Coefficient of Restitution (COR) Calculator
An engineering tool to calculate coefficient of restitution using delta v (relative velocities).
| Parameter | Value | Unit |
|---|---|---|
| Relative Velocity of Approach | 10 | m/s |
| Relative Velocity of Separation | 8 | m/s |
| Coefficient of Restitution (e) | 0.80 | Unitless |
What is the Coefficient of Restitution?
The coefficient of restitution (COR), often denoted by the symbol e, is a dimensionless quantity that measures the “bounciness” of a collision between two objects. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach along the line of impact. [2, 4] This value provides crucial information about the elasticity of the collision.
The value of ‘e’ ranges from 0 to 1. [2]
- e = 1: A perfectly elastic collision where no kinetic energy is lost. The objects rebound from each other with the same relative speed at which they approached. [11]
- 0 < e < 1: A real-world inelastic collision. In these collisions, some kinetic energy is converted into other forms, like heat, sound, or permanent deformation of the objects. [2]
- e = 0: A perfectly inelastic collision where the objects stick together after impact, moving with a common velocity. This represents the maximum possible loss of kinetic energy. [2]
This calculator helps you easily calculate the coefficient of restitution using the delta v (change in velocity) principle, making it a valuable tool for students and professionals in physics and engineering. For more details on collision types, you might want to read about elastic vs inelastic collisions.
Coefficient of Restitution Formula and Explanation
The formula to calculate the coefficient of restitution using delta v (relative velocities) is straightforward:
e = Vseparation / Vapproach
This equation directly relates the post-collision and pre-collision relative speeds. [5]
| Variable | Meaning | Unit (auto-inferred) | Typical Range |
|---|---|---|---|
| e | Coefficient of Restitution | Unitless | 0 to 1 |
| Vseparation | The relative speed at which the objects move apart after the collision. | m/s, ft/s, etc. | Non-negative |
| Vapproach | The relative speed at which the objects move together before the collision. | m/s, ft/s, etc. | Positive |
Practical Examples
Understanding the concept with real-world numbers can be helpful. Here are two examples.
Example 1: A Bouncy Ball Collision
Imagine a high-performance superball colliding with a rigid wall.
- Inputs: The ball approaches the wall at 10 m/s and bounces back. Due to high elasticity, its separation speed is 9.5 m/s.
- Units: m/s
- Results: e = 9.5 / 10 = 0.95. This high value indicates a very elastic collision, with minimal energy loss. The Kinetic Energy Calculator could show how little energy was dissipated.
Example 2: A Car Crash
Consider two cars of similar mass in a head-on collision where they crumple and stick together.
- Inputs: They approach each other with a relative velocity of 50 mph. After the crash, they are stuck together, so their relative separation velocity is 0 mph.
- Units: mph
- Results: e = 0 / 50 = 0. This is a perfectly inelastic collision, where all the relative kinetic energy is absorbed by the deformation of the car bodies. Analyzing the Momentum Calculator would be the next step in this scenario.
How to Use This Coefficient of Restitution Calculator
- Enter Approach Velocity: In the first field, input the relative speed at which the two objects are moving towards each other before they collide.
- Enter Separation Velocity: In the second field, input the relative speed at which the two objects move away from each other after they collide.
- Select Units: Choose the unit of velocity (e.g., m/s, km/h) from the dropdown. Ensure you use the same unit for both approach and separation velocities.
- Interpret Results: The calculator instantly provides the coefficient of restitution (e), which is a value between 0 and 1. It also classifies the collision as perfectly elastic, inelastic, or perfectly inelastic and visualizes the velocities in a chart.
Key Factors That Affect Coefficient of Restitution
The COR is not just a theoretical number; it’s influenced by several real-world physical properties. [1]
- Material Properties: The inherent elasticity and plasticity of the colliding materials are the most significant factors. A steel ball bearing has a much higher COR than a lump of clay. [1]
- Impact Velocity: For many materials, the COR decreases as the impact velocity increases. High-speed impacts can cause more plastic deformation, dissipating more energy. [1]
- Temperature: Temperature can alter material properties. For example, many polymers become more brittle at low temperatures or softer at high temperatures, affecting their bounce. Squash balls are intentionally warmed up to increase their COR. [8]
- Geometry (Shape): The shape of the colliding objects affects how stress is distributed during impact, which can influence energy loss.
- Surface Conditions: Surface roughness and the presence of contaminants can increase frictional forces and energy dissipation, thereby lowering the COR. [1]
- Internal Structure: The internal design of an object can have a major impact. For instance, the “trampoline effect” in modern golf clubs is a result of a thin, flexible face designed to have a high COR upon impact with a golf ball. [3]
Frequently Asked Questions (FAQ)
A COR of 1 signifies a perfectly elastic collision, where the total kinetic energy of the system is conserved. The objects bounce off each other with the same relative speed they had before the impact. [11]
In typical passive collisions, no. However, a value greater than 1 is possible in “superelastic” collisions where stored internal energy (like a chemical explosion or a compressed spring) is released during the impact, increasing the post-collision kinetic energy. [2]
Yes. Because it is a ratio of two velocities (speed/speed), the units cancel out, leaving a dimensionless quantity. [2]
You must use a consistent unit for both the approach and separation velocities. Whether you use m/s, ft/s, or mph, as long as it’s the same for both inputs, the resulting ratio ‘e’ will be correct.
In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is still conserved, but some kinetic energy is lost to other forms like heat or sound. [12] Our Elastic Collision Calculator focuses on the former case.
The bounce is directly related to the COR. A basketball has a high COR, meaning it loses very little energy on impact with the floor. The materials and inflation pressure are designed to maximize this property. Regulations for sports like tennis and basketball often specify a required COR for the balls. [2, 3]
If the velocity of approach is zero, the objects are not moving towards each other, and a collision wouldn’t occur in this context. The formula would involve division by zero, which is undefined. Our calculator handles this by showing an error or invalid result.
It’s critical in many fields: vehicle crash analysis for designing safer crumple zones, sports equipment design (golf clubs, tennis rackets, balls), and modeling particle dynamics in industrial processes. [1]