What is Elastic collisions: Definition and 117 Discussions

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy.
During the collision of small objects, kinetic energy is first converted to potential energy associated with a repulsive or attractive force between the particles (when the particles move against this force, i.e. the angle between the force and the relative velocity is obtuse), then this potential energy is converted back to kinetic energy (when the particles move with this force, i.e. the angle between the force and the relative velocity is acute).
Collisions of atoms are elastic, for example Rutherford backscattering.
A useful special case of elastic collision is when the two bodies have equal mass, in which case they will simply exchange their momenta.
The molecules—as distinct from atoms—of a gas or liquid rarely experience perfectly elastic collisions because kinetic energy is exchanged between the molecules’ translational motion and their internal degrees of freedom with each collision. At any instant, half the collisions are, to a varying extent, inelastic collisions (the pair possesses less kinetic energy in their translational motions after the collision than before), and half could be described as “super-elastic” (possessing more kinetic energy after the collision than before). Averaged across the entire sample, molecular collisions can be regarded as essentially elastic as long as Planck's law forbids black-body photons to carry away energy from the system.
In the case of macroscopic bodies, perfectly elastic collisions are an ideal never fully realized, but approximated by the interactions of objects such as billiard balls.
When considering energies, possible rotational energy before and/or after a collision may also play a role.

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  1. C

    I Thomson Scattering -- elastic collisions conundrum

    Teacher described the Thomson scattering effect through the lens of the electric field changing as a moving particle is accelerated. The changing electric field of the electron accelerating carries with it an amount of energy, and this energy radiates out from the acceleration event. (there were...
  2. Andrew1235

    Conservation of energy for a series of elastic collisions

    The speed of the block after the nth collision is $$ V_n=(2e)^n*v_0 $$ By conservation of energy the block travels a distance $$V_n^2/(2ug)$$ on the nth bounce. So the total distance is $$ d=1/(2ug)∗(v_0^2+(2ev_0)^2...) $$ $$ d=1/(2ug)∗(v_0^2/(1−4e^2)) $$ $$ d=1/(2ug)∗(v_0^2∗M^2/(M^2−4m^2))...
  3. 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...
  4. E

    Conservation of Momentum involving Vf, elastic collisions

    I tried solving it using this method and I got 12.5m/s, and assumed the collision was elastic. The answer is actually 6.32m/s [41.5 degrees counterclockwise from the original direction of the first ball]; the collision is not elastic: Ek = 12.1J Ek`= 10.2J I have absolutely no idea how the...
  5. J

    Conservation of Momentum (Elastic Collisions)

    Part (iii) is the part I am stuck on and is a 5 mark question. I have some idea of how to attempt it shown below momentum is conserved so mux = mvy + mvz (where ux is the initial velocity before the collision of ball x, vy is the velocity after the collision of ball y and vz is the velocity...
  6. T

    Maximizing Transferred Energy between n bodies in linear collisions

    Homework Statement My problem has two parts. 1) We have two point masses ##m,M##. and there is another mass ##m_1## between them.They are all aligned in a line. Mass ##M## is moving with speed ##u_1## toward ##m_1## and after collision and all other masses are not moving. we want to find...
  7. YMMMA

    What is the direction of the velocity/ elastic collisions.

    Homework Statement in the attached file Homework Equations Momemtum = mass - velocity The Attempt at a Solution I solved it E. Since object 2 has the larger mass, the effect is less and will move backwards a little bit.
  8. A

    A Could the 3D percolation model explain Regge-Trajectories?

    Regge-theory succesfully explains the latest LHC ##pp## elastic scattering experimental results and total cross-sections: https://arxiv.org/pdf/1711.03288 https://arxiv.org/abs/1808.08580 Three different Regge-trajectories are needed: one Reggeon, one (soft) Pomeron and one Odderon. The...
  9. neilparker62

    I How does the motion of colliding billiard balls change under Special Relativity?

    Assuming equal mass billiard balls and elastic collisions, classical physics shows that after any collision the motion of the colliding balls will be orthogonal. How does that situation change under SR ? More generally for an elastic collision between objects m and M with m<M, is maximum angle...
  10. A

    A Is field theory needed in Regge-theory?

    I have been reading some papers from G.F. Chew and S. C. Frautschi and they do not even bother to introduce the concept of "Field" when they describe hadron interactions. My impression is that they do not need to because interactions seem to be described by single Regge-trajectories. However...
  11. A

    Analyzing Elastic Collisions w/ Conservation of Energy and Momentum

    Homework Statement There is a 4 kg mass that has a speed of 6 m/sec on a horizontal frictionless surface. The mass collides head-on and elastically with an identical 4 kg mass initially at rest. The final speed of the first 4 kg mass is: (a) 0 m/s (b) 2 m/s (c) 3 m/s (d) 6 m/s Homework...
  12. gibberingmouther

    Analyzing Elastic Collisions

    Homework Statement "For a two-particle interaction, the relative velocity between the two vectors is independent of the choice of relatively inertial reference frames." and "The change in kinetic energy is independent of the choice of relatively inertial reference frames." My textbook says...
  13. R

    Elastic collisions and Newton's third law

    Hi everyone, I am new to this forum, and I'm having a hard time understanding Newton's third law and collisions, first of all I want to say that it is not homework and that I do know the basics of physics, vectors, energy, work, and momentum I also know and understand Newton's first and second...
  14. C

    Momentum, Energy, and Elastic Collisions

    Hello guys. So this is less about about the physics problem and more about the concepts behind it. I don't need help with any solution but I am framing my questions around the example given. So there are two steel balls with equal mass that are hanging from a point by a string. Both strings are...
  15. C

    Gun-projectile Elastic Collisions

    So I'm reading my textbook and there's a problem asking what the muzzle speed of a projectile would be if the gun it is being fired from is free to recoil. I'm given the muzzle speed of the projectile when the gun is stationary, the mass of the projectile, and the mass of the gun. I'm also told...
  16. minnyveller

    Why does the equation for elastic collisions work like this?

    Hi guys. Feels dumb coming back to this but I seem to have confused myself I was helping a friend with the problem: You shoot protons going v=4.2e7 m/s through a particle accelerator. They collide with gas particles of an unknown mass (pretend no velocity) and all bounce back elastically at...
  17. P

    Energy transfer in elastic collision.

    How do I derive the energy transfer equation in an elastic collision of two bodies of masses m and M respectively,using the energy and momentum conservation relations in the laboratory frame? $$\frac{1}{2} m_1 v_0^2 = \frac 1 2 m_1 v^2 + \frac 1 2 m_2 V^2$$ $$m_1 v \cos(\phi)=m_1 v_0 -m_2 V...
  18. G

    Elastic gravitational collision

    Hi all. Our lecturer gave us an exercise the other day regarding an elastic gravitational collision between a planet and a satellite where the satellite slingshots using the gravitational field of the planet. The question asks to show that ##v_{f} - v_{i} = 2v_{0}## where ##v_{f}## is the final...
  19. Flinze

    Elastic Collisions between two objects

    Homework Statement You have an inertia of 52 kg and are standing at rest on an iced-over pond in your skates. Suddenly, your 60-kg brother skates in from the right with x component of velocity -4.9 m/s and collides elastically with you. 1. What is the siblings' relative speed after the...
  20. B

    How do I solve elastic collisions?

    A 2-kg ball is moving at 3 m/s toward the right. It elastically collides with a 4-kg ball that is initially at rest. Calculate the velocities of the balls after the collision. I know that kinetic energy is conserved in elastic conditions, but I don't know how to use that to calculate this. I...
  21. A

    Elastic collisions of particles

    Homework Statement Three particles, A, B, and C, with masses M, 2M, and 3M respectively, lie at rest in that order in a straight line on a smooth horizontal table. The particle A is then projected directly towards B with velocity U. Assuming the collisions are perfectly elastic, I need to find...
  22. I

    Understanding Elastic Collisions in 2D: Exploring Velocity and Rotation

    Hi all! I'm developping a program, I wish if somebody helps me since I'm not good in physics, we know that: v'1=v1-(j / m1)*n v'1=v2+(j / m2)*n 1) when we use negative and positive sign? if we change them, there is error sometimes. 2)In 2d, do I have to calculate vx, and vy separately, what...
  23. Y

    Energy, momentum and elastic collisions

    Homework Statement A particle (of mass m velocity v) makes a perfect elastic collision with a stationary particle. After the collision both particles travel 30 degrees from original path. Use conservation of momentum/energy to obtain 3 equations relating the masses/velocities. Homework...
  24. Valerie Prowse

    Conservation of momentum question - elastic collisions

    Homework Statement A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown. If the first ball moves away with angle 30° to the original path, determine a. the speed of the first ball after the collision. b. the speed and direction of the second...
  25. J

    Confusion with non-head-on elastic collisions

    Homework Statement Two pucks of equal masses collide in a non-head-on collision. Puck 1 with a velocitiy ##u_1 = 2.50\ m/s## impacts puck 2 at rest, in a 28-degree angle. Assuming no friction between the pucks, find their final velocities. Data: ##m_1 = 5.00\ kg## ##u_1 = 2.50\ m/s##...
  26. A

    Conservation of momentum in perfect elastic collisions

    I learned that momentum conservation is vectorial, and now, when i read about perfect elastic collisions, I can't understand why they use a scalar conservation. I tryed to use vectorial coervation to see the diference and it's true: it's needed a scalar conservation. But why?
  27. S

    How Do Speeds Change After an Elastic Collision?

    Ball A, a 0.055 kg ball, moving with a speed of 2.50 m/s collides head-on with ball B, a 0.095 kg ball initially moving away from it at a speed of 1.15 m/s. Assume a perfectly elastic collision. Take the initial velocity of ball A to be in the positive x direction. (A) What is the speed of...
  28. P

    Analyzing 2D Elastic Collisions with Varying Masses and Velocities

    Homework Statement A 1.0-kg particle is moving in the +x direction at 4.0m/s when it collides elastically with a 4.0-kg particle moving in the −x direction at 1.0m/s After colliding the 1-kg particle moves off at 130 counterclockwise from the positive x-axis. Find the final speeds of both...
  29. R

    Zero Momentum in Elastic Collisions

    Is it possible to have a zero vector? The question arises in the context of conservation of momentum. In center of mass reference frame, the momentum of two masses involved in an elastic collision is zero before (as well as after) collision. It is because the two masses have equal and oppposite...
  30. B

    Solving Elastic Collisions - Momentum & Final Velocity

    Please clear up this problem... Mass 1 = 8 kg, and v = 3 m/s to the right. Mass 2 = 4 kg, and v = -3 m/s to the left. Both objects are on the same x-plane. Totally elastic collision. Momentum of mass 1 is 24, and momentum of mass 2 is -12. How do I determine final momentum for each...
  31. K

    Solving Elastic Collisions: 25g & 10g Objects

    Homework Statement A 25g object moving to the right at 20cm/s overtakes and collides elastically with a 10g object moving in the same direction at 15 cm/s. Find the velocity of each object after the collision Homework Equations Ʃp=Ʃp' v1+v1'=v2+v2' The Attempt at a Solution First...
  32. W

    Why Does Toilet Water Splash Back Up?

    Now although this is silly and quite crude (You have been warned), it is a legitimate physics question. I was sitting on the toilet a few days ago and I got some splash back. I started thinking about elastic collisions and how no matter what, nothing is perfectly elastic (correct?). Why would...
  33. B

    What is the rigorous proof for elastic collisions?

    Suppose that a mass M1 is moving with speed V1 and collides with mass M2 which is initially at rest. After the elastic collision they make, both momentum and kinetic energy are conserved. m_{1}v_{1f} + m_{2}v_{2f} = m_{1}v_{1i} \frac{1}{2}m_{1}||v_{1i}||^{2}=...
  34. G

    Number of collisions; elastic collisions

    Homework Statement Hi! I have found an interesting statement. It says, that if we have a system of two masses and a wall (all collisions will be elastic ones) with one mass (lets label it as 1) trapped between the other mass (2) and the wall and if there is no friction, then if ratio of...
  35. C

    Understanding Elastic Collisions in Two Dimensions

    So the way we learned to solve elastic collisions is to use the center of mass reference frame. I calculated that the COM is moving at v=1.66 m/s relative to the lab frame. Next I calculated the velocity of the white ball to be +1.66 m/s relative to the COM frame and the black ball to have...
  36. D

    Elastic collisions of a moving ball hitting a stationary ball

    Homework Statement A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball. If the first ball moves away with an angle 30 degrees to the original path, determine the speed of the first ball after the collision, and the speed and direction of the second...
  37. B

    Elastic Collisions: billiard ball problem with a twist

    Homework Statement A billiard ball ( mass = 10kg, initial velocity is 5 m/s) is launched along x-axis at a stationary billiard ball ( mass = 5kg). After collision, the first ball goes off at 30 degree angle above x-axis and 2nd ball goes off at 45 degree angle below x-axis. Calculate the...
  38. M

    Simple derivation for elastic collisions, where is my mistake?

    Homework Statement http://postimage.org/image/j2ccrtjp1/ Here is a scan of my work. The problem is on the scan. Just trying to derive the velocity of the target in an elastic collision, as sketched in the image... Can't seem to find the problem for the life of me.
  39. W

    Alpha Particle Elastic Collisions

    Homework Statement A proton strikes a stationary alpha particle (4He nucleus) head-on. Assuming the collision is completely elastic, what fraction of the proton’s kinetic energy is transferred to the alpha particle? Homework Equations Pi = Pf Ki = Kf The Attempt at a Solution For...
  40. D

    Friction and elastic collisions

    Someone told me I'd be more likely to get help here. Say you have these two balls moving in opposite directions. The balls float in the air and thus by themselves have negligible friction, but each is carrying a (detachable) bar across the ground, which has friction. On the very instant the...
  41. D

    About friction and elastic collisions

    Say you have these two balls moving in opposite directions. The balls float in the air and thus by themselves have negligible friction, but each is carrying a (detachable) bar across the ground, which has friction. On the very instant the balls collide with each other, they let go of their...
  42. L

    Elastic collisions between multiple bodies

    When considering the case of two or more point masses colliding in a 2 dimensional plane, is there any way to determine the final state completely from the initial conditions? if not is it not a blow to the deterministic ways of classical physics...
  43. O

    Kinetic Theory and Elastic Collisions

    Homework Statement When deriving the Ideal Gas Formula from the Kinetic Theory of Gases, we assumed that the gas molecules made perfectly elastic collisions with the walls of the container. This assumption is not necessary as long as the walls are at the same temperature as the gas. Why? The...
  44. FeDeX_LaTeX

    Elastic Collisions (Oblique Impact)

    http://desmond.imageshack.us/Himg843/scaled.php?server=843&filename=23518417.jpg&res=medium The crucial thing I'm not understanding here is how they know that after the collision (shown at the bottom of the picture), the horizontal velocities of each particle are reversed. Surely we don't...
  45. Seydlitz

    Using Special Case of Elastic Collisions in one dimension

    Is it to possible to use the special case of elastic collisions in one dimension with bodies that posses different mass. Ordinarily I know that if the body has same mass the velocity of the bodies will simply be exchanged but is the fact also hold for body with different masses? v_1 - v_2 =...
  46. A

    Simpler equation for perfectly elastic collisions.

    Perfectly elastic collisions problems usually involve calculating the final velocities of two masses from their initial momenta. Trying to derive such formula I got a different result, a shorter formula to solve the same problem: Take two masses a and b with their respective initial...
  47. T

    Elastic Collisions and Conservation of Momentum

    Homework Statement A 1 Kg car moving at 2m/s collides elastically with a stationary car. The first car rebounds opposite to the original direction at 1m/s and the second car moves off in the original direction of the first car. A) What is the mass of the 2nd car B) What is the speed of...
  48. K

    Elastic Collisions & Center of Mass

    1. A bumper car with mass m1 = 105 kg is moving to the right with a velocity of v1 = 4 m/s. A second bumper car with mass m2 = 98 kg is moving to the left with a velocity of v2 = -3.8 m/s. The two cars have an elastic collision. Assume the surface is frictionless. 2.Vcm= (m1v1+m2v2)/m1+m2 V1 in...
  49. F

    Energy Sharing in Elastic Collisions

    A stationary object with mass mb is struck head-on by an object with mass ma that is moving initially at speed v0. If the collision is elastic, what percentage of the original energy does each object have after the collision? I don't know how to find percentage.