Momentum and energy Definition and 39 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. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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...
  6. 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...
  7. 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...
  8. 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...
  9. 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...
  10. ItsukaKitto

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

    Diagram attached at the end I 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...
  11. Achintya

    Emergency elevator safety feature calculations

  12. 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...
  13. 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 : , they take a distance equal to ##d = 4\times10^{-10} m##. In all cases, the same formula is applied ...
  14. 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...
  15. 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(...
  16. 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...
  17. 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...
  18. 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?
  19. 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...
  20. 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...
  21. E

    Momentum and Kinetic Energy

    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...
  22. 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...
  23. 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...
  24. 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...
  25. 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...
  26. 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...
  27. J

    Find speed and direction of a particle after collision

  28. 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...
  29. 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...
  30. 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...
  31. B

    Inverted garbage can

    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...
  32. 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)...
  33. 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.
  34. Y

    Relativistic elastic collision

    Homework Statement Homework Equations et Em and pm be the energy and momentum of the mass m after the collision. Let p and p' be the momentum of mass M before and after the collision. From conservation of 4 momentum: \begin{bmatrix}E+m \\ p\end{bmatrix}=\begin{bmatrix}E_m+E' \\...
  35. R

    A Linear enercy transform (LET) and momentum

    I have some understanding of Liner Energy Transfrom (LET), but when I compare it with other terminologies such as momentum, then it gets little contradicting. For example, I know that if talk about particles and ions, then a gold ion (AU) has much higher LET than an Iron particle (Fe). And...
  36. jakec

    Momentum conservation (ballistic pendulum)

    Homework Statement A .01kg bullet is fired into a 1.2kg block hanging from a 1m wire. The bullet exits the block with a speed of 200m/s and the block swings to a height of .2 meters. What is the original velocity of the bullet? What percentage of the original energy of the bullet is no longer...
  37. Blockade

    How to tell if energy was conserve in a momentum problem?

    How can you determine if energy was conserve in a momentum problem? Let's say a small mass "m" hits a larger stationary mass "5m" where the smaller mass "m" flies bounces upward and the larger mass "5m" bounces in a negative downward direction. So from them bouncing off each other I know that...
  38. ultralightbeam

    Mass propelled backwards in 1 second?

    Homework Statement Cross sectional area: 4.5x10^-2 m Speed: 3.5ms-1 Density of sea water: 1030 kg m-3 Calculate the mass of water propelled backwards in 1 s. Homework Equations The Attempt at a Solution Could someone just guide me through it, maybe give me a starting point like which...
  39. P

    Easy collision question, momentum and energy

    Homework Statement A spring (k=4200N/m) and box A (mA=120kg) are on a frictionless incline, as shown below . Box A is pressed against the spring such that it is compressed 1.0m, and then released. Box A then hits, and sticks to box B, 1.0m farther up the ramp from the uncompressed position of...