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. RoySRamirez

    Change in Free Energy when Heating a Substance

    Hello everyone! I'm new to the forum, and I've been trying to solve a problem that seems farily but I can't still convince myself of having the right (or wrong) answer. Imagine you warm up one mol of for example potassium hydride from standard temperature 298.15K to 673.15K (400 deg C). It is...
  2. snoopies622

    B Does E=mc^2 apply to gravitational potential energy?

    I'm reading Schutz's A First Course In General Relativity and in chapter 5 he discusses an idealized experiment in which an object is dropped from a tower, then turned into a photon and sent back up to its original height. In classical mechanics we would say that as the object falls it loses...
  3. Quantum23

    A Energy condition respecting warp drives in Einstein Cartan theory

    I read this paper where if you take the alcubierre metric calaculations while including torsion in GR you get positive energy spin requirements instead of exotic matter. Here is the link: https://arxiv.org/abs/1807.09745 Could it be because a spinning quantum vacuum will be less stiff like a...
  4. A

    A Why do we extremize the Lagrangian in the Hamilton principle instead of energy?

    I know that by extremizing lagrangian we get equations of motions. But what if we extremize the energy? I am just little bit of confused, any help is appreciated.
  5. aspodkfpo

    Energy loss in simple harmonic motion causes the time period to shorten?

    https://www.asi.edu.au/wp-content/uploads/2016/10/ASOEsolns2012.pdf Q11 D) Markers comments: Few students reached part (d) and very few of those who did realized that the amplitude does affect the time taken for each of Mordred’s bounces. i.e. the energy losses results in shorter periods...
  6. Haorong Wu

    I Does vacuum excitation violate the conservation of energy?

    Hi, there. I am reading the article Relativistic quantum optics: The relativistic invariance of the light-matter interaction models by Eduardo Martin-Martinez el al (2018). Here he calculate the transition probability of a vacuum excitation for a detector. Suppose there is a lab where the...
  7. Diracobama2181

    Single Particle Expectation of Energy Momentum Tensor

    $$\hat{T}_{\mu v}(x)=e^{i\hat{P}x}\hat{T}_{\mu v}(0)e^{-i\hat{P}x}$$, so $$\bra{\overrightarrow{P'}}\hat{T}_{\mu v}(x)\ket{\overrightarrow{P}}=e^{iP'x}\bra{\overrightarrow{P'}}\hat{T}_{\mu v}(0)\ket{\overrightarrow{P}}e^{-i\hat{P}x}$$ Now, $$\partial^{\mu}\Phi=\int\frac{d^3 k_1}{2\omega_{k_1}...
  8. Like Tony Stark

    Conservative forces vs friction

    Hello I've written that homework statement as an example to illustrate my doubt: How can I tell if a force is conservative or not? I've read that, if the curl of the force is 0, it's conservative. But what about the friction force (##f=\mu N##)? Its curl is also zero, but it's not conservative...
  9. M

    Is the change in internal energy really a state function?

    Here is the figure: The answer is $$Q_A<Q_B$$ which I can show by calculation using the above equations. What's confusing to me is I thought that the change in internal energy was a state function. Which would mean since the initial and final points are the same, $$\Delta E_A=\Delta E_B$$ or by...
  10. LCSphysicist

    Thermodynamics: internal energy and pressure

    The question is simply why i can't use ∂U/∂V = -P? (
  11. cwill53

    Solving for Electrical Potential Energy: Durcell's Example

    This question is an example in Durcell's Electricity and Magnetism. The solution goes as follows: [In this case] there are four different types of pairs. One type involves the center charge, while the other three involve the various edges and diagonals of the cube. Summing over all pairs yields...
  12. A

    Thermal energy/ heat in a parallel connection

    In a parallel connection heat is produced. R1 = 5 Ohm R2 = 10 Ohm What is the relation of W1/W2? 1:4 1:2 2:1 1:8 3:1 I’d tend to say 1:2, but I am not really sure…
  13. R

    When is the rate of change of Kinetic Energy maximum here?

    Because, ##F=ma=kv##, therefore, ##a=kv/m##. Clearly, the net acceleration ##A=-(g+a)##. Also, ##A=dv/dt=-(g+ \frac {kv} m )##, so cross multiplying and integrating LHS with respect to ##v## and RHS with respect to ##t## gives me: $$ v= e^{ \frac {-tk} m } * (u + \frac {gm} k) - \frac {gm} k $$...
  14. shintashi

    B What is the energy required to approach near absolute zero?

    I'm trying to understand if the amount of effort/energy required to get to absolute zero approaches infinity, or if its a linear thing... is there a point in which dropping near 0 kelvin changes from a 1:1 to an exponential curve? Is the whole thing a curve or is there a static point, like 1...
  15. bsharvy

    Energy Conservation and the Dragons (Game of Thrones)

    I thought I'd calculate how much heat was required to melt the Iron Throne, and then multiply that by the number of flame-gushes during the sack of Kings Landing, to get a total amount of energy expended. Then I'd convert that to calories and use the average number of calories per goat to...
  16. D

    Why Does Kinetic Energy Increase More with Higher Initial Velocities?

    I have a problem regarding Kinetic Energy which as we know is 1/2 m v squared. Say I have a 1kg mass moving at 10 meters/second. I have a 1 Newton rocket which I attach to the back and it burns for 1 second accelerating the mass by 1 m/sec/sec to 11 m/sec. The KE originally was 50 joules and it...
  17. Hamiltonian

    Gravitational potential energy -- Why is it always negative?

    the gravitational potential energy of a body at any point is defined to be negative of the work done by the conservative force(gravity in this case) from bringing it to that point from a given reference point. if the reference point is taken to be at infinity and the potential energy at this...
  18. E

    Work & energy VS conservation of angular momentum

    Summary:: Would energy method give us a different answer from conservation of angular momentum? Hello, I do not know how to type equations here. So, I typed my question in Word and attached it here. Please see photos. Note: This question is not a homework. I did not find it in textbooks or...
  19. R

    I Is the energy of this system conserved?

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  20. LCSphysicist

    Total energy of the normal mode on a string

    What you think about this question? Seems a little strange to me, that is, it considers the maximum kinetic energy when the displacement of the oscillators is maximum, i don't think this is right.
  21. TytoAlba95

    Chemistry MCQ- What is the Gibbs free energy value?

    Where have I gone wrong? According to the key, the right option is a.
  22. Stephen Bulking

    What is the formula for calculating reaction energy in an α decay?

    I tried momentum conservation, which gives: -pα = pdaughter <=> 2mKα = 2mKdaugther (squaring two sides) Using the given mass ratio, I found Kdaughter to be 0.0864MeV Adding the two Kinetic energy of the product particles and converting it to Joules, I got A But I don't understand why adding the...
  23. madafo3435

    Energy conservation .... contradiction?

    In b). Since the force T is perpendicular to the trajectory of the mass m, T does not perform any work on m, therefore the translational mechanical energy is conserved, from which I deduce that the initial speed is equal to the final speed, moreover, the speed is constant. Now, when analyzing...
  24. Adrian Tudini

    Energy level diagram of a chemical reaction

    Hi For a personal project, has the energy level diagram of the below reaction been derived? Voltage Applied4B+2LiNO3+C ------------->B4C+2LiNO2+O2 Thanks,
  25. G

    How Do Kinetic and Potential Energy Differ in Physics?

    I know that (1/2)m(u^2) is KE and initially I thought this showed PE=KE but I don't think so anymore... I believe this has something to do with acceleration and Centripetal force but I'm so so confused
  26. Vivek98phyboy

    What am I Missing? Solving Conservation of Energy

    By solving conservation of energy, I was able to find the linear velocity which is [10g(H-R-Rsin(theta))/7]^½ and by differentiating this with respect to "t", I arrived at the tangential acceleration value of -(5gcos(theta))/7 and found it to be in agreement with the solution provided in the...
  27. Sagittarius A-Star

    B Potential Energy formula in Special Relativty

    Reference frame is an accelerated frame in SR (uniformly accelerated with "g" in flat spacetime). An object is falling with relativitic velocity of up to 0.8 c in the pseudo-gravitational field in this frame. From Newton's theory, I know the formula for potential energy in such a scenario: ##W...
  28. LarryS

    I Are Energy Eigenstate Coefficients Real-valued?

    Given any system with discreet energy eigenstates, φn(x)e-iEnt . The φn are functions only of position. But are they also almost always real-valued?Thanks in advance.
  29. Arman777

    I Exploring Negative Energy Density and its Impact on Universe Models

    There are some universe models where ##\Lambda < 0##. In this case, the energy density of the dark-energy becomes negative. At this point, does it make sense to talk about "negative dark energy density"? Or is it possible to think of this energy as curvature on space-time? Such that, ##\Lambda <...
  30. A

    Energy conservation of metallic balls

    I did energy conservation, considering that the final velocity of the largest mass would be zero and I used moment conservation. But I am not finding the answer . Where I maked a mistake?
  31. Prabs3257

    Understanding Momentum Conservation in Simple Harmonic Motion

    I first got the velocity of the combined mass with conservation of momentum and as it was in the mean position the velocity can be written as v = wA ( w= angular frequency , A = amplitude ) as we have to take it back to natural length i put A as the initial extension but i am getting a wrong ans...
  32. S

    Energy consumed for same work with different power?

    As per me the energy required by a man with 60 age and 21 age to cover same distance is same.
  33. Arman777

    I Meaning of the inertial energy density

    I am reading an article, which talks about graduated dark energy (gDE) model. In this model, it's assumed that the inertial mass density exhibits power-law dependence to its energy density $$\rho_{inert} = \gamma\rho_0(\frac{\rho}{\rho_0})^{\lambda}$$ Where ##\gamma## and ##\lambda## are real...
  34. D

    Calculating the energy required to spool a turbocharger

    I am interested in figuring out a general formula for how much energy it takes to spin up a turbocharger if we know the diameter of the wheel,mass, target rpm, and time to go from stationary to full speed. The goal is to get a general idea of what engine speed is required to get a turbo to spool...
  35. J

    I Normal modes of vibration from the total energy

    A mass ##m## is restricted to move in the parabola ##y=ax^2##, with ##a>0##. Another mass ##M## is hanging from this first mass using a spring with constant ##k## and natural lenghth ##l_0##. The spring is restricted to be in vertical position always. The coordinates for the system are ##x##...
  36. A

    I Particle Creation function of beam energy

    This seems like it should be an easy and obvious thing to look up, but I had the hardest time finding it. Is there any graph which shows, as I increase the beam energy of a particle accelerator, what particles can be produced at each energy? Just looking for something ballpark here. Obviously...
  37. E

    Force derived from magnetic energy of a current carrying spring

    The magnetic energy of a current carrying spring, with ##N## turns, length ##x## and cross sectional area ##A##, is $$E_m = \frac{\mu_0 N^2 I^2 A}{2x}$$The (negated) spatial derivative of this yields a quantity with dimensions of force,$$F = - \frac{dE_m}{dx} = \frac{\mu_0 N^2 I^2 A}{2x^2}$$How...
  38. E

    Force on a capacitor plate as the derivative of the energy -- is it a fluke?

    Bit of a random question... capacitors can be a bit weird, in that if we connect one up to a source of EMF and do positive external work to separate the plates of the capacitor, the energy of the capacitor decreases (and instead the work you do plus the decrease in capacitor energy goes into the...
  39. Amitkumarr

    Chemistry HOMO-LUMO energy gap of compounds

    According to me Option A is a correct option because as the energy difference between two atomic orbitals increases, their interaction, and thus the value of E (or E*) decreases. Here, E is the energy difference between the bonding molecular orbital and the atomic orbital of lower energy , while...
  40. JackHolmes

    A Help with the Derrick scaling argument and topological solitons

    I have been reading Manton & Sutcliffe for some time now and can't quite wrap my head around something. If you take the Hopf invariant N of a topological soliton ϕ then its Skyrme-Faddeev energy (which I hope I've gotten right up to some constants) E=∫∂iϕ⋅∂iϕ+(∂iϕ×∂jϕ)⋅(∂iϕ×∂jϕ) d3x satisfies...
  41. Andrea Vironda

    Automotive Aerodynamic drag on a car and recovering some of that energy using a fan

    I think that driving at 130-140 km/h a car could dissipate 5-10 kW of energy only because of aerodynamic drag. Why cars don't have a fan somewhere to exploit the aerodynamic drag? For example a Pelton turbine
  42. C

    How Is the Energy Density of EM Waves Related to Capacitors and Inductors?

    The energy density of an EM wave is given as (1/2) ϵ E^2 + (1/(2μ)) B^2. This is derived from the energy density of the electric and magnetic fields of capacitors and inductors, respectively. But why should the energy density of the fields of capacitors and inductors be the same as that of...
  43. Saptarshi Sarkar

    Conservation of angular momentum and rotational kinetic energy

    I first tried to get the solution by conserving the rotational kinetic energy and got ##\omega'=\frac2{\sqrt5} \omega##. But, it was not the correct answer. Next I tried by conserving the angular momentum and got ##\omega'=\frac 45 \omega##, which is the correct answer. Why is the rotational...
  44. T

    Conservation of energy problem: Two masses, a pulley and an incline

    If M moves ##x## along the plane, her height variation in ##x \cos(\alpha)##, and, but I don't know how to find the variation of the height of ##m##
  45. Nathaniel Fisher

    B Did energy begin to exist? Can energy exist without space and time?

    Did energy begin to exist at the Big Bang? Can energy exist without space and time? Or don't we know? When I've tried to research this I get a mix of different answers. I have virtually no understanding of science or physics in general FYI.
  46. P

    Conservation of momentum and energy problem

    In an elastic collision, a 400-kg bumper car collides directly from behind with a second, identical bumper car that is traveling in the same direction. The initial speed of the leading bumper car is 5.60 m/s and that of the trailing car is 6.00 m/s. Assuming that the mass of the drivers is...
  47. AlonZ

    Mechanics- Conservation of energy

    My, supposedly rational thought is that if the pendulum will drop from a height higher than the top of the loop's height, by the law of conservation of energy, it'll have enough velocity to complete the loop. The teacher's final result shows a different approach. Am I right? Wrong? Thanks
  48. K

    What is the origin of magnetic potential energy?

    Recently I have encountered the following expression for the potential energy of a magnetic dipole of moment ##\boldsymbol{\mu}## placed in an external magnetostatic field B: $$U=-\boldsymbol{\mu} \cdot \textbf{B}$$. However, I was told that magnetic fields are non-conservative, so we can't...
  49. anuttarasammyak

    Energy transfer and conservation cases for pendulum motion and EM wave

    Let me ask a very primitive question. To and fro motion of pendulum under gravity tells us potential energy + kinetic energy = const. At the top points potential energy: max kinetic energy :0 At the bottom point potential energy: 0 kinetic energy :max EM wave is usually illustrated as...
  50. Superposed_Cat

    I Pair production via Quantum Tunneling has negative Kinetic energy?

    If we have a photon being converted to a positron-electron pair, but we lack enough energy for this to happen (hv<2Me*c^2) but the difference is smaller than the uncertainty amount, such that tunneling may be possible, would the resultant pair have net negative energy? Would tunneling even be...
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