Enter the relative speed of separation after collision and the relative speed of approach before collision into the calculator (use any consistent units). The calculator will evaluate the Coefficient of Restitution.
Coefficient of Restitution Formula
e = \frac{\left|V_{\mathrm{rel,after}}\right|}{\left|V_{\mathrm{rel,before}}\right|}Variables:
- e is the Coefficient of Restitution (unitless)
- Vrel,after is the relative speed of separation after collision (e.g., m/s)
- Vrel,before is the relative speed of approach before collision (e.g., m/s)
To calculate the Coefficient of Restitution, divide the relative speed of separation after the collision by the relative speed of approach before the collision.
How to Calculate the Coefficient of Restitution?
The following steps outline how to calculate the Coefficient of Restitution.
- First, determine the relative speed of separation after collision (m/s).
- Next, determine the relative speed of approach before collision (m/s).
- Next, gather the formula from above: e = Vrel,after / Vrel,before.
- Finally, calculate the Coefficient of Restitution.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
relative velocity after collision (m/s) = 35
relative velocity before collision (m/s) = 60
Frequently Asked Questions
What is the Coefficient of Restitution?
The Coefficient of Restitution (e) measures how “bouncy” a collision is along the line of impact. It is defined as the ratio of the relative speed of separation after the collision to the relative speed of approach before the collision.
How does the Coefficient of Restitution affect a collision?
The Coefficient of Restitution is related to how much kinetic energy is lost in a collision (the exact kinetic energy loss also depends on the masses and the collision geometry). A value of 1 indicates a perfectly elastic collision (no kinetic energy loss for the system along the line of impact), while a value of 0 indicates a perfectly inelastic collision in which the objects stick together and the kinetic energy loss is maximal for the given initial momenta.
Can the Coefficient of Restitution be greater than 1 or negative?
For most ordinary (passive) impacts, e is between 0 and 1. However, e can be greater than 1 in a superelastic collision, where stored internal energy (for example, from a spring or explosive mechanism) is released during impact. By definition, e is typically taken as a nonnegative ratio of relative speeds; negative results usually come from using signed velocities with an inconsistent sign convention rather than from a “negative” coefficient.
How can the Coefficient of Restitution be used in real-world applications?
The Coefficient of Restitution is used in various fields such as sports science to design better sports equipment, automotive industry for improving vehicle safety by studying collisions, and in mechanical engineering for analyzing and designing collision-involved machinery.
