Does the coefficient of restitution depend on the collision "type"?

In summary, the coefficient of restitution is a measure of the elasticity of a collision between two objects. It can be calculated by comparing the initial and final velocities of the objects. However, this coefficient may vary depending on the type of collision being performed, such as a 1-dimensional collision on a horizontal table or dropping an object onto another from a height. Additionally, if the collision is strong enough, the objects may break apart, making the coefficient of restitution invalid. Further research and experiments may be needed to fully understand the relationship between the coefficient of restitution and different types of collisions.
  • #1
erfz
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 1-dimensionally with ##m_2##, and the coefficient of restitution is calculated from the initial and final velocities.

If instead I had ##m_2## on a table and ##m_1## was dropped from a height ##h_i## onto ##m_2##, and then came up to a height ##h_f##, would the calculated coefficient of restitution be the same here as in the first situation?
 
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  • #2
erfz said:
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 1-dimensionally with ##m_2##, and the coefficient of restitution is calculated from the initial and final velocities.

If instead I had ##m_2## on a table and ##m_1## was dropped from a height ##h_i## onto ##m_2##, and then came up to a height ##h_f##, would the calculated coefficient of restitution be the same here as in the first situation?

If you dropped one mass from high enough, then possibly the objects would break apart, rather than bounce off each other.

This suggests to me that the coefficient of restitution for two objects would tend to be approximately constant across a limited range of collision velocities, but in general a single coefficient would not apply across all possible collisions.
 
  • #3
PeroK said:
If you dropped one mass from high enough, then possibly the objects would break apart, rather than bounce off each other.

This suggests to me that the coefficient of restitution for two objects would tend to be approximately constant across a limited range of collision velocities, but in general a single coefficient would not apply across all possible collisions.
But assuming that they do not break, the coefficient can be applied to both scenarios?
 
  • #4
erfz said:
But assuming that they do not break, the coefficient can be applied to both scenarios?
In general you may get cracks or permanent deformations, which I suspect will be non-linear in nature.

Have you tried looking online for articles on experiments looking at this?
 
  • #5
PeroK said:
In general you may get cracks or permanent deformations, which I suspect will be non-linear in nature.

Have you tried looking online for articles on experiments looking at this?
No, but that is a good idea.
Thank you!
 

1. What is the coefficient of restitution and how is it related to collisions?

The coefficient of restitution is a measure of the elasticity of a collision. It is defined as the ratio of the relative velocity of the two objects after the collision to the relative velocity before the collision. In simpler terms, it is a measure of how much energy is conserved during a collision.

2. How is the coefficient of restitution calculated?

The coefficient of restitution can be calculated using the formula e = (v2-v1)/(u1-u2), where e is the coefficient of restitution, v1 and v2 are the velocities of the two objects after the collision, and u1 and u2 are the velocities before the collision.

3. Does the coefficient of restitution depend on the mass of the objects involved in the collision?

Yes, the coefficient of restitution is affected by the mass of the objects involved in the collision. In general, a higher mass will result in a lower coefficient of restitution, meaning that less energy is conserved during the collision.

4. How does the type of collision affect the coefficient of restitution?

The type of collision does have an impact on the coefficient of restitution. In an elastic collision, where there is no loss of energy, the coefficient of restitution will be 1. In an inelastic collision, where some energy is lost, the coefficient of restitution will be less than 1. In a completely inelastic collision, where the objects stick together after the collision, the coefficient of restitution will be 0.

5. Can the coefficient of restitution be greater than 1?

Yes, the coefficient of restitution can be greater than 1 in certain cases. This is referred to as a superelastic collision, where the objects gain additional energy after the collision. However, these types of collisions are rare and usually only occur at the microscopic level.

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