##P2##. $$ h_{LM}\ne 0 $$ Method 1： $$dP=\frac{\partial P}{\partial x}dx+\frac{\partial P}{\partial y}dy+\frac{\partial P}{\partial z}dz$$$$\phantom{\rule{0ex}{0ex}}\rho \overset\rightharpoonup{a}=-\triangledown p+\rho...
  36. P

    I Exploring the Relationship between Quantum Numbers and Energy in Atomic Systems

    The quantum number n determines the energy, and for each n the allowed values for the angular momentum quantum number are -(n-1),...,(n-1). This doesn't seem resonable to me. Classically increasing the orbital angular momentum will result in an increase in the energy of the system. But why is it...
  37. S

    Big announcement about fusion energy coming soon (Dec-2022)

    https://nypost.com/2022/12/12/us-set-to-announce-major-fusion-energy-breakthrough/
  38. P

    Understand Gibbs Free Energy & Activation Energy

    Hi everybody, I don't understand what changes between these two graphs. In particular, why does free energy reach a minimum in one graph and a maximum in the other? Shouldn't a chemical reaction always have an energy maximum, represented by the activation energy?
  39. A

    Energy absorbed by water illuminated by an LED source

    Good morning, I was wondering if I am thinking correctly. I am trying to establishing some step by step to calculate the amount of energy is being absorbed by a water body when a LED pendant is shining right above. Being the parameter that I want to calculate, the energy absorbed by the...
  40. phos19

    Falling stick problem (no friction): What is the kinetic energy?

    Since there is no friction : $$ m \ddot{x} = 0 $$ (no x motion).For the kinetic energy , I've tried: $$ K = 1/2 I_{cm} \dot{\alpha}^2 + 1/2 m v^2_cm = 1/2 I_{cm} \dot{\alpha}^2 + 1/2 m \dot{z}^2$$ . Giving me a weird expression , shouldn't the kinetic energy just be half the the moment...
  41. H

    Dimensional Analysis: Forster Energy Transfer equation

    I'm trying to calculate Forster's Resonance Energy Transfer rate, but I just can't seem to get the units right. I'm trying to teach my students how to calculate them. Here is the (relatively) original technical note of FRET equation, made by the original author...
  42. ermia

    Krotov problem: how to write Energy conservation for this fluid?

    I wrote some potentials but they were wrong. I used the cm of all fluid parts and I used the radius which is $$ \sqrt S/ \pi $$ .
  43. Differentiate it

    The kinetic energy of a spring

    I tried just using the formula for kinetic energy but that was apparently the wrong answer. The answer key says it's (1/6)mv². I don't understand how they got that answer. Could someone explain?
  44. Elaren

    Final velocity of a block on a spring pulled downhill

    Note: wording is ambiguous so I assumed spring started from equilibrium, in which case it stretches as we go downslope. Final height (at lower point on slope) is 0. Distance along slope = Distance the spring stretches = d= ##s_f## = ##2/cos{\theta}## =2.13 Height change = h = ##2 tan{\theta}##...
  45. M

    I Energy levels of atoms and spectroscopic analysis

    Hello ! My question is how the energy levels and sublevels that atoms are considered to have were obtained, and if these energy levels and sublevels were obtained as a result of the different spectroscopic analyzes of energy emission and absorption of atoms, or as it was concluded that atoms...
  46. A

    A Kirkendall effect: vacancy concentration and pair interaction energy

    I am reading the following article on Kirkendall effect leading to the Formation of a hollow binary alloy nanosphere: a kinetic montecarlo study. I am unable to understand or find in references the reasoning to obtain equation (1):
  47. mpross

    B Dark Energy, Dark Matter and the Speed of Light

    Quote from NASA: My understanding of dark energy is based on NASA's report: https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy; were NASA state as follows: "It turns out that roughly 68% of the universe is dark energy. Dark matter makes up about 27%. The rest - everything on...
  48. B

    A Time dependent perturbation theory applied to energy levels

    Hello! I am reading this paper and in deriving equations 6/7 and 11/12 they claim to use second oder time dependent perturbation theory (TDPT) in order to get the correction to the energy levels. Can someone point me towards some reading about that? In the QM textbooks I used, for TDPT they just...
  49. B

    A Trying to reproduce the energy levels of a molecule from a paper

    Hello! This is quite a specific question, so if anyone knows the details I would really appreciate your help (@Twigg ?). I am trying to reproduce figure 1 from this paper (it's for the PV experiment performed on BaF). While I am getting quite close to it, the levels don't fully match (I am...
  50. Shreya

    2 Capacitors and energy density

    I developed three arguments to answer this question. Argument no 2 seems to be wrong, but I cant figure out why. I know one/more of my arguments are flawed. Please be kind to help me figure this out. Argument 1) Since they have same charge on them, the ##E## between them must be same. The one...
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