# Kinetic energy problem during collision

1. Oct 12, 2013

### coldblood

Hi friends,
I have an issue in solving a Kinetic energy problem during collision.
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.

2. Oct 13, 2013

### 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?

3. Oct 14, 2013

### coldblood

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.

4. Oct 14, 2013

### 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

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Last edited: Oct 14, 2013
5. Oct 14, 2013

### coldblood

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.

6. Oct 15, 2013

### 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

7. Oct 15, 2013

### coldblood

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))

8. Oct 15, 2013

### ehild

And the kinetic energy of the system?

ehild

9. Oct 15, 2013

### coldblood

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

10. Oct 15, 2013

### ehild

You are welcome.

ehild