Prediction of Motion After Ideal Collision - Masses M & m

In summary, the conditions given are ideal for the collision, meaning there is no external force acting on the objects and the collision is perfectly elastic. However, in reality, perfectly elastic collisions do not exist and models are used to approximate the results. The coefficient of restitution, which determines the amount of kinetic energy lost in a collision, needs to be specified. This depends on the nature of the objects, such as their rigidity and density.
  • #1
mathmaniac1
158
0
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...
 
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  • #2
Is the collision perfectly elastic, i.e., there is no loss of kinetic energy?
 
  • #3
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?
 
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  • #4
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.
 
  • #5
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...
 
  • #6
I think it's more a matter of rigidity than density, but yes, it depends on the nature of the objects.(Nod)
 
  • #7
Aren't both the same?rigidity and density?
 
  • #8
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.
 
  • #9
MarkFL said:
Rigidity is stiffness

something related to friction?
 
  • #10
No, rigidity relates more to resistance to deformation. A rigid object is less likely to bend under pressure, or be dented by collisions.
 

FAQ: Prediction of Motion After Ideal Collision - Masses M & m

How do you determine the velocity of two masses after an ideal collision?

The velocity of two masses after an ideal collision can be determined using the law of conservation of momentum, which states that the total momentum of a closed system remains constant. This means that the sum of the initial momenta of the two masses before the collision is equal to the sum of their final momenta after the collision.

What is an ideal collision?

An ideal collision is a theoretical concept in which two objects collide without any external forces acting on them. This means that there is no loss of energy during the collision, and the total momentum of the system is conserved.

How does the mass of the two objects affect the prediction of their motion after an ideal collision?

The mass of the two objects plays a crucial role in determining their motion after an ideal collision. According to the law of conservation of momentum, the velocities of the two objects are inversely proportional to their masses. This means that the lighter object will experience a larger change in velocity compared to the heavier object.

Can an ideal collision occur in real life?

No, an ideal collision cannot occur in real life as there will always be some external forces acting on the objects, such as friction and air resistance. These forces will cause a loss of energy, and the total momentum of the system will not be conserved.

How accurate are predictions of motion after an ideal collision?

The accuracy of predictions of motion after an ideal collision depends on the assumptions made in the calculation and the accuracy of the initial conditions. In reality, there will always be some degree of error due to external factors, but the predictions can provide a good estimate of the objects' motion.

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