Kinetic energy problem during collision

[coldblood]

Hi friends,
I have an issue in solving a Kinetic energy problem during collision.
Please Help me in solving this.
Thank you all in advance.

The problem is as:

https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn2/1375160_1432382953655477_313625437_n.jpg

Attempt:

https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-prn1/993716_1432381396988966_2038831136_n.jpg
https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-ash4/q87/s720x720/1380153_1432381516988954_1217795620_n.jpg

Friends according to question all the options, (A),(B),(C),(D) are correct. Please try to help me in this.
I will appreciate the help.

 

[haruspex]

As you know, the total energy should be the same at all times. If the KE is going to vary during the collision, where else is energy being stored?

 

[coldblood]

As you know, the total energy should be the same at all times. If the KE is going to vary during the collision, where else is energy being stored?

I think In the terms of heat or sound. But as the question perfectly states that the collision is elastic hence the total K.E. should remains same. And it is happening also before collision and after collision K.E. is 3 J. total.

 

[ehild]

The problem is about the process of collision. The particles are like elastic balls. As the first one reaches the stationary particle, they start to interact and push each other. The balls deform and the deformation goes on till they move with respect to each other. At an instant, they move together with the same velocity, like in an inealastic collision, but the energy is not lost, it is stored as elastic energy, as in a compressed spring. During the second stage of the process, the elastic force between the compressed balls starts to accelerate them away from each other, till the balls completely separate. The PE is maximum when the balls move together with the same velocity.

ehild

 

[coldblood]

The problem is about the process of collision. The particles are like elastic balls. As the first one reaches the stationary particle, they start to interact and push each other. The balls deform and the deformation goes on till they move with respect to each other. At an instant, they move together with the same velocity, like in an inealastic collision, but the energy is not lost, it is stored as elastic energy, as in a compressed spring. During the second stage of the process, the elastic force between the compressed balls starts to accelerate them away from each other, till the balls completely separate. The PE is maximum when the balls move together with the same velocity.

ehild

Well,l it is clear that, during collision some amount of K.E. will be stored as the elastic P.E. in both the balls.
But still how the minimum K.E. can be calculated in this process. It is not clear.

 

[ehild]

The KE is minimum when the PE is maximum, and it is maximum at maximum compression. At that instant, the balls move together, like in an inelastic collision. What is that common velocity? ehild

 

[coldblood]

The KE is minimum when the PE is maximum, and it is maximum at maximum compression. At that instant, the balls move together, like in an inelastic collision. What is that common velocity?


ehild

for initial, K.E. = 1/2 mv² = 3 J
v = √(6/m)

At the instant of collision,

Common velocity will me v/3
i.e. 1/3(√(6/m))

 

[ehild]

And the kinetic energy of the system?

ehild

 

[coldblood]

And the kinetic energy of the system?

ehild

Yes it is fulfilling the requirement. Thanks for taking intrust in it. See you around.

 

[ehild]

You are welcome.

ehild