The coefficient of restitution
Coefficient of restitution
The coefficient of restitution (COR) is a measure of the "restitution" of a collision between two objects: how much of the kinetic energy remains for the objects to rebound from one another vs. how much is lost as heat, or work done deforming the objects.
How do you calculate the coefficient of restitution?
The coefficient of restitution is found by the formula. Coefficient of Restitution = speed up/speed down. In order to find speed we had to use the average height, that we measured, and put it in the formula. v = √ (2gh) Where v = velocity, g = 9.8m/s 2, and h = average height measured.
How do I derive the formula of coefficient of restitution?
v 2−v 1=−e (u 2−u 1). This formula is Newton’s law of restitution. The coefficient of restitution always satisfies 0≤e≤1. When e=0, the balls remain in contact after the collision. When e=1, the collision is elastic: there is no loss of kinetic energy.
Can the coefficient of restitution be greater than 1?
Yes. If a body explodes then Coefficient of restitution can be greater than 1. Going by the definition of Coefficient of restitution, it is simply the ratio between relative velocities of particles before and after an interaction. Mathematically, it is capable of assuming values greater than 1.
What is the doctrine of restitution?
The principle of the doctrine of restitution is that on the repeal of a decree, the law inflict an constraint on the party to the suit who received the benefit of the faulty decree to make restitution to the other party for what he has lost.
Can coefficient of restitution be negative?
Can the coefficient of restitution be negative? No, the coefficient of restitution is always positive.
What does a low coefficient of restitution mean?
If the coefficient is high (very close to 1.00) it means that very little kinetic energy was lost during the collision. If the coefficient is low (close to zero) it suggests that a large fraction of the kinetic energy was converted into heat or was otherwise absorbed through deformation.
What does coefficient of restitution less than 1 mean?
This means kinetic energy along the common normal is 0. Kinetic energy is converted to heat or work done in deforming the objects. 0 < e < 1: This is a real-world inelastic collision, in which some kinetic energy is dissipated.
What does coefficient of restitution describe?
Definition of coefficient of restitution : the ratio of the relative velocity of two elastic bodies after rebounding to velocity before impact.
What does coefficient of restitution signify on what factor does it depends?
The coefficient of restitution is defined as the ratio of the final velocity to the initial velocity between two objects after their collision. Another way of saying this is that the coefficient of restitution is the ratio of the velocity components along the normal plane of contact after and before the collision.
What is coefficient of restitution how it explains elastic and inelastic collision?
The coefficient of restitution is a number between 0 and 1 which describes where an interaction falls on the scale between perfectly inelastic (0) and perfectly elastic (1).
Can coefficient of restitution be less than zero?
The coefficient of restitution for any collision 'generally' lies between zero and one. However, there are cases when it can be less than zero implying the objects passed through one another without fully engaging resulting in an an incomplete transfer of momentum [e.g. a bullet passing through a target].
What is the coefficient of restitution for inelastic collision?
The value of the coefficient of restitution in case of a perfectly inelastic collision is e=0.
How is the coefficient of restitution related to the energy loss on impact?
The relevant coefficient of restitution was found to decrease with impact angle, and the kinetic energy loss rate increased. Finally, the kinetic energy before and after the impact was found to significantly affect the COR and energy loss rate and the results can provide basis for mitigation measures.
How do you increase coefficient of restitution?
The coefficient of restitution increases as the temperature is lowered. A small hole is put in a 2.60 g table-tennis ball. The ball is allowed to bounce on tiles below a motion detector.
What is the type of collision when negatively charged body collides with positively charged body?
perfectly inelastic collisionwhat is the type of collision when a negative charged body collide with a positively charged body? This type of collision is known as perfectly inelastic collision in which the colliding masses coalesce and move as one after collision.
What is the coefficient of restitution for a tennis ball?
The coefficients of restitution vary according to the ball used; the tennis ball had the highest value (e = 0.82) and the cricket ball the lowest value (e = 0.48). This means the tennis ball bounced much higher than the cricket ball because much less energy was lost during impact.
How is the coefficient of restitution related to the energy loss on impact?
The relevant coefficient of restitution was found to decrease with impact angle, and the kinetic energy loss rate increased. Finally, the kinetic energy before and after the impact was found to significantly affect the COR and energy loss rate and the results can provide basis for mitigation measures.
What is the importance of coefficient of restitution in a colliding body?
The coefficient of restitution is important because it is what determines whether a collision is elastic or inelastic in nature. Determining whether a collision is elastic or not shows if there is any form of loss of kinetic energy as a result of the collision.
Does height affect the coefficient of restitution explain it?
If the relationship between the drop height of the object and the coefficient of restitution is the square root of an inverse then as the drop height increases, Cr should decrease.
How do you increase coefficient of restitution?
The coefficient of restitution increases as the temperature is lowered. A small hole is put in a 2.60 g table-tennis ball. The ball is allowed to bounce on tiles below a motion detector.
What is the coefficient of restitution?
The coefficient of restitution ( COR, also denoted by e ), is the ratio of the final to initial relative speed 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.
What does e = 0 mean?
e = 0: This is a perfectly inelastic collision. This means kinetic energy along the common normal is 0. Kinetic energy is converted to heat or work done in deforming the objects.
Why is the translational kinetic energy value less than 1?
The value is almost always less than 1 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 .
Can a rigid wall be a steel block?
A perfectly rigid wall is not possible but can be approximated by a steel block if investigating the COR of spheres with a much smaller modulus of elasticity. Otherwise, the COR will rise and then fall based on collision velocity in a more complicated manner.
Can the COR be used for inelastic collisions?
The equations for collisions between elastic particles can be modified to use the COR, thus becoming applicable to inelastic collisions, as well, and every possibility in between.
Coefficient of Restitution and Its Derivation
The coefficient of restitution is a parameter whose magnitude is defined as the ratio of the difference in final velocity to the difference in initial velocity between two objects after an event called a collision. It is a dimensionless quantity which means that it has no dimensions.
Dimensional Formula of Coefficient of Restitution
The coefficient of restitution is the ratio of the difference in final velocity to the difference in initial velocity after the collision. As the coefficient of restitution is a dimensionless parameter, therefore it has no dimensional formula.
Effect of Coefficient of Restitution on Collision
The coefficient of restitution has different effects on the different types of collision. The value of the coefficient of restitution ranges from 0 to 1 and that parameter decides the types of collisions.
Conclusion
This article concludes with the conceptual aspects of the coefficient of restitution by defining the coefficient of restitution and its formula and briefly explaining the effects of the coefficient of restitution for different types of collision.
Why is coefficient of restitution wrong?from physics.stackexchange.com
If you don't, it becomes wrong because of the little negative sign. The coefficient of restitution is a number with a value that lies in the range of 0 to 1. It can never be negative. If the formular is presented in that form, the denominator represents the relative "velocity" of approach and the numerator (excluding the negative sign) ...
Why do we put a negative sign in an equation?from physics.stackexchange.com
The negative sign in the equation is put in order create some sought of a sign balance. Let's say e=1 , equating the denominator to the numerator without the negative sign wouldn't be right since we mentioned that either one is always negative ( due to the approach and separation of an object with our reference frame) so in order to compansate for that we have to plug in a negative sign to the formula at the correct side. Which is the one shown above.
How to correct a formula that is wrong?from physics.stackexchange.com
Firstly replace the bars with brackets to make the formula correct. If you don't, it becomes wrong because of the little negative sign.
Can a relative velocity of separation have a negative sign?from physics.stackexchange.com
Now since one object is always chosen as the frame of reference of the other, either of the two (i.e relative velocity of approach/relative velocity of separation) can have a negative sign as a consequence of calculation, not both.
What does it mean when the coefficient of variation is negative?from quant.stackexchange.com
With coefficient of variation you refer to the relative standard deviation σ μ I suppose? In this case, negative values occur, as your historical data exhibits a negative drift, which means your estimate of μ is negative. In my understanding, the coefficient of variation should only be used for data in a ratio scale, or, more general, for data which does not exhibit negative values - this is not really appropriate for return time series.
What are the two related concepts of coefficient of variation?from formpl.us
As you dive deeper into the coefficient of variation, you'd come across several related concepts, including mean, standard deviation, and dispersion. Understanding these related concepts would help you apply coefficients of variation to your data sets accurately. Let's discuss some of them in this section.
What is the difference between coefficient of variation and variance?from formpl.us
On the other hand, coefficient of variation measures the relative distribution of data points around the mean.
Why do researchers use coefficients of variation?from formpl.us
Researchers use coefficients of variation to compare outcomes of systematic investigations across different populations. For example, you can use COV to measure the variability of spending among high-income earners and low-income households.
What is the difference between standard deviation and coefficient of variation?from formpl.us
Both standard deviation and coefficient of variation calculate the variations in an original data set. However, the coefficient of variation goes further to determine the ratio of the variability of the data set’s mean.
Why do financial analysts use coefficients of variation?from formpl.us
Financial analysts use coefficients of variation to evaluate investment risks for better decision-making. When presented with multiple investment options, coefficient of variation helps you compare both options in terms of risks and returns and choose the option with the highest ROI.
Why are dispersions liable to yield inappropriate results?from formpl.us
They are liable to yield inappropriate results as there are different methods of calculating the dispersions.
If the estimated regression coefficient is negative, what does it mean?
Many researchers chose linear regression analysis to reveal how the influence of the independent variable on the dependent variable. Researchers can make estimates using the data they have to interpret the results.
Simple Linear Regression Case Study
To obtain the estimated regression coefficient value, the researcher must first analyze the example of a simple linear regression case study. In the case study example, the researcher aims to determine the effect of the selling price on bread sales at a bread company in Indonesia.
How to Analyze Simple Linear Regression in SPSS
After the researcher collected the annual time series data from the bakery company, the data analysis was carried out. Data analysis can be conducted using either statistical software or manual calculations.
Linear Regression Analysis Steps in SPSS
Simple linear regression analysis using SPSS will help researchers to get the estimated regression coefficient faster than calculated manually. The manual calculations and SPSS output results will obtain the same regression estimation coefficient.
Simple Linear Regression Estimation Coefficient Output
The output of simple linear regression analysis using SPSS will get a model summary, ANOVA, and coefficient. After you click OK on the linear regression analysis step using SPSS, the output will be displayed in a separate window. Another screen will appear if you take additional steps in SPSS.
Negative Regression Estimation Coefficient Interpretation
Based on simple linear regression output, the regression estimation coefficient for the selling price variable is -1.397. The estimated coefficient value is negative, in line with the title of this article, namely, “If the estimated regression coefficient is negative, what does it mean?”
What to do if the estimated regression coefficient is negative?
The interpretation results showed that if the estimated coefficient is negative, it showed the opposite effect. If the researcher performs a correlation analysis, it can be analogous to the same. Namely, the negative coefficient indicates the opposite relationship.
Overview
The coefficient of restitution (COR, also denoted by e), is the ratio of the final to initial relative speed 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 100…
Further details
Line of impact – It is the line along which e is defined or in absence of tangential reaction force between colliding surfaces, force of impact is shared along this line between bodies. During physical contact between bodies during impact its line along common normal to pair of surfaces in contact of colliding bodies. Hence e is defined as a dimensionless one-dimensional parameter.
e is usually a positive, real number between 0 and 1:
Equations
In the case of a one-dimensional collision involving two objects, object A and object B, the coefficient of restitution is given by:
• is the final speed of object A after impact
• is the final speed of object B after impact
• is the initial speed of object A before impact
Speeds after impact
The equations for collisions between elastic particles can be modified to use the COR, thus becoming applicable to inelastic collisions, as well, and every possibility in between.
• is the final velocity of the first object after impact
• is the final velocity of the second object after impact
See also
• Bouncing ball
• Collision
• Resilience
External links
• Wolfram Article on COR
• Bennett & Meepagala (2006). "Coefficients of Restitution". The Physics Factbook.
• Chris Hecker's physics introduction
• "Getting an extra bounce" by Chelsea Wald