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I have been reading a published article which tried to explain collisions between rigid and non-rigid bodies and it mentioned the following :

"The deformation prone mass in humans has been referred to as ‘‘wobbling mass’’ and is unable to transmit impact forces as effectively as rigid mass (Gruber et al., 1998). During a collision the greater the rigidity of the impacting mass, the less elastic the collision. The less elastic a collision, the greater the momentum imparted into the target or opponent (Pain & Challis, 2002)."

But I thought the more rigid a body is , the more elastic the collision, like the collision between 2 billiard balls. There is no virtually no deformation and 'kinetic energy/momentum' can be assumed conserved.

But isn't the collision between 2 rubber balls also an approximate elastic collision, which seems to contradict the billiard ball example?

So does the rigidity of an impacting mass affect the momentum transfer to the impacted mass?

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But I thought the more rigid a body is , the more elastic the collision, like the collision between 2 billiard balls.

And you would be correct.

I'm not sure what they were thinking when they said "During a collision the greater the rigidity of the impacting mass, the less elastic the collision". Perhaps they were using the term "elastic" only in terms of something that is capable of being stretched or expanded?

The only requirement for a collision to be elastic is that there be no permanent deformation, which would mean some loss of kinetic energy. It is not required that an object stretch or expand for a collision to be elastic, only that said stretching or expansion not result in permanent deformation.

Perfectly rigid bodies do not, by definition, deform. If they can't deform then obviously there can't be any permanent deformation. So their collisions are perfectly elastic.

On the other hand, the collision between a moving rigid body and fixed ideal spring is also perfectly elastic. Although the ideal spring deforms, it does so with no permanent deformation. During the collision kinetic energy of the rigid body is temporarily converted to elastic potential energy with is then converted back into kinetic energy of the rigid body.

Hope this helps.

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  • $\begingroup$ Isn't a mass rebounding off a spring a very good example of an elastic collision? The argument seems to be that a collision involving an ideal spring must be less elastic than one involving an ideal rigid body, simply because the spring is less rigid. But an ideal spring doesn't dissipate any energy, just like an ideal rigid body doesn't - I'm not sure I agree with "more rigid = more elastic". $\endgroup$ Nov 8, 2023 at 15:41
  • $\begingroup$ @NuclearHoagie Actually, my original draft answer included the spring example. I'll add it back in. Thanks. $\endgroup$
    – Bob D
    Nov 8, 2023 at 15:45
  • $\begingroup$ Right, elasticity just requires that we don't lose much energy in the collision. You can do that by either not deforming much, or by deforming in a reversible manner. The first part of this answer suggests you can only do the former, but making an ideal spring more rigid does not make collisions with it any more elastic. I might agree that deformable objects have a greater potential to dissipate energy than objects that can barely deform at all, but I don't see a requirement that they always actually do dissipate more energy - the spring example shows it may not. $\endgroup$ Nov 8, 2023 at 16:30
  • $\begingroup$ Many thanks for your replies and helping me understand elasticity from a physics perspective. $\endgroup$
    – Dubious
    Nov 9, 2023 at 16:24

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