MHB Prediction of Motion After Ideal Collision - Masses M & m

[mathmaniac1]

A body of mass M moves with velocity V and collides with a body of mass m moving at v.Given,the conditions are ideal(vaccum),can you find everything that happens next like final speed,acceleration,distance moved ...etc?

Thanks in advance for any help...

 

[MarkFL]

Is the collision perfectly elastic, i.e., there is no loss of kinetic energy?

 

[mathmaniac1]

Even if there is,doesn't that depend on the objects...
I have given a unique situation so the prediction will also be unique.Isn't that right?

 

[MarkFL]

In reality, a perfectly elastic collision does not exist (with the exception of some large-scale interactions like the slingshot type gravitational interactions between satellites and planets), but models are used for simplicity to get useful results that are very close to reality. We normally deal with the loss of kinetic energy with a coefficient of restitution, which needs to be specified. Some problems (such as collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force) are sufficiently close to perfectly elastic that they can be approximated as such. In this case, the coefficient of restitution equals to one.

When two rubber balls collide for example, some of the kinetic energy is lost when the balls are deformed, which converts some of the kinetic energy to internal thermal energy, where the interiors of the balls are heated by the collision.

I suggest reading this article:

Collision - Wikipedia, the free encyclopedia

You will find other links to follow for further information.

 

[mathmaniac1]

So it depends on the nature of the object,right?
Ah!Yes.Its obvious!1kg of cotton colliding with any other object is not same as the same object colliding with 1kg of dense iron...

 

[MarkFL]

I think it's more a matter of rigidity than density, but yes, it depends on the nature of the objects.(Nod)

 

[mathmaniac1]

Aren't both the same?rigidity and density?

 

[MarkFL]

No, aluminum is much more rigid than gold, but far less dense.

Rigidity is stiffness, whereas density is mass (or sometimes weight) per unit volume.

 

[mathmaniac1]

Rigidity is stiffness

something related to friction?

 

[MarkFL]

No, rigidity relates more to resistance to deformation. A rigid object is less likely to bend under pressure, or be dented by collisions.