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 postcollision velocity.
Coefficient of restitution
(
e
)
=

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.
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?
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...
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...
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...
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...
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 1dimensionally with ##m_2##, and the...
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...
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 2body 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...
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...
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...
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...
Homework Statement
Does anyone know how to plot a displacementtime graph that will give the average velocity of a bouncing ball? The ball bounces 5 times and I would like to know it's average velocity. What equations would I use?
Homework Equations
0.5mv^2=mgh?
The Attempt at a Solution
I...
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...
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')/(Vv)
The Attempt at a Solution
I thought maybe...
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 (headon) in one dimension. The initial parameters are as follows (units are irrelevant):
m1=1;m2=2;u1=3;u2=4;
Also, suppose that exactly...
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...
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...
Homework Statement
A small smooth sphere of mass 3 kg moving on a smooth horizontal plane with speed 8 ms1 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...
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...
Homework Statement
A particle moving with initial velocity vi = (3i + 5j) ms−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) ms−1. The coefficient of restitution for this collision is
Ans...
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 ...
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...
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...
Homework Statement
A 1300kg car is backing out of a parking space at 5.0 m/s . The unobservant driver of a 1700kg 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...
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...
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)...
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...
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...
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...
If you have the impact force on the yaxis (in Newtons) and the time on the xaxis (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...
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...
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
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.
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...
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...
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...
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...
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...
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,
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...
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...
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...
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...
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 xcomponent velocity: 0.853 m/s
Homework...
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...
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...