# What is Elastic collision: Definition and 531 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. ### Elastic collision with a massless box

Using elastic equation I think the box and the block would stich together [Mentor Note -- Sideways, dark image fixed up]
2. ### Elastic Collision troubles...

So i started off breaking up the problem into two sequences, right before the collision and after the collision has happened. I need to find the first ball's speed immediately before the collision which is no problem. PEi = KEf > mghi = (1/2)mvf (vf being the velocity right before the collision...
3. ### What was the mistake in solving for the speeds of two marbles after a collision?

Solved equation 1 for v1f and then substituted into equation 2 and solved for v2f. Got 2.22 as the answer, but it said the answer is incorrect.
4. ### MIT OCW 8.01 PS11.3: Elastic Collision Between Ball and Pivoted Rod

Given that we're working with an elastic collision we want to populate the following system: ##k_{i} = k_{f}## ##p_{i} = p_{f}## Solve for kinetic energy just before and after the collision: ##k_{i} = \frac{1}{2}mv_{i}^{2}## ##k_{f} = \frac{1}{2}mv_{f}^{2} + \frac{1}{2}I_{P}^{sys}...
5. ### I Moving Spacecraft propellent less?

Assuming there are four robot inside a stationary spacecraft (mass 2 ton) , robot A has an electric gun that can shoot iron balls weighing 1kg at a speed of 8m/s. These balls collide with red balls at a 45-degree angle in a two-dimensional elastic collision. Each ball has a mass of 1kg. The red...
6. ### B Elastic collision - should final velocities be asymmetric?

The portion from the text : I copy and paste the portion from the text. After discussing a situation where the result should be symmetric, he discusses one where we should not expect the answer to be symmetric. In this case, he means that were we to substitute the values of the masses, that is...
7. ### Solving Elastic Collision of Two Balls: Theory & Solutions

With given information in the problem I can't decide which direction balls will go after collision. I assumed they will go in opposite directions. I know that is not a full solution, but I can't come up with anything else. From conservation of energy we have...
8. ### 2-D Momentum Problem -- Elastic collision of two spheres

Hi, Here is the problem What is required to answer this question is two assumptions. Firstly, the component of the momentum normal to the centre line is the same before and after. Therefore, secondly, A must recoil entirely in the horizontal plane. This is the only way to answer this question...
9. ### Question about the solution to this elastic collision

I found that 1/2m1v1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2 =>0.5*200*55^2+0.5*46*0^2=0.5*40^2*200+0.5*46*0*vf^2=>vf=78.713 m/s. The true answer is 65.2 m/s and is solved using m1v1i+mvv2i=m1v1f+m2v2f. Are these equations not interchangeable? Why can I not use the equation I used?
10. ### Question about two elastic collision formulas

Equation 1 is equating the kinetic energies of the objects before and after the elastic collision. Equation 2 is equating the momentums of the objects after the elastic collision. They can be used interchangeably as long as the collision is elastic. Am I right in my conclusion?
11. ### Perfectly elastic collision between two electrons in ⊥ B-field

For this problem, The solution is, However, is the reason why they don't include electrical potential energy because the time interval for which we are applying conservation of energy over is very small so the change in electric potential energy is negligible? Also, when they said, "electrons...
12. ### How to find resulting velocity in a perfectly elastic collision?

Using principle of conservation of momentum: m×u=m×v1 + M×v2 Where m=mass of moving particle in the beginning u=Initial velocity of particle m v1= final velocity of particle m v2=velocity of object M m×u-(mv1)=Mv2 (mu-mv1)÷M=v2 My answer is this (mu-mv1)÷M However, it is nowhere close to...
13. ### Elastic Collision Between Two Balls

I'm a little confused as to what the answer could be. This was one of my homework questions that I got wrong as I chose 0.5 v as the answer. Would someone be able to tell me what the correct answer would be?
14. ### Conservation of Momentum of Rocket Exploding after Takeoff

-Solved for vf using equation 3 to get 20.0m/s (speed before explosion) then solved for the distance to reach the explosion using equation 4, to get 20.0m, which felt wrong having the same numbers but that may just be coincidence. -Found the distance travelled of the lighter piece using 530m -...
15. ### I Elastic collision between two spheres

Suppose I have two spheres in 3 dimensions of equal mass. In cartesian coordinates, sphere A is traveling with velocity uAi, and sphere B travels with vBi. They will collide elastically. I want to find the final velocities after the collision, ie uAf and vBf. Am I correct in saying that...
16. ### Correct statement about elastic collision

From conservation of momentum: m1u1 + m2u2 = m1v1 + m2 u1 - u2 = v1 + v2 (u2 is negative because the object moves to the left) From conservation of KE, I got answer (C) So there are two correct answers, (B) and (C)? Thanks
17. ### Maximum Deflection Angle In Elastic Collision

I started by writing the equation v1i + v1f = 2v and then drawing a triangle with v1i, v1f, and 2v as the three sides. Then I used the Law of Cosines to solve for cos theta but this did not lead to a solution. Could I have a hint on how to begin? Thank you!
18. ### I Problem with understanding angular momentum

I have a problem in understanding angular momentum equation (mrv), especially the part where radius is involved. imagine an elastic collision occurred between sphere of mass (M) attached to a string forming a circle of radius (R) and moving with velocity (V) and another stationary sphere having...
19. ### Glancing Elastic Collision Questionnaire

I was able to solve for the velocity of MB and got my answer as 4.47m/s. The main issue right now for me is how to get the angles. I'm really confused on what most people have been posting as we didn't get a groundwork on this topic and so most of the basics I had them self taught. So far I...
20. ### B Alternative elastic collision formula / physical interpretation

Standard formula for final velocities ##v_1##, ##v_2## in elastic collision with masses ##m_1##, ##m_2## and initial velocities ##u_1##, ##u_2## is given by $$v_1 = \frac{m_1-m_2}{m_1+m_2}u_1+\frac{2m_2}{m_1+m_2}u_2$$$$v_2 = \frac{2m_1}{m_1+m_2}u_1+\frac{m_2-m_1}{m_1+m_2}u_2$$. By rearranging...
21. ### 1D Elastic Collision between an Elephant and a Fly

1 = elephant 2 = fly So I am trying to find v'2 which is the final velocity of the fly. I have v1 the initial velocity of the elephant 2.1m/s. So I plug it into the equation and have v'2=(2m1/(m1+m2))*2.1m/s. We are not given the masses so I just know m1>m2 but I don't understand how that will...
22. ### Bobsled Impulse and Force -- ELASTIC collision problem

I attempted to do mvf-mvi to find the impulse, but had trouble figuring out what to use as v (where does the angle of 3degrees come in?), and thought that there had to be more to the problem considering the other details I was given. I then attempted to maybe calculate the kinetic energy lost...
23. ### Elastic collision: Determine the deceleration

My approach so far is to use F = ma. The forces acting on the block in the horizonital direction are friction and the force of the spring. Choosing the direction towards the spring as the positive axis. Therefore: F = ma -Fr - kx = ma Solving for a = (-Fr - kx)/m If I plug in values I end up...
24. ### Elastic collision of particle and rotating disc

Consider the system of the mass and uniform disc. Since no external forces act on the system, the angular momentum will be conserved. For elastic collision, the kinetic energy of the system stays constant.Measuring angular momentum from the hinge: ##\vec L_i = Rmv_0 \space\hat i + I \omega_0...
25. ### Elastic collision in 2 dimensions

https://en.wikipedia.org/wiki/Elastic_collision By the angle θ they mean some angle before or during the collision, or after the collision?
26. ### Elastic collision considering the angle of impact

https://www.plasmaphysics.org.uk/collision2d.htm This is the only one I found, but when I plug in the numbers of his example I get a wrong result. Do you know any others who solved it i.e. considering the angle of impact? Angle of impact I name the angle that is shaped between the initial dx...
27. ### Elastic collision formulas -- Derivation blunder

https://en.wikipedia.org/wiki/Elastic_collision μα+mβ=μx+my, μα^2+mβ^2=μx^2+my^2 I want x in relation of all variables except y, therefore I need to replace-eliminate y: μα+mβ=μx+my =>y=(μα+mβ-μx)/m μα^2+mβ^2=μx^2+my^2=>y=((μα^2+mβ^2-μx^2)/m)^0.5 and it is eliminated if I equate these two parts...
28. ### Elastic Collision and Momentum of Ice Skaters

1. Hello, so the difficulty I am having with this problem is that is seems relatively straightforward. I have tried to solving it by assuming that this is a collision in which momentum is conserved. Therefore, I found the total momentum before the collision and used this to resolve it must be...
29. ### 2 contradicting approaches for a 1D elastic collision

So I've managed to confuse myself on this problem :) Since the problem says we can assume ##m_p << m_b##, I'm assuming that the velocity of the bowling ball will be unchanged, such that ##\vec v_{b,i} = \vec v_{b,f} = -v_{b,0} \hat i## I started out using the energy-momentum principle, ##(\vec...
30. ### Elastic collision between two balls with different masses

Since in an elastic collision, both momentum and energy is conserved, P(initial)=P(final) m1(3v)=m1v+m2v m2/m1=2 Which was the given answer but if we use conservation of energy, K.E(initial)=K.E(final) 1/2*m1*(3v)^2=1/2*m2*v^2+1/2*m1*v^2 m2/m1=8 Why do we get two different answers and why...
31. ### Elastic Collision of Hydrogen and Carbon Atoms

1.p=mv Before the collision: p hydrogen = 1.7x10^-27 * 500 =8.5*10^-25 kg ms^-1 p carbon = 2.0x10^-26 * 0 = 0 kg ms^-1 p total before = 8.5*10^-25 kg ms^-1 The sum of momentum prior to the collision is equal to the total momentum after a collision, momentum is constant, therefore; p before = p...
32. ### 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...

34. ### What is the role of Poisson's ratio in determining stress and stiffness?

Hello Can someone please tell me what is the use of poisson's ration in determinig stress cos what I know in this case we should have stress=E*strain and so now use for poison
35. ### How is it that momentum is being preserved in a non elastic collision?

How is it that momentum is being preserved in a non elastic collision? for example let's say that two balls are colliding head-on, not elastically and heat is produced, does that not reduce the momentum of the system?
36. ### Rotation and effective gravity on Earth

I'm interested in calculating effective gravity for a point-mass in a spinning gyro or swinging pendulum bob on a rotating planet undergoing any translational velocities and/or accelerations. I want to investigate the theoretical effects of high-energy mechanical oscillation on orbital...
37. ### Conservation of Momentum: Elastic Collision of Two Masses

I really want to know which answer is correct. I don’t really know if I should include velocities to the left as negative velocities in the equation. Is it -1 or 4.33? Please help! Thanks!
38. ### One dimensional elastic collision

A simple model often used to explain solar system gravitational slingshots is to consider a mass moving to the right with initial velocity v1i and a much larger mass moving to the left with initial velocity v2i. After the collision, the first mass is moving to the left with velocity v1f and the...
39. ### Finding the equation for final velocity in a perfectly elastic collision

So after not being able to solve this problem I did some researching online. I was looking around and came across this video, where they give the following equations for solving for the final velocities of both balls: v1f=((m1-m2)/(m1+m2))*v1i v2f=(2m1/(m1+m2))*v1i I plugged in my numbers and...
40. ### Elastic Collision: how do the forces and work done make sense?

Okay, say we have two balls(equal mass and size), 1 and 2. #1 has kinetic energy and #2 is at a standstill, they collide. Ignore all friction, heat, sound losses etc.. Now I know that 1 exerts a force on 2, hence doing work, which in turn uses its kinetic energy up. Therefore, 2 speeds up...
41. ### 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...
42. ### Understanding Force and Momentum in Angular Elastic Collisions

The speed of the sphere after the impact will be the same since the collision is elastic and the kinetic energy remains the same. So the change of momentum will be given by the cosine law right? What bothers me is the second question about the force that acts on the sphere (which can be given by...
43. ### Real life elastic collision and variation of kinetic energy

How small should ##\Delta T## be in a collision to be considered elastic? In elastic collisions ##\Delta T =0##, but as far as I know, just atomic collisions are considered perfectly elastic. Then, which criterias are used to considere a collision between two objects elastic?
44. ### Correct statement about perfectly elastic collision

Homework Statement In perfectly elastic collision between two atoms, it is always true to say that a. the initial speed of one atom will be the same as the final speed of the other atom b. the relative speed of approach between two atoms equals their relative speed of separation c. the total...
45. ### Collision with a ball spinning about its vertical axis

Homework Statement A ball A is rotating on a table with an angular velocity ω about its vertical axis. An identical ball B collides with the ball A elastically. After collision the ball A starts sliding over the table. The coefficient of friction is µ. Find: 1) the angle α between the angular...
46. ### 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...
47. ### Collisions Toolkit: Impulse, Momentum & Energy Formulas

Just thought I'd post a couple of formulas which I have found useful when assisting (or should I say attempting to assist!) with collisions problems in the "Homework" forums. These formulas work on the basic premise that a collision is essentially a "Newton 3 event" in which equal and opposite...
48. ### How do I solve for an elastic collision going up a ramp?

Homework Statement : Two blocks with masses m1=3kg and m2=4.5kg are moving on a platform with velocities v1 and v2, respectively. The platform is inclined with θ=30ο and is frictionless. Mass m2 has a very stiff spring with constant k=3000kg/s2 attached as shown in the figure. The two blocks...
49. ### Finding two objects velocity after an elastic collision

Homework Statement A 4-kg block moving at 7m/s makes a head-on collision with a stationary block of mass 3kg. Find the velocities of the two blocks after the collision. m1=4kg, vi1=7m/s m2=3kg, vi2 = 0m/s Trying to find vf1 and vf2 2. Homework Equations Using the conservation of momentum...
50. ### Elastic collision with particles, find the kinetic energy

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 Tried finding...