# The simple yet best challenge i ve ever seen

1. Feb 17, 2012

### hercules68

the simple yet best challenge i ve ever seen !!!

Fine lets keep it simple

Assume a mass of 'm' moving at velocity 'v'.

now if I somehow increase the mass of it to '2m' (by some means as a mass sticking on to it newly ... or any other means of no loss of energy ... now dont tell me its impossible )

by conservation of momentum ...

new velocity = ( old velocity ) / 2

by conservation of energy

new velocity = ( old velocity ) / (root 2)

??????????????????????????

2. Feb 17, 2012

### nasu

Re: the simple yet best challenge i ve ever seen !!!

The kinetic energy is not conserved in this process. It's like a non-elastic collision.

3. Feb 17, 2012

### hercules68

Re: the simple yet best challenge i ve ever seen !!!

fine if the object has some ideal adhesive over it ... then few particles stick to it

how is the energy lost

4. Feb 17, 2012

### nasu

Re: the simple yet best challenge i ve ever seen !!!

The whole second body will be attached to the first one. This is what you said.
Not just some particles.

You have initially one object moving with velocity v and another one at rest.
When you put them in contact the internal forces (maybe friction) will accelerate the second body and slow down the first one so you end up with both moving with the same speed.
These internal forces are the ones decreasing the kinetic energy of the system.

5. Feb 17, 2012

### MrAnchovy

Re: the simple yet best challenge i ve ever seen !!!

Imagine the first body is a train and the second body is a car on a crossing. Some of the kinetic energy of the train is expended making a mess of the car.

If you change the scale so that you have a smaller object that is moving more slowly there is much less kinetic energy; when it hits something it makes less of a mess (perhaps just a bit of noise and heat), but all you have done is change the scale not the principal so kinetic energy is always lost in the collision.

6. Feb 17, 2012

### hercules68

Re: the simple yet best challenge i ve ever seen !!!

energy is lost as heat only if there is relative motion between the bodies after contact. and if this happens in vaccuum there is no sound as well

7. Feb 17, 2012

### MrAnchovy

Re: the simple yet best challenge i ve ever seen !!!

.. or one or both of the bodies deform after contact. How is the first body going to speed up the second body unless there is either relative motion or deformation?

You are coming at it from the wrong angle, clearly the kinetic energy is converted somewhere, look for where it could be going and that is where you are likely to find it!

8. Feb 17, 2012

### zoobyshoe

Re: the simple yet best challenge i ve ever seen !!!

Superficially, the loss is built in to the formula:

The energy is lost because the velocity is squared in the energy formula. Cutting the velocity in half results in a 4:1 reduction ratio of that factor, while doubling the mass merely doubles that factor. (Example: 82 gets you 64 to multiply by the mass, but half that velocity, 4, squared only gets you 16 to multiply by the mass, a reduction of 4:1.)

9. Feb 17, 2012

### hercules68

Re: the simple yet best challenge i ve ever seen !!!

considering an ideal rigid body upon which the laws hold true it is possible to have zero relative motion and by the way where is the energy lost !

10. Feb 17, 2012

### MrAnchovy

Re: the simple yet best challenge i ve ever seen !!!

No it isn't, this would imply instantaneous acceleration and therefore infinite force. I am going to leave you to think this out for yourself now.

11. Feb 18, 2012

### nasu

Re: the simple yet best challenge i ve ever seen !!!

It may be the case that you don't understand your own problem?
The two bodies do have relative motion, to start with. It has nothing to do with their rigidity or other properties. One is moving with v, the other is at rest. Or maybe they both move with v, from the beginning?

If it's the first case, as they end up by moving together after they get in contact, there must be some interaction force between the two bodies. You can even assume that the second body accelerates instantaneously (and the second decelerates same way). You'll have an infinitely large force acting for an infinitely short time. The final effect: change in relative speed and change in kinetic energy.

I don't understand why you call this a challenge.
If you read a little bit about plastic collisions or conservation laws in systems of particles it should became less challenging.