What is Momentum and energy: Definition and 160 Discussions

In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum. It can be written as the following equation:

This equation holds for a body or system, such as one or more particles, with total energy E, invariant mass m0, and momentum of magnitude p; the constant c is the speed of light. It assumes the special relativity case of flat spacetime. Total energy is the sum of rest energy and kinetic energy, while invariant mass is mass measured in a center-of-momentum frame.
For bodies or systems with zero momentum, it simplifies to the mass–energy equation






{\displaystyle E=m_{0}c^{2}}
, where total energy in this case is equal to rest energy (also written as E0).
The Dirac sea model, which was used to predict the existence of antimatter, is closely related to the energy–momentum relation.

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  1. K

    Jackhammer on Vehicle Suspension, Unsprung Mass, Tire patch load

    Hello all, I wanted to know what would happen if I put a jack hammer system on the unsprung part of the suspension, I posted this on the engineering forum but couldn't get a complete answer. https://www.eng-tips.com/viewthread.cfm?qid=512117 Basically the argument was if the reaction would...
  2. Ahmed1029

    I How is photon momentum compatible with special relativity?

    In relativity, momentum of a body is given by ##p=mv/\sqrt{1-v^2/c^2}##, but if mass is exactly zero and velocity is exactly ##c##, how is the photon momentum even defined? I don't think this problem can be resolved by simply stating the other formula relating energy to momentum, since it was...
  3. sachin

    Newton's laws--Block sliding up a frictionless semi-circular track

    While coming across a question on Newton's laws,I found a case when a block slides on another block kept horizontally as in the figure.All surfaces are frictionless. My concern is for the blocks to be in contact that is to move together will the horizontal velocities of both the blocks be the...
  4. M

    B Why is KE not conserved when momentum is?

    Its clear in elastic collision that both KE and momentum is conserved. Bodies exchange their velocities. It is seen clearly in this video. There is no decrease in speed. Total KE is constant. But in an inelastic collision momentum is conserved again but not the KE. There is loss in KE (I guess...
  5. J

    I Do measurements modify angular momentum and energy?

    While physics is generally believed to be CPT symmetric, there are processes for which such symmetry is being questioned - especially the measurement. One of examples of (allegedly?) going out of QM unitary evolution is atom deexcitation - we can save its reversibility by remembering about...
  6. Svend

    A How to derive the Momentum and Energy Operators from first principles?

    So we all know that the form of the momentum operator is: iħd/dx. And for energy it is iħd/dt. But how do we derive these operators? The only derivations of the i have seen is where the schrødinger equation was used, but that makes the logic circular, because the Schrødinger-Equation is derived...
  7. M

    Momentum in different referance frames

    I aready got the solution for this exercise. However, the solution used the referance frame from the car: What I'm trying to understand is the line: Because before reading the solution, I was trying to solve it using the lab frame. So this is my work so far: Using conservation of momentum and...
  8. C

    What type of ball can bounce and travel the most?

    From what I have investigated, I know that dimples do a large part of the process of going far, and elasticity for sure is something of the main bounce thing, but things that confuse me like if the ball is empty affects both characteristics, or if the same dimples affect the bounce of the ball...
  9. shankk

    I Is the classical relation between energy and momentum valid in QM?

    Here we are talking about non-relativistic quantum physics. So we all know kinetic energy T = E - V = \frac{1}{2}mv^2 in classical physics. Here V is the potential energy of the particle and E is the total energy. Now what I am seeing is that this exact same relation is being used in quantum...
  10. mattlfang

    A ball hitting a two-ball system (with a spring between them)

    I honeslty don't quite know how to start. It seems like the Hooke's coefficent k is independent of the answer to this problem. I would also appreciate any clue of expressing the condition when "balls will collide again". The fact that all balls can keep moving make this rather difficult. It...
  11. SilverSoldier

    Collisions, Impulses and Impulsive Tension

    1. When an object attached to a fixed point with a string, is given a velocity and the string goes taut. So it says in this book (Applied Mathematics 1 by L. Bostock and S. Chandler) that when the string goes taut, the component of the velocity of the particle becomes zero in the direction...
  12. I

    Help with elastic collisions please

    After simplifying the equations, I got: m1(v1-v1') = m2v2' (momentum) and m1(v1-v1')(v1+v1') = m2v2'^2 (kinetic energy) From there, I'm not sure what to do. I referred to a textbook and it said to divide the energy equation by the momentum equation (the simplified versions) and then do a...
  13. ItsukaKitto

    Maximum height a block reaches after separating from a curved moving ramp

    Diagram attached at the endI personally think there's something wrong with this question, and I'd like if someone can tell me whether it's the question that is wrong or my approach. If I attempt the solution thinking that M should be stationary, the solution is simple. 0 - 1/2 mv^2 = -mgh...
  14. 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...
  15. LCSphysicist

    Collision, angular momentum and energy

    IS my solution right? Comparing with the other solutions, the answer just exchange the signals, i don't know why, THats what ifound. And here is the three equations: {i use the point which occurs the collision} Lo = Lf >> 0 = Iw + M*Vcm(block) Eg = ct> mvo² = mvf² + MVcm² + Iw² I = ml²/3...
  16. LCSphysicist

    Understanding Angular Momentum and Energy Equations

    Since the equations are, actually, the question, i will post the image with relevant equations here: it seems strange, I'm almost sure that I didn't make a mistake in the differentiation, but differentiating 9.8b I found 9.7a with both positive terms
  17. L

    Momentum and energy in Center-of-Momentum frame

    To my mind because one particle has momentum ##\vec{p}## and the other one ##\vec{0}##. It is for instance necessary to find reference frame where one momentum will be for instance ##\frac{1}{2}\vec{p}## and the momentum of other particle should be ##-\frac{1}{2}\vec{p}##. So it is necessary to...
  18. V

    Moment of inertia, conservation of angular momentum and energy

    When I solved the problem using the conservation of angular momentum, I have got the correct result (ω = 0.006 rad/s). However, when I tried to find the answer using the conservation of energy the result was incorrect and I do not understand why.
  19. L

    I Momentum and energy calculation in special relativity

    ## \ \ \ \ \ ##In ##K##,System ##M## is composed of a spring ## N ## and four particles ## P, Q, A and B ##. The ends of spring ## N ## are fixedly connected with particles ## P and Q ## respectively. Particle ## A ## is adjacent to particle ## P ##, and particle ## B ## is adjacent to particle...
  20. Josep767

    Physics problem - Momentum and energy

    Does anyone know how to solve this problem? I translate the full statement: A 200g bullet is shot against a ballistic block passing it through and making an inelastic collision. The initial speed of the bullet is 200meters/second, the mass of the block is 3kg and the string that holds the block...
  21. A

    Momentum and impulse of a football

    Homework Statement: Joe Varsity kicks a football of mass 0.9 kg. As his foot makes contact with the ball, it exerts a force which gradually increases to a maximum value over 5 milliseconds, then falls immediately to zero, as shown in the graph above. The force is given by the equation...
  22. F

    Momentum of intertia for a dihydrogen molecule

    I don't know if the value for distance between protons given in the homework is right (##d = 74.14 pm##). Indeed, on the following link : https://brainly.in/question/7147660 , they take a distance equal to ##d = 4\times10^{-10} m##. In all cases, the same formula is applied ...
  23. jisbon

    Conservation of momentum and energy

    So to start off, the piece that hits the ground first is the smaller piece. So I can form the equations where: where ##8(u_{8kg})= m_{1}v_{1}+m_{2}v_{2}## ##m_{1}+m_{2}= 8## After 2 seconds, ##30 = v_{1}(2)+\frac{1}{2}at^{2}## ##v_{1}= 5.2m/s## ##(30-16) = v_{2}(2)+\frac{1}{2}at^{2}## ##v_{2}=...
  24. Gundyam

    Chain Hangs Over a Pulley and Starts Moving

    Homework Statement: A chain hangs over a pulley. Part of it rests on a table, and another part rests on the floor. When released, the chain begins to move and soon reaches a certain constant speed v. Can we find the height h of the table? I think this question need some tricks. I've tried some...
  25. Shivam

    Two balls of mass 4kg and 2 kg are moving in 1-D, answer the following

    My attempt- a) used equation { MV + mv = (M+m) V' } and got the right answer. b) I assumed that potential energy was asked for when the two balls were moving together with velocity 9.3m/s, so I used that when before the collision K.E( of m) + K.E( of M) will be equal to K.E(of M+m) +P.E(...
  26. T

    Calculate the *Acceleration* after a (mostly) elastic collision?

    How can I calculate the ACCELERATION of a stationary steel ball after being hit by a moving steel ball. I know how to get the final velocity but how long does it take to accelerate to that velocity from zero? Does it depend on the elasticity of the materials? I guess we need to know long did...
  27. K

    4 momentum mass non-conservation, special relativity

    Homework Statement A particle with mass M and speed v along the positive x-axis hits a stationary mass m. Two particles, each with mass µ, emerge from the collision, at angles with respect to the x-axis. (a) Write the equation for conservation of the 4-momenta, for arbitrary angles θ_1, θ_2 of...
  28. negative

    I Diffracted photon/partice momentum

    when a single photon is supposed to form a diffraction pattern, they hit the detector by different angles at the slit. so then what cancels this photon's momentum change? what happens to the photon's energy/frequency?what measurements has been done to confirm the answer?
  29. P

    Final velocities of two objects in a 2D elastic collision

    Homework Statement An atomic nucleous of mass m traveling with speed v collides elastically with a target particle of mass 3.0m (initially at rest) and is scattered at 45o (a). What are the final speeds of the two particles? Advice: eliminate the target particle's recoil angle by manipulating...
  30. N

    Calculate Internal Angular Momentum and Energy

    Homework Statement Four particles of mass 1 Kg each, are moving on a plane with the velocities given in the figure. Homework EquationsThe Attempt at a Solution First I calculated the position of the CoM: Xcm=7/4(i + j) Then I calculated the velocity of the CoM: Vcm= ½i + ¼j For the internal...
  31. S

    Maximum amount of energy the neutron can lose

    A 1 keV fast neutron (relative mass 1) in a moderator collides elastically with a helium atom He (relative mass 4) at rest. What is the maximum amount of energy the neutron can lose? My answer is 16/25 of 1ke but while deriving this answer I simply solved based on the question as if the...
  32. E

    Calculating Change in Kinetic Energy for a Collision on a Frictionless Air Table

    Homework Statement On a frictionless, horizontal air table, puck A (with mass 0.250 kg ) is moving toward puck B (with mass 0.360 kg ), that is initially at rest. After the collision, puck A has a velocity of 0.125 m/s to the left, and puck B has velocity 0.655 m/s to the right. I already...
  33. Manolisjam

    Prove the average external force is Zero

    1.Problem statement Prove the average external force of a system of particles N starting from rest and ending at rest is zero.Homework Equations If the system moves periodically prove the av. external force is zero in a period The Attempt at a Solution I don't quite understand what i am asked...
  34. E

    Momentum and energy conservation in a vertical loop

    Homework Statement Two beads with masses of M and m are threaded on a vertical loop with radius of R. M is released without velocity from a height of 1.5R from the bottom of the loop. The collision between the beads is completely elastic. What is the smallest mass M that will make the second...
  35. Amaterasu21

    I Getting Invariant Curvature from Momentum & Energy

    Hi all, I understand the mathematics behind special relativity pretty well, but I only have a bare conceptual understanding of general relativity. My understanding is that energy, momentum and stress (as described in the energy-stress tensor) are what contribute to space-time curvature and...
  36. S

    Finding the total momentum of system

    Homework Statement A car of mass 1500 kg is at rest on a platform of mass 3000 kg, which is also at rest. The platform has frictionless wheels attached to its bottom. The whole system is initially at rest. The car starts to move forward at a speed of 5.0 m/s with respect to the ground...
  37. R

    Momentum comparing between two bodies

    Homework Statement There are two objects m and 2m and Force F is applied on both objects. They move a certain distance X. Which one have greater momentum and find out 2m has √2 times more momentum than m. Homework Equations momentum P=mv The Attempt at a Solution 2m has greater momentum...
  38. T

    Block sliding down hill splits into two blocks

    I am currently working on this problem and I am stuck as to how to approach or solve it. The problem is that a block of mass 11000kg is sliding down a slope with a height of 1000m, angle of 40 degrees and the coefficient of friction between the block and the slope is 0.1. The block splits...
  39. C

    Inelastic collision and the sum of internal forces

    Homework Statement Suppose I have a system which contains two bodies m1 and m2 with initial velocities v1 and v2 , respecitvely. they hurl toward each other and make an inelastic collision. such that they are now one body of mass m1 + m2 I know that the difference in momentum is...
  40. F

    Momentum/conservation of momentum problem

    Homework Statement A 0,15kg frame, when suspended from a coil spring, stretches the spring 0,070m. A 0,200kg lump of putty is dropped from rest onto the frame from a height of 30,0cm. Find the Maximum distance the frame moves downward from its initial position. Homework Equations I tried to...
  41. Asmaa Mohammad

    The momentum and the kinetic energy

    Homework Statement Multiple choice question: The momentum of a body has increased by 25%, then its kenitic energy will roughly increase by... 1. 25% 2. 5% 3. 38% 4. 56% 5. 65% Homework Equations Pl = mv (Pl is the momentum, m is mass and v is velocity) K.E = 0.5 mv^2 The...
  42. D

    Momentum Energy and relativity question

    Homework Statement A particle of mass m is moving along the positive x direction with momentum p and energy E It collides with a particle of the same mass at rest to form a new particle of mass M. Show that M^2 = 2m/c^2 * (E + mc^2) 2. Homework Equations E^2= p^2c^2 + m^2c^4 The Attempt...
  43. B

    Find the Maximum Height of an Inverted Garbage Can Suspended by a Geyser

    Homework Statement An inverted garbage can of weight ##W## is suspended in air by water from a geyser. The water shoots up the ground with speed ##v_0##, at a constant rate ##dm/dt##. The problem is to find the maximum height at which garbage can rides. 2. Homework Equations The Attempt at a...
  44. Deadawake

    Splitting/Exploding object & Momentum

    Hi, Homework Statement A free falling object of mass "m" falling from some height, collides the floor in speed of 20 m/s (perfectly elastic collision). In his 1/2 height back up he splits into 2 pieces- ¼m which going downward and ¾m keeping upward. The ¼m reaching the floor after ½ second. 1)...
  45. S

    Velocity, momentum and energy values for a Pendulum swing

    Homework Statement This is my 'carrying out a practical investigation' assignment for Maths. I've attached the coursework (what I've wrote up to now) and my main concern is whether I've got the right differential equation to find 3 new velocity values throughout the pendulum trajectory...
  46. A

    I Momentum and energy in QM and QFT

    Hi all - apologies, I'm starting a new thread here for something buried at the end of another thread - but I think the topic of that thread had changed sufficiently to warrant a more succinct top-level post. Thanks very much to PeterDonis for his very useful answers in the previous thread...
  47. E

    Relativistic Collision - Momentum and Energy

    Two chunks of rock, each having a mass of 1.00 kg, collide in space. Just before the collision, an observer at rest in the reference frame of a nearby star determines that rock A is moving toward the star at 0.800 c and rock B is moving away from the star at 0.750 c . If the rocks stick...
  48. A

    B Measuring the energy of particles

    If i have the momentum of the particle, could I measure their energy ? I'm talking about particles in a beam, they are moving in a relativistic speed.