What is Coefficient of restitution: Definition and 64 Discussions

The coefficient of restitution (COR), also denoted by (e), is the ratio of the final to initial relative velocity between two objects after they collide. It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision. A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic. It is measured in the Leeb rebound hardness test, expressed as 1000 times the COR, but it is only a valid COR for the test, not as a universal COR for the material being tested.
The value is almost always less than one due to initial translational kinetic energy being lost to rotational kinetic energy, plastic deformation, and heat. It can be more than 1 if there is an energy gain during the collision from a chemical reaction, a reduction in rotational energy, or another internal energy decrease that contributes to the post-collision velocity.

Coefficient of restitution



Relative velocity after collision



Relative velocity before collision


{\displaystyle {\text{Coefficient of restitution }}(e)={\frac {\left|{\text{Relative velocity after collision}}\right|}{\left|{\text{Relative velocity before collision}}\right|}}}

The mathematics were developed by Sir Isaac Newton in 1687. It is also known as Newton's experimental law.

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  1. Vladimir_Kitanov

    Impact and the Coefficient of Restitution

    Last post with picture, after this i will use Latex. She say that correct answer is 41 ft/m. Is this correct?
  2. Kaushik

    What is the value of e (coefficient of restitution) for the following?

    This is the setup. My attempt: The ball must have the same velocity before collision as it has just after the collision as it has to return through the same path. Hence ##V_{approach} = V_{separation} \implies e = 1##. Is it correct? If not, why and how should I approach this question?
  3. Benjamin_harsh

    How is the coefficient of restitution zero for this problem?

    ##coefficient\; of \;restitution = \large\frac{Relative\; speed \;after \;collision}{Relative\; speed\; before\; collision} \normalsize= 0##
  4. T

    How can we find the missing equation for solving spatial collisions of bodies?

    Good Morning May I ask about spatial collisions of bodies? In undergraduate dynamics, we study that when two particles college, we have two final unknowns: the final velocity of each particle. We first use the conservation of linear momentum. However, we supplement the analysis with the...
  5. P

    B Confusion regarding the coefficient of restitution

    I learned that there are two different definitions for the coefficient of restitution: e = final relative velocity / initial relative velocity and e = √(final KE/initial KE). However, I don't understand how these two definitions will always give the same value. If one particle with mass m...
  6. T

    B Question about the validity of Coefficient of Restitution

    Specifically as to the validity of CoR as a metric for the bounciness of an object. CoR is inherently a property of /two/ objects, say, the interaction between rubber and steel. Is it truly the case that given two objects, it's impossible to say that one object is bouncier than another? This is...
  7. G

    B How Is the Coefficient of Restitution Linked to Conservation of Energy?

    Where does the Coefficient of Restitution equation come from, in terms of the Conservation of Energy? The measure of efficiency is the velocity after the collision divided by the velocity before the collision, but how does it get to that point? I'm trying to view this focused on an object that...
  8. E

    Does the coefficient of restitution depend on the collision "type"?

    Probably a very simple question: Does the coefficient of restitution depend on the collision being performed? Consider two masses ##m_1## and ##m_2##. They are placed on a frictionless horizontal table and ##m_1## is given an initial velocity, collides 1-dimensionally with ##m_2##, and the...
  9. C

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    Homework Statement A ball of mass m hits the floor with a speed v making an angle of incidence theta with the normal. The coefficient of restitution is e. Find the speed of the reflected ball and the angle of reflection of the ball. The Attempt at a Solution I know that momentum is conserved...
  10. unseeingdog

    B Coefficient of Restitution in x and y

    I am currently studying collisions in high school and my teacher told us that, in order to calculate the direction of each object after a 2-body collision, we could change the values in the relative velocity terms of the equation of the coefficient of restitution to the components in x and y. Is...
  11. C

    Coefficient of Restitution problem

    Hello, I have this simple COR problem that I seem to be a bit stuck on. Homework Statement A 1.25 kg squash racquet swung at 37 m/s contacts a ball moving at 42 m/s in the opposite direction. Immediately after impact the racquet has a velocity of 25 m/s and the ball has a velocity of 50 m/s...
  12. M

    MHB Max Value of Coefficient of Restitution for 3 Sphere Collision

    three spheres of mass 1kg,2kg and 3kg move in the same line with velocities 5i,i and 3i respectively. the smaller masses are the first to collide.if only one collision takes place find the maximum value for the coefficient of restitution between the smaller masses. what I've got so far...
  13. UnterKo

    Can Gravity Make a Hoop Rise Off Its Support When Beads Slide Down?

    Hello, I've got a problem and I have no idea how to start. I'll be happy for any hint. Thanks Homework Statement Two beads each of mass m are at the top (Z) of a frictionless hoop of mass M and radius R which lies in the vertical plane. The hoop is supported by a frictionless vertical support...
  14. J

    Coefficient of restitution of a ball question

    Why is the coefficient of restitution of a ball independent of the height it is dropped from? A mathematical explanation would be best. Thank you.
  15. J

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  16. Y

    What Determines the Coefficient of Restitution in a Two-Object Collision?

    Homework Statement As shown in the figure below, small object A (mass: M) collides with small object B (mass: m), which is initially at rest, on top of a horizontal stand fixed to a horizontal floor. Both A and B proceed to shoot horizontally off the stand and fall to the floor. Horizontal...
  17. x2017

    Find Coefficient of Restitution with just height of the ball after one bounce

    Homework Statement A ball is dropped from a height of 9.02 m. After hitting the ground, the ball then rebounds to a height of 1.78 m. What is the coefficient of restitution associated with the ball and ground impact? Homework Equations e=(V'-v')/(V-v) The Attempt at a Solution I thought maybe...
  18. R

    Coefficient of restitution in different frames of references

    To simplify my question I would like to use a random example (although, the issue holds regardless of the numbers you pick). Suppose two objects collide (head-on) in one dimension. The initial parameters are as follows (units are irrelevant): m1=1;m2=2;u1=3;u2=-4; Also, suppose that exactly...
  19. B

    How do you find the coefficient of restitution with only d?

    Homework Statement If a rubber ball is dropped from the height of 120 cm from the floor, and rebounds to a height of 80 cm, what is the value of e, the coefficient of restitution? Show your reasoning and justify your solution. initial distance 1= 120 cm final distance 1= 0 cm initial distance...
  20. Arlan

    Calculating Rebound Height for a Ball Colliding with Steel Plate

    Question: The coefficient of restitution for ball colliding with steel is 0.95. If ball is dropped from height h sub o above steel plate, to what height will the ball rebound? Please help me with this one, Is there a formula for this? all I know is e equals velocity of the first object...
  21. toforfiltum

    Find inequality for coefficient of restituition

    Homework Statement A small smooth sphere of mass 3 kg moving on a smooth horizontal plane with speed 8 ms-1 collides directly with a sphere of mass 12 kg which is at rest. Given that the spheres move in opposite directions after the collision, obtain the inequality satisfied by e. Homework...
  22. P

    Coefficient of restitution and velocity

    We know that the ratio of velocity of separation to the velocity of approach of two bodies in a head on collision is called coefficient of restitution .Is there no possibility that the velocity of separation is quite larger than that of approach? or vice versa? can't the ratio be more than 1 or...
  23. E

    Coefficient of restitution of a particle

    Homework Statement A particle moving with initial velocity vi = (3i + 5j) m-s−1, collides with a smooth plane wall placed at some orientation to the particle’s trajectory. The resulting velocity of the particle is vf = (−2i − j) m-s−1. The coefficient of restitution for this collision is Ans...
  24. mahnoor_manoo

    What Does the Coefficient of Restitution Signify and Depend On?

    What does coefficient of retitution signify? On what factor does it depends?
  25. C

    Why Is the Coefficient of Restitution Less Than 1 in a Tennis Racket Collision?

    1. calculate the coefficient of restitution when a player hits a ball traveling into a racket at 10m/s and the racket is stationary before the ball hits it. after the ball hits it, the ball has a velocity of 5m/s and the racket is moving in the opposite direction at 1 m/s (Velocity before a -...
  26. D

    Calculating Time and Speed of Rebounds with Coefficient of Restitution

    Homework Statement I drop a ball downwards vertically onto a smooth table. The coefficient of restitution is 0<e<1. The ball rebounds upwards vertically with speed x. What is the time taken between the time that the ball was dropped to its nth rebound? Also, what is the time taken before the...
  27. K

    Impulse and Coefficient of Restitution from Ball Drop

    A 1.2kg ball dropped from a height of 3m onto a steel plate rigidly attached to the ground bounces back up to a height of 2.5m.(a). What is the impulse delivered to the ball by the plate? (b). What is the coefficient of restitution of the collision?I know my instructor wants me to use something...
  28. B3NR4Y

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    Homework Statement A 1300-kg car is backing out of a parking space at 5.0 m/s . The unobservant driver of a 1700-kg pickup truck is coasting through the parking lot at a speed of 3.2 m/s and runs straight into the rear bumper of the car. (a). What is the change in internal energy of the...
  29. F

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    The coefficient of restitution, e, of a ball hitting the floor is defined as the ratio of the speed of the ball after it rebounds from the impact to the speed of the ball right before it hits the floor. Derive a formula for the coefficient of restitution when a ball is released from an initial...
  30. Greg Bernhardt

    What is the coefficient of restitution

    Definition/Summary For a collision between two objects, the coefficient of restitution is the ratio of the relative speed after to the relative speed before the collision. The coefficient of restitution is a number between 0 (perfectly inelastic collision) and 1 (elastic collision)...
  31. K

    Colision with a wall/platform and coefficient of restitution

    1. A ball is launched against a solid wall with straight trajectory and a velocity of Vo. It hits the wall on a 3ft height and it falls on the ground at a 2ft distance (by the left of the wall). Then, an elastic platform is positioned on the exact height of the collision of the ball, and it is...
  32. Saitama

    Finding the coefficient of restitution

    Homework Statement A body is fired from point P and strikes at Q inside a smooth circular wall as shown in figure. It rebounds to point S (diametrically opposite to P). The coefficient of restitution will be: (Ans: ##\tan^2\alpha##) Homework Equations The Attempt at a Solution...
  33. D

    Coefficient of restitution of a ball bouncing down steps

    Homework Statement A small ball is placed at the edge of the top step of a flight of steps. Each step has identical dimensions. The ball is kicked horizontally, perpendicular to the edge of the top step. On its first and second bounces it lands exactly in the middle of the first and second...
  34. M

    Can you deduce the coefficient of restitution from impace force plot?

    If you have the impact force on the y-axis (in Newtons) and the time on the x-axis (in milliseconds), can you get the coefficient of restitution from just this? The plot is for the force of impact exchanged between two balls as a function of time. I know the coefficient of restitution is the...
  35. U

    Find the coefficient of restitution

    Homework Statement Two equal balls are in contact on a table. A third equal ball strikes them simultaneously and remains at rest after the impact. Show that the coefficient of restitution is 2/3. I have attached an image for clarity of problem. Please open it. Homework Equations...
  36. B

    Calculating Impact Velocity Using Coefficient of Restitution

    Hi all, I know this may see basic but how would I go about calcualting Impact velovity? The only information I have is: Height dropped, height bounced and from here I can calculate the CofR... But how would I go about finding impact velocity
  37. B

    How Do You Calculate the Coefficient of Restitution from a Bounce Height?

    Homework Statement A ball falls freely to the ground from a height of 5m and rises back to a height of 2.5m after the first rebounce. Find the coefficient of restitution.
  38. F

    Coefficient of restitution, Karate and deformation energy

    Hello Forum, I was reading a book about the physics of sports. It talks about karate and deformation energy that gets transferred to a target when a punch hits it... The formula for the deformation energy contains the coefficient of restitution and say that a small coefficient belongs to...
  39. S

    Coefficient of restitution problem

    Homework Statement The two identical steel balls A and B moving with initial velocities VA = 6 m/s and VB = 8 m/s collide, as shown in figure Q4. If the coefficient of restitution is e = 0.7, determine the magnitude and direction of the velocity of each ball just after impact. (See...
  40. P

    What Is the Coefficient of Restitution for a Baseball Hitting a Human at 100mph?

    I have been trying to find this on the internet but am having no luck. What do you guys think the coefficient of restitution for a baseball hitting a human beings body would be if the baseball were traveling at 100mph and the baseball player that it hit were stationary. I know it's hard to...
  41. D

    Angular Momentum and Coefficient of Restitution

    Here is my problem. A rod spinning about it's cg of angular speed omega. So there is no linear momentum, I believe that's correct. Just angular momentum. A ball, v_i = 0, impact the rod at radius, r. The coefficient of restitution is e. How do I use this to find the final velocity of...
  42. S

    Coefficient of Restitution for pneumatic wheels

    Hello all. I'm trying to find impact forces acting upon a stare climbing robot. I'm using the impulse = change of momentum principle. In order to figure out the change in momentum in a pneumatic wheel bouncing off a stare when it hits it, I need the Coefficient of Restitution of a pneumatic...
  43. P

    Coefficient of restitution and damping

    Can someone please explain me the difference between damping and Coefficient of restitution (COR)? Are both the same or how do they relate to each other? Thank you,
  44. B

    Finding Coefficient of Restitution for 2D Collision

    Linear momentum 2d collision Homework Statement Two particles A and B of mass m and 3m respectively, A collides with B. Find the coefficient of restitution e if \textbf{v}_{A} is purely in the \textbf{j}-direction. Velocity of each particle before collision. \dot{\textbf{r}}_{A}=9...
  45. D

    Coefficient of restitution factors

    Homework Statement On what all factors does coefficient of restitution depend?i mean do we have 1 for a pair of surfaces in contact or a surface has one irrespective of the surface of the other colliding body?Also,practically,does coefficient of restitution change/vary?If yes,could anyone...
  46. A

    Momentum + coefficient of restitution this is driving me nuts

    Momentum + coefficient of restitution this is driving me nuts! Homework Statement A Mass of 2kg traveling at 2m/s is struck by a mass of 4 kg traveling at 3m/s. If the coefficient of restitution for the two materials is 0.4 calculate their final velocities. Homework Equations...
  47. F

    Can Coefficients of Restitution Be Assigned Arbitrarily in Simulation Software?

    I'm working on a software project that simulates spheres colliding in free space. We were thinking of having the coefficient of restitution different for each sphere (arbitrarily or randomly assigned at run time) but I forgot that the coefficient of restitution depends on the collision, not the...
  48. P

    Horizontal coefficient of restitution

    Homework Statement I'm supposed to determine the [vertical] coefficient of restitution of a tennis ball, and the horrizontal coefficient of restitution, and if possible produce an equation or ratio connecting the two. Vertical CoR: 0.760 Constant x-component velocity: 0.853 m/s Homework...
  49. B

    Coefficient of Restitution between two balls

    Hi All, I conducted some experiments on snooker balls and am trying to find the coefficient of restitution between the balls. For the sake of the experiment, I have stated that the balls are sliding rather than rolling, and from an earlier experiment, I have discovered that there is a...
  50. H

    Coefficient of Restitution of Water

    I am doing my A level physics coursework on bouncing ball bearings off water. The basic set up is to fire a ball bearing of mass approx 10g and diameter 1cm out of an air gun at approx 20m/s and model its motion as it bounces off the surface of the water. Is it appropriate for me to be...