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



E
=

m

0



c

2




{\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. M

    Does the Equation for Kinetic Energy Loss Still Apply When Both Objects are in Motion?

    http://hyperphysics.phy-astr.gsu.edu/hbase/inecol.html When a block in motion(M1) collides with a a stationary object (M2) in a perfectly inelastic collision, the fraction of KE final/KE initial can be modeled as M2/M1+M2. My question is if M2 has to be stationary for this equation to...
  2. M

    Conservation of momentum and Energy

    In an isolated system, momentum is conserved. I understand this. However, I also learned that that the motion and energy of the particles inside of an isolated system is defined by the average kinetic energy (temperature). Do we have to assume that every collision is elastic and that kinetic...
  3. E

    Minimum Momentum and Energy from Schrödinger Equation

    Homework Statement I have a 2D square well with sides a. What is the minimum momentum and energy for this well? Homework Equations Minimum momentum given by Δp≈ℏΔx and Δp≈ℏΔy Minimum energy given by ΔE≈ℏΔt This might be right. It says to consider the Schrödinger Equation in 2D. I've never...
  4. O

    What is the change in energy required for the Earth to escape the Sun's orbit?

    Homework Statement Determine the energy and change in orbital speed required for the Earth to escape from its orbit around the Sun. Homework Equations I guess: Change In E = E total of o - E total of s (Egs) E total of orbit = (0.5)Eg of oribit The Attempt at a Solution Don't really know...
  5. B

    Conservation of momentum and energy problem

    Homework Statement A uniform rod has a mass 2m and a length l, and it can spin freely in a horizontal plane about a pivot point O at the center of the rod. A piece of clay with mass m and velocity v hits one end of the rod, and causes the rod-clay system to spin. After the collisions...
  6. B

    Gravitation & Conservation of Momentum and Energy

    1. Two spheres having masses M and 2M and radii R and 3R, respectively, are simultaneously released from rest when the distance between their centers is 12R. Assume the two spheres interact only with each other and we wish to find the speeds with which they collide. Write an equation from one of...
  7. 3

    Conservation of Momentum and Energy of metal pucks

    I recently did an experiment in class that involved two parts, 1) the collision of 2 metal pucks 2) the collision of 2 magnetic pucks following the analysis, i discovered that in part 1, 75% of the original kinetic energy, and 93% of the original momentum was conserved after the collision...
  8. S

    Momentum and energy two sled questions for physics

    momentum and energy two sled questions for physics... I have tried to solve these questions but sleds to me are just very confusing and hard...I really need help with this. A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in the figure. a)...
  9. Z

    Conservation of momentum and energy

    Homework Statement Hi, new to the forums and I was wondering if someone could help me figure out what I am doing wrong. Thanx in advance. Gayle runs at a speed of 4.38 m/s and dives on a sled, which is initially at rest on the top of a frictionless snow-covered hill. After she has descended a...
  10. B

    Relativistic momentum and energy

    Homework Statement A gamma ray photon with wavelength=2.0 * 10^-15m is traveling in the positive x direction undergoes a one dimensional collision with a stationary proton. a.) find the relativistic momentum and energy of the photon and proton before the collision. b.) assuming the...
  11. T

    Momentum and Energy related Bullet Question

    A 5.00 g bullet is fired into a 6.00 kg block, which is suspended from a string 1.00 m long. The string deflects through an angle of 12.0°. How fast was the bullet moving?a Transitional KE = ½ mv2 Rotational KE = ½ I2 Elastic PE = ½k L 2 I'm not sure those are the right formulas...
  12. S

    Conservation of momentum and energy question

    Hello everyone, Let's say there was gun and a bullet with a mass of 1kg at rest. The bullet and guns speeds were 2 m/s in opposite directions after firing if I right the equations. Kinetic energy 0.5m1v12 + 0.5m2v12 = 0.5m1v22 + 0.5m2v22 Why doesn't this equation work when objects are at...
  13. C

    Linear momentum and energy problem

    Homework Statement Jane, whose mass is 50 kg, needs to swing across a river having width D (50 m). She must swing into a wind with force F = 100 N while on a vine of length L (40 m) and initially making an angle theta of 50 degrees with the vertical. What minimum speed must Jane have to just...
  14. F

    High school algebra -> relativistic conservation of momentum and energy

    "high school" algebra -> relativistic conservation of momentum and energy Homework Statement Consider a head-on, elastic collision between a massless photon (momentum po and energy Eo) and a stationary free electron. (a) Assuming that the photon bounces directly back with momentum p (in the...
  15. Y

    What Happens to Energy When a Ball Bounces off a Wall?

    Change in momentum of a ball Please note, instead of making a new thread I just edited my new question into this thread Homework Statement A ball is rolled into a wall and bounces back at the same speed, the change in momentum is? Homework Equations Ein = Eout The Attempt at a Solution...
  16. I

    Momentum and Energy problem (ball and incline collision)

    Homework Statement A ball, with mass m_{1}=6 kg and speed v_{0} (unknown) hits an inclined plane (as shown) of mass m_{2}=42 kg at rest on a frictionless floor. there is no friction between the ball and the plane. the angle \beta is 10 degrees. Question: what is the value of \alpha?2. Diagram...
  17. R

    Basic Momentum and Energy and time

    Basic Momentum and Energy! and time! 1. A 5.36 g bullet moving at 681.8 m/s penetrates a tree trunk to a depth of 3.79 cm. a) Use work and energy considerations to find the magnitude of the force that stops the bullet.Answer in units of N. for this i did 1/2mv^2=w=fd so...
  18. R

    How Does a Bullet's Momentum Determine the Force Stopping It in a Tree Trunk?

    Basic Momentum and Energy! 1. (part 1 of 2) A 4.78 g bullet moving at 510.8 m/s penetrates a tree trunk to a depth of 4.93 cm. a) Use work and energy considerations to find the magnitude of the force that stops the bullet. Answer in units of N. for this i did 1/2mv^2=w=fd so...
  19. R

    Conservation of Momentum and Energy in Fisherman-Boat Interaction

    Basic Momentum and Energy! Note: Take East as the positive direction. A(n) 88 kg fisherman jumps from a dock into a 123 kg rowboat at rest on theWest side of the dock. If the velocity of the fisherman is 4.1 m/s to the West as he leaves the dock, what is the final velocity of the fisherman...
  20. R

    Momentum of a Child and Bike: What is the Total and Individual Momentum?

    1. (part 1 of 3) A 25 kg child is riding a 6.4 kg bike with a velocity of 4.2 m/s to the northwest. a)What is the total momentum of the child and the bike together? Answer in units of kg · m/s. 2. (Part 2 of 3) b) What is the momentum of the child? Answer in units of kg · m/s. 3. (part 3...
  21. R

    Calculate Momentum & Energy for 15 Metric Ton Train

    part (1 of 3 ). A 15 metric ton train moves toward the south at 70 m/s. At what speed must it travel to have five times its original momentum? A metric ton is 1000 kg. Answer in units of m/s. and Part (2 of 3 ). At what speed must it travel to have a momentum of 5 × 105 kg · m/s...
  22. E

    How Far Do the Bird and Arrow Land After Collision?

    Homework Statement A Hunter shoots a 500g arrow at a 2 kg bird perched on a tall tree growing on flat, level ground. The arrow is launched from ground level with a speed of 40 m/s at an angle of 30 degrees above the horizon. It is traveling horizontally when it embeds in the bird. How far from...
  23. Z

    Momentum and Energy: Find Maximum Energy Stored in Bumper

    Homework Statement Blocks a (mass 3.50 kg ) and b(mass 10.00 kg ) move on a frictionless, horizontal surface. Initially, block b is at rest and block a is moving toward it at 2.00 m/s . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and...
  24. J

    Conservation of momentum and energy

    Homework Statement a) At t=1 second, a 0.5 kg cart is at x=0.5 m, traveling at 0.5 m/s. At t=3 seconds, the cart is at 1.4 m, traveling at 0.4 m/s. What is the acceleration due to friction, the frictional force and the work done by friction? What is the change in kinetic energy of the cart...
  25. J

    Conservation of momentum and energy

    a) At t=1 second, a 0.5 kg cart is at x=0.5 m, traveling at 0.5 m/s. At t=3 seconds, the cart is at 1.4 m, traveling at 0.4 m/s. What is the acceleration due to friction, the frictional force and the work done by friction? What is the change in kinetic energy of the cart? b) If a cart of mass...
  26. K

    Conservation of momentum and energy

    Homework Statement A nucleus originally at rest splits into two fragments of unequal mass. The fragment with smaller mass has a larger 1.momentum 2.speed 3.Kinetic energy A. 1only B. 3only C. 1&2 only D. 2&3 only E. 1,2 &3 The Attempt at a Solution well, i can figure out the...
  27. W

    Relativistic momentum and energy of a particle

    Homework Statement In a certain reference frame, a particle with momentum of 7 MeV/c and a total energy of 9 MeV. Determine the mass of the particle. I did not mistype this problem, this is the way it appears on my assignment. Homework Equations Total Relativistic Energy...
  28. B

    What Happens to Momentum and Energy During an Inelastic Collision?

    Homework Statement Each equal ball shown in figure 1 is suspended on a separate inextensible string of equal length R. The strings are attached to a rigid support and the attachment points are separated by a distance equal to the diameter of the balls. Both balls are initially stationary in...
  29. N

    Relativistic Momentum and energy conservation

    Hello everyonea. I was studying special relativity and i got stuck on an example. Here it is:'to an observer,two bodies of equal rest mass collide head on with equal but opposite velocities 0.8c and cohere. To a second observer,one body is initially at rest. Find the apparent velocity of the...
  30. Q

    Electromagnetic Momentum and Energy

    I've been presented with these concepts, and the first time i saw them i thought they were just mathematical mambo-jumbo, but of course i didn't gave much importance to these thoughts. I've been constructing an idea of these after seeing how they behave in different circumstances, but really, i...
  31. C

    Special Relativity- momentum and energy

    [b]1. a. An electron of rest mass (0.511Mev) is accelerated in a linear accelerator so it has a total energy of 40 Gev. i).What fraction of the total energy is kinetic energy? ii).what is the reletivistic linear momentum of the electron? iii).What is its relativistic mass? b.A particle of...
  32. R

    Law of conservation of linear momentum and energy

    Homework Statement A body of 2M(KG) mass at velocity V collided with a body of mass M(KG) at rest. The first body after collision has a velocity ao 1/3V , and the second moves at 4/3V. Verify both laws of conservation of linear momentum and energy with explanation. Homework Equations...
  33. T

    Solving Momentum & Energy Homework: Glider Collision

    Homework Statement Two air track gliders of mass 0.30kg and 0.20 kg are moving towards each other with speeds of 0.50 m/s and 1.0m/s respectively. Take the direction of the more massive glider as positive. A) if the collision is elastic, find the velocity of each glider after the collision...
  34. J

    Momentum and energy in collisions, bullet problem

    Homework Statement A bullet of mass 0.125 kg traveling horizontally at a speed of 250 m/s embeds itself in a block of mass 3.5 kg that is sitting at rest on a nearly frictionless surface. (a) What is the speed of the block after the bullet embeds itself in the block? v = ? m/s (b)...
  35. T

    Momentum operator for a free particle with a definite momentum and Energy

    Hi! I need an explanation: Is the momentum operator for a free particle with a definite momentum and energy the same as what we know as the momentum operator in general? Is it just -ih/2PI()*partial/partial_x? With the justification that since the momentum is definite, delta p is 0...
  36. H

    Momentum and Energy gives different answer

    So this may be an easy question, I'm not sure, but I could not find an answer online. Basically here is the scenario. There are two balls, one has a mass of 1g and the other has a mass of 100g. The 1g ball is traveling at 10m/s, and strikes the other ball. According to momentum, m1v1=m2v2...
  37. 2

    Momentum & Energy: 10kg Block Hit by 300m/s Bullet

    Homework Statement The non-moving 10-kg block is held frictionlessly inclined at 30 degrees by a stop at point A . A 0.010-kg bullet is moving at 300 m/s hits the block and embeds into it. http://img386.imageshack.us/img386/9305/68906392wf8.jpg I'm unsure which is the horizontal...
  38. D

    Momentum and Energy sliding blocks

    Homework Statement A cube of mass m slides down a circular path of radius r cut into a larger block of mass M. M rests on a table, and friction is ignored. Both blocks start at rest and m starts at the top of the circular path. What is the velocity v of the the small cube as it leaves the...
  39. C

    Solving Momentum & Energy: Student Throws Books Homework

    Homework Statement A 64kg student is standing in the middle of a frozen pond with a frictionless surface while carrying 2 books, a physics book with a mass of 2.5kg and a biology book with a mass of 3.5kg. The physics book is thrown with a speed of 6m/s relative to the student to the right...
  40. C

    Momentum & Energy Homework: Isolated System at Rest

    Homework Statement An isolated system is initially at rest. Is it possible for parts of the system to be in motion at some later time? Explain. Homework Equations N/A The Attempt at a Solution My guess is no because if the system is at rest, the only way the system could get...
  41. C

    Can Follow-Through Increase Golf Ball Distance?

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  42. W

    Conservation of Angular Momentum and Energy

    Homework Statement We measure a comet at perihelion to have a radial distance r1 and a velocity v1. Find the radial distance and velocity when it reaches aphelion. Homework Equations L=mvr=I*\omega E=.5mv^2+U The Attempt at a Solution My professor skipped the chapter on Newton's...
  43. R

    Conservation of momentum and energy

    Homework Statement A pendulum consists of a 0.5 kg bob attached to a string of length 1.6 m. A block of mass m rests on a horizontal frictionless surface. The pendulum is released from rest at an angle of 53° with the vertical and the bob collides elastically with the block. Following the...
  44. B

    Photon Momentum and Energy: A Smooth Transition to a Tardyon's Properties?

    photon momentum and energy is a frequent topic on the forum. consider a tardyon (u<c) the momentum of which transforms as p=gp'(1+V/u') (1) E=gE'(1+Vu'/c^2) (2) state that special relativity theory ensures a smooth transition from the properties of the tardyon to the properties...
  45. P

    How Do You Calculate the Height of a Wedge in a Physics Problem?

    A small block of mass m1 = 0.300 kg is released from rest at the top of a curved wedge of mass m2 = 2.00 kg, which sits on a frictionless horizontal surface as in Figure P6.59a. When the block leaves the wedge, its velocity is measured to be 4.00 m/s to the right, as in Figure P6.59b...
  46. M

    Momentum and Energy of a car of mass

    I had a couple homework questions that I was having trouble solving..I was hoping someone could help me out.. 1. A car of mass 1430 kg traveling at 26 m/s is at the foot of a hill that rises 120 m in 3.8 km. At the top of the hill, the speed of the car is 10 m/s. Find the average power...
  47. C

    How does friction affect the distance of a sliding object?

    Hi guys, in need again for some help...thanks to everyone who helped before on my previous thread on potential energy i understand it a little better now. again I am stuck on three problems if you guys could provide me some insight i'd greatly appreciate it. 1) Sliding in socks. Suppose that...
  48. K

    Conserv. of Momentum and Energy Question

    I was able to get the answer to Conservation of Momentum but couln't get the same answer using conservation of energy? Steps are shown below. Where did i go wrong using the conserv. of engery method? Assume frictionless surface and inelastic collision. Q: A 10 gram bullet with a velocity of...
  49. K

    Conservation of Momentum and energy problem help

    SOmeone explain to me this because I am lost. i got 2 masses one velecity. the equation is like is mass times volocity + mass times velocity=0 122kg*22m/s+14kg*v=0 I made these numbers up what i do is multiply and add then move my anwser to the other side becoming negative but that doesn't...
  50. C

    Conservation of momentum and energy problem

    I read the answer of it, but I don't get why the answer is that. And the answer is 1/2 M gun x (M bullet * V bullet / M gun)^2 - 1/2 M gun+you x (M bullet * V bullet/ M gun+you) ^2thx!
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