Coefficient of restitution and velocity

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Discussion Overview

The discussion revolves around the coefficient of restitution in the context of collisions, specifically addressing the relationship between the velocities of separation and approach. Participants explore theoretical implications, energy conservation, and the concept of superelastic collisions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question whether the velocity of separation can exceed the velocity of approach, suggesting that the coefficient of restitution could be greater than 1 or less than 0.
  • Others clarify that in a perfectly inelastic collision, the separation velocity is zero, indicating a distinct scenario.
  • There is a discussion about the implications of a coefficient of restitution greater than one, with some suggesting it would mean the velocity of separation is greater than that of approach.
  • Participants raise questions about the implications for energy, particularly whether mechanical energy is conserved in such scenarios.
  • One participant introduces the concept of superelastic collisions, where kinetic energy after the collision exceeds that before, suggesting that mechanical energy is not conserved.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the coefficient of restitution and the conservation of mechanical energy, indicating that multiple competing views remain without a consensus.

Contextual Notes

The discussion includes assumptions about the nature of collisions and energy transformations, which are not fully resolved. The implications of a coefficient of restitution greater than one and the definition of superelastic collisions are also areas of ongoing exploration.

Parikshit M
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We know that the ratio of velocity of separation to the velocity of approach of two bodies in a head on collision is called coefficient of restitution .Is there no possibility that the velocity of separation is quite larger than that of approach? or vice versa? can't the ratio be more than 1 or less than 0 ?
 
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Parikshit M said:
Is there no possibility that the velocity of separation is quite larger than that of approach? or vice versa?
Those are two very different situations. For example, if the bodies stick together (a perfectly inelastic collision) the separation velocity will be zero.

What do you think a coefficient of restitution greater than one would imply?
 
Doc Al said:
Those are two very different situations. For example, if the bodies stick together (a perfectly inelastic collision) the separation velocity will be zero.

What do you think a coefficient of restitution greater than one would imply?
It would imply that the velocity of separation is greater than that of approach .
 
And what of the energy?
 
Parikshit M said:
It would imply that the velocity of separation is greater than that of approach .
Well, yes. But what does that imply as far as energy goes?
 
energy increases?.. due to increase in velocity , kinetic energy increases and hence final kinetic energy will be greater.So does that mean mechanical energy is not conserved?
 
Parikshit M said:
So does that mean mechanical energy is not conserved?
That's correct. A collision where the kinetic energy is greater after the collision than before would be an example of a superelastic collision--mechanical energy is not conserved. Some internal energy of the system must have been converted to mechanical kinetic energy. Not the typical collision between two objects.
 
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thanks a lot my books never said anything about super elastic collisions , delighted ! thanks again
 

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