# What is Relativistic kinetic energy: Definition and 31 Discussions

In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.
In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is

1
2

m

v

2

{\displaystyle {\begin{smallmatrix}{\frac {1}{2}}mv^{2}\end{smallmatrix}}}
. In relativistic mechanics, this is a good approximation only when v is much less than the speed of light.
The standard unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound.

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1. ### B How to relate relativistic kinetic energy and momentum

Hi guys, a special relativity problem requested to choose the right graph representing relativistic momentum ##p## as a function of rel. kinetic energy ##K##, from these four: At first, I tried writing ##p## as a function of ##K##, in order to then analyze the function's graph and see if it...
2. ### B Questions about the relativistic kinetic energy expressions

<Moderator's note: Moved from New Member Introduction.> I am asking assistance in addressing several questions I have with the relativistic kinetic energy expressions given as {I am sorry for the format of the notations. It was inadvertently distorted.} KE=mc2 [1/sqrt(1-(v2/c2)) -1]...
3. ### B Relativistic Kinetic Energy: Does Mass Change?

Hello, According to Special Relativity, the mass of an object must increase as its speed approaches the speed of light. m=m0γ In the formula that allows us to calculate the kinetic energy of a body, KE=0.5mv2, should we take into consideration such increase in mass? Weam Abou Hamdan Wednesday...
4. ### Help me find my error in a relativistic kinetic energy calculation

Hi everyone. Given: an asteroid with the mass of 50,000,000 kg, which is moving with the velocity of oh-my-god particle -- 99.99999999999999999999951% of c. Due to relativistic effects, its total kinetic energy will be 1.44 E+36 Joules (Lorentz factor = 3.2 E+11). A hypothetical particle...
5. ### I What does this symbol represent?

In my nuclear engineering class we are looking at relativity right now. For one of our homework problems we have to derive an equation for a particle moving at relativistic speed showing the kinetic energy in terms of the particles momentum. In the answer they have a term mc and I have no idea...
6. ### Relativistic kinetic energy and momentum

Homework Statement A proton has a speed of 0.2c. Find the speed of an electron that has (a) the same kinetic energy as the proton, and (b) the same momentum as the proton. Homework Equations K=ϒmc^2-mc^2 The Attempt at a Solution This is what I did for the same kinetic energy part, but I...
7. ### I Relativistic Kinetic Energy Derivation

Hello, I tried a different route to derive relativistic kinetic energy and I cannot see why it doesn't work. Here is my work: 8.00000000000000E+01 RM, Rest mass of object 7.50000000000000E+05 v, velocity of object 6.00001877636573E+07 Momentum, p,= RM/Sqrt(1-(v^2/c^2))*v...
8. ### Relativistic Kinetic Energy Derivation

Homework Statement This problem comes from an intermediate step in the textbook's derivation of relativistic energy. It states that E_k\:=\:\int _0^u\frac{d\left(\gamma mu\right)}{dt}dx then leaves the following intermediate calculation as an exercise to the reader: Show that...
9. ### Correction to non relativistic KE

Homework Statement find series expansion of relativistic energy formula, At what speed is there a 10% correlation to the non relativistic KE. Homework Equations $$E=\frac{mc^2}{\sqrt(1- \frac{v^2}{c^2})} = mc^2 + \frac{1}{2}mv^2 + ...$$ The Attempt at a Solution I found the series above...
10. ### Relativistic Kinetic Energy as a solution to a DE

Has anyone ever seen KE derived this way? The only non-classical assumption is that mass = Energy/c^2 (I know, that's a big one) and that it accumulates as mass as the object is accelerated. (sorry for the plain text formatting, I need to learn how to do it right, I may reply with my first try)...
11. ### Relativistic kinetic energy - particle decay

Homework Statement A pion at rest (mπ = 273me) decays into a muon (mμ = 207me) and an antineutrino (mn ≈ 0). Find (a) the kinetic energy of the muon and (b) the energy of the antineutrino in electron volts. Homework Equations K = (γ-1)mc2 E = γmc2 ER = mc2 E2 = p2c2 + (mc2)2 I didn't...
12. ### Relativistic Kinetic energy, momentum, speed.

Homework Statement An Electron (rest mass=9.11*10^-31kg) is accelerated to an energy (mass energy+kinetic energy) of 30*10^6 eV (30 MeV). What is its kinetic energy? Its momentum? Its speed? (Note: 1 eV = 1.602*10^-19 Joules; c=2.998 * 10^8 ms^-1) Homework EquationsThe Attempt at a Solution...
13. ### Relativistic kinetic energy derivation (from Work expended)

Hi, I'm trying to get the relativistic kinetic energy, ## T ##, from the work expended, ## W ##, (assuming that the body is at rest initially) and I'm doing it like this (in 1D): $$W = T = \int F ds = m \int \frac{d(\gamma u)}{dt}u dt = m\int u d(\gamma u)$$ Where...
14. ### Why Does 1/2mγv^2 Fail to Accurately Calculate Relativistic Kinetic Energy?

Homework Statement Show that 1/2mγv^2 does not give the correct kinetic energy. Homework Equations 1/2mγv^2 γ = 1/(sqrt(1-v^2/(c^2))) The Attempt at a Solution Well, since the classical mechanics version of kinetic energy was the integral of momentum with respect to v, I felt I could...
15. ### Why Does Integrating Relativistic Kinetic Energy Lead to Different Results?

I am doing the integral DK = ∫pdv = mv/(√1-v2/c2)dv , in the same way as they do the ∫Fds = ∫mvdv if you separate the integrals. Where is my mistake and istead of (γ-1)mc2 I get -mc2/γ . I know that I am mistaken, I did see some equations but I don't get the 'theoretical' part.
16. ### Which Equation Correctly Represents Relativistic Kinetic Energy?

What is the correct equation for relativistic kinetic energy? Is it KE=mγc^2-mc^2 or KE=mc^2(γ-1)?
17. ### Deriving formula for Relativistic Kinetic Energy

Homework Statement Hey all, I am encountering a problem with a derivation of the formula K_{ineticEnergy}=mc^2-m_{0}c^2 as it is described by my textbook. I need someone to explain to me how the author changes the integral and the upper limit of it in the final part. I'll now give you the...
18. ### Darwin and relativistic kinetic energy correction for hydrogen

Homework Statement Combine the Darwin correction with the relativistic kinetic energy correction for l=0 to show that the fine structure formula: \DeltaE_{fs}= - \frac{(E^{(0)2}_{n})}{2mc^{2}}[\frac{4n}{j + 1/2}-3] remains valid for l=0 Homework Equations From a previous problem...
19. ### Relativistic kinetic energy and force.

classically, an electron accelerating from rest in a uniform electric field will have a kinetic energy proportional to the distance 'd' from its point of origin. will this continue to hold even when the electron is moving at relativistic velocity? I understand that the formula for...
20. ### Relativistic Kinetic Energy & Gamma

Homework Statement (7.) If its kinetic energy is 3000 MeV, find its speed as a multiple of c. In this case you cannot use the nonrelativistic approximation. m=4000 MeV/c^2 (rest energy=4000MeV) ^from previous problem, of which this one is a continuation Homework Equations...
21. ### How Does Relativistic Kinetic Energy Derive from Force Integration?

In the derivation of the relativistic kinetic energy, K=\int_{x_1}^{x_2}F\,dx = \int_{0}^{v}\frac{d}{dt}(mv)\,dx = \int_{0}^{v}(mv\,dv+v^2\,dm) here, my lecturer told us without showing that mv\,dv+v^2\,dm = c^2\,dm Can someone please give me hints on how to combine these two integrals? I...

Hey guys, I'm new here. In fact I'm new to the site. Anyway, I just need this question answered. Is it possible to skip the equations for kinetic energy by simply adding gamma to the Newtonian kinetic energy equation? If so, could you give an example?
23. ### Relativistic kinetic energy comapred to Newtonian

Homework Statement Find the speed of a particle whose relativistic kinetic energy is 40% greater than the Newtonian value for the same speed. Krel = relativistic kinetic energy Knew = Newtonian kinetic energy Homework Equations Krel = (gamma - 1)mc^2 Knew = 0.5mv^2 gamma =...
24. ### Is Kinetic Energy Different in Relativity?

I am currently reading Einstein's book "Relativity: The Special and General Theory", and I came across I point I don't quite understand. Einstein says: In accordance with the theory of relativity the kinetic energy of a material point of mass m is no longer given by \frac{1}{2}mv2 but...
25. ### Which expression for Relativistic Kinetic Energy is correct?

I saw that the Relativistic Kinetic Energy calculation for these two sources, seems to be different : http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html see : Conservation of Energy EK = gamma*m*c^2 While here : http://en.wikipedia.org/wiki/Kinetic_energy see ...
26. ### Relativistic kinetic energy and proton collisions

[SOLVED] Relativistic kinetic energy and proton collisions Homework Statement Find the minimum proton kinetic energy required to produce an antiproton in the reaction P+P\rightarrow P+P+P+\overline{P} for protons: (a) Incident on protons of equal and opposite momentum, (b)...
27. ### The Relativistic Mass-Energy Relationship

I am reading "Relativity" by Einstein right now, and I came across a formula he gave for kinetic energy in accordance with his theory of relativity. He says that "the kinetic energy of a material point of mass m is no longer given by the well-known expression .5m(v^2) but by the...
28. ### Does Relativistic Kinetic Energy Account for Mass Increase at High Speeds?

i ask clarifications about this issue, K_e = mc^2 -m_0c^2 is the kinetic energy of a hight speed particle (http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/releng.html) my question is: according to Newton a body to be accelerated requires energy, according to einstein the mass of...
29. ### Understanding Relativistic Kinetic Energy in Modern Physics

Hi Everyone, I'm reading in my modern physics book about relativistic kinetic energy. I'm a little confused about what rule of calculus allows the following statement: KE = \int_{0}^{s} \frac{d(mv)}{dt} ds = \int_{0}^{mv} v d(mv) I see that they must be saying KE = \int_{0}^{s}...
30. ### Proving Relativistic Kinetic Energy: (1/2)*(gamma)mv^2

How do you prove that (1/2)*(gamma)mv^2 doen't equal the kinetic energy of a particle moving at relativistic speeds?
31. ### This relativistic kinetic energy equation makes no sense to me

This "relativistic kinetic energy" equation makes no sense to me Presently, I'm reading an e-book I found on the internet titled "Relativity: The Special and General Theory", which may or may not have been written by Albert Einstein. Here's the part which has me in deep patatoes: The author...