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Coefficient of Restitution

What is the Coefficient of Restitution?

The coefficient of restitution (COR) is a measure of how much kinetic energy remains for the objects after they collide compared to before the collision. It is a value between 0 and 1, where:

  • A COR of 1 indicates a perfectly elastic collision, where no kinetic energy is lost.
  • A COR of 0 signifies a perfectly inelastic collision, where the objects stick together, and maximum kinetic energy is lost.

Understanding the COR helps in analyzing and predicting the behavior of objects during impacts.

Factors Affecting the Coefficient of Restitution

Several factors influence the coefficient of restitution, including:

Material Properties

Different materials have varying levels of elasticity. For instance, rubber typically has a higher COR compared to steel, meaning rubber bounces back more effectively after a collision.

Surface Texture

The texture of the colliding surfaces can impact the COR. Smoother surfaces tend to have higher restitution values as there is less energy lost to friction.

Impact Velocity

The speed at which objects collide can affect the COR. At higher velocities, materials may behave differently, potentially altering the restitution value.

Temperature

Temperature changes can influence the elasticity of materials. For example, colder temperatures may make materials more rigid, affecting their ability to bounce.

Applications of the Coefficient of Restitution

The COR is applied in various fields to design and analyze systems involving collisions:

Sports Equipment Design

In sports like basketball or tennis, understanding the COR helps in designing balls and surfaces to achieve desired performance characteristics.

Automotive Safety

Engineers use the COR to design crumple zones in vehicles, enhancing safety by managing energy distribution during collisions.

Robotics and Automation

Robotic systems that interact with objects rely on accurate COR values to predict and control movements post-impact.

Typical Coefficient of Restitution Values

Material Pair

Coefficient of Restitution

Steel-Steel

0.60

Rubber-Rubber

0.90

Steel-Wood

0.50

Rubber-Wood

0.80

Tennis Ball-Racket

0.70

This table provides typical COR values for common material pairs, illustrating how different combinations affect the elasticity of collisions.

Frequently Asked Questions

What does a higher coefficient of restitution indicate?

A higher COR indicates a more elastic collision, meaning less kinetic energy is lost during the impact.

Can the coefficient of restitution be greater than 1?

No, the COR ranges between 0 and 1. Values above 1 are not physically possible as they would imply gaining energy from a collision.

How is the coefficient of restitution measured?

The COR is measured by comparing the relative velocities of two objects before and after a collision.

Does the coefficient of restitution change with repeated collisions?

Yes, repeated collisions can alter the COR due to factors like material fatigue and surface wear.

Is the coefficient of restitution the same for all types of collisions?

No, the COR varies depending on the materials involved, the nature of the collision, and external factors like temperature and surface texture.

 

About the author

Chin Trento

Chin Trento holds a bachelor’s degree in applied chemistry from the University of Illinois. His educational background gives him a broad base from which to approach many topics. He has been working with writing advanced materials for over four years in Stanford Advanced Materials (SAM). His main purpose in writing these articles is to provide a free, yet quality resource for readers. He welcomes feedback on typos, errors, or differences in opinion that readers come across.

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