# Why is KE not conserved?

1. Jan 4, 2005

### UrbanXrisis

When two isolated objects collide in an inelastic collision, why is kinetic energy not conserved?

I was going a problem where it gave me three choices. They were Totaly Energy, Linear Momentum, and Kinetic energy. I picked that all three were conserved. Total energy always must be conserved, momentum is always conserived. I wasnt sure about KE. Can someon explain to me why that is?

Lets say a 2kg cart moving at 2m/s eastward collides inelastically with a 1kg cart moving at 1m/s westward.

The total KE is 4.5J
$$KE_{total}=.5m_{1}v_{1}^2+.2m_{2}v_{2}^2$$
$$KE_{total}=.5*2kg*(2m/s)^2+.2*1kg*(1kg)^2$$
$$KE_{total}=4+.5=1.5J$$

After the carts colide....
$$v_{final}=(m_{1}v_{1}+m_{2}v_{2})/(m_{1}+m_{2})$$
$$v_{final}=v_{final}=(2kg*2m/s+1kg*1m/s)/(2kg+1kg)$$
$$v_{final}=5/3$$

$$KE_{total}=(1/2)(3kg)(5/3)^2$$
$$KE_{total}=25/6=4.17J$$

What happened to the 0.33 joules?

2. Jan 4, 2005

### chroot

Staff Emeritus
When a collision is not elastic, some changes take place in the bodies that collide, using up some of the initial kinetic energy. Perhaps the bodies deform, or heat up a bit, or make a sound when they hit. The total energy is always conserved, but an inelastic collision converts some of the initial kinetic energy into other forms.

- Warren

3. Jan 4, 2005

### Pandaren

Kinetic enegy is not conserved in an inelastic collusion because energy has lost do to non conservative forces, such as friction, or the object to changes shape

4. Jan 4, 2005

### marlon

generally, some of the energy in these collsions is lost to thermal degrees of freedom, like heating of the two colliding objects or energy dissipation caused by frction between the two colliding surfaces...But however normally the example that you gave can be treated as an elastic colission (by good approximation) and thus kinetic energy is conserved in this case...

regards
marlon

5. Jan 4, 2005

### UrbanXrisis

Thank you.

Why is KE in an elastice collisions conserved? Wouldn't the bodies "deform" or heat up" and lose thermal energy as well?

6. Jan 4, 2005

### chroot

Staff Emeritus
UrbanXrisis,

In the real macroscopic world, with real tennis balls and locomotives and so on, there are really no such things as purely elastic collisions -- they are an idealization. The very ideal of an elastic collisions is that the bodies must not deform or otherwise gain thermal energy, and no such macroscopic bodies behave this way. You can buy nearly frictionless air-tracks with small carts with well-designed rubber bumpers to approximate purely elastic collisions in a laboratory, but even their collisions are not truly purely elastic.

However, you can bounce subatomic particles off each other, and they do collide elastically. Electrons cannot deform, and they do not have any mechanism by which to store thermal energy.

- Warren

7. Jan 4, 2005

### UrbanXrisis

Then why aren't inelastice collisions idealized as well?

8. Jan 4, 2005

### chroot

Staff Emeritus
They are; the "ideal," or completely inelastic collision is when the two bodies stick together or otherwise merge into one.

- Warren

9. Jan 4, 2005

### UrbanXrisis

and this "merging" deforms the objects? and an ideal deformation would cause the system to create thermal energy and there for lower the KE? Why is this not ture for elastic collisions?

10. Jan 4, 2005

### chroot

Staff Emeritus
It's just a definition. A purely elastic collision is defined as a collision in which all the kinetic energy the system starts with remains in the form of kinetic energy after the collision. A purely inelastic collision is one where all the starting kinetic energy is dissipated in other forms. Most real collisions are somewhere in between.

- Warren

11. Jan 4, 2005

### UrbanXrisis

so ideal inelastic collisions do lose KE while ideal elastic collision retain their KE?

I feel that all ideal situations should conserve KE.

12. Jan 4, 2005

### Andrew Mason

That is not necessarily true. An inelastic collision of two isolated objects can result in both objects having the same kinetic energy at a point after the collision.

Inelastic refers to the type of 'collision' and does not require that energy be lost to the isolated system. It simply requires that kinetic energy be converted, in the collision, to some other form of energy. In an 'inelastic collision' where the objects collide and stick together and available kinetic energy is converted into potential energy (of a spring, for example), that energy can be recovered and the objects can later regain their original kinetic energy.

AM

13. Jan 5, 2005

### Andrew Mason

Perhaps this may help:

The reason kinetic energy is not conserved in a collision where the two colliding objects stick together is this: in the frame of reference of the centre of mass of the system (which in this case is a frame of reference moving at 5/3 m/s) the two objects approach each other from opposite directions with equal and opposite momenta and stop. There is non-zero KE before the collision and 0 kinetic energy after.

If KE can disappear in one frame but not in another, there would be a fundamental frame-dependent asymmetry to the laws of physics.
There are a couple of mistakes here:

KEtotal=.5m1v12+.5m2v22

KEtotal=.5*2kg*(2m/s)2+.5*1kg*(1m/s)2
KEtotal= 4+.5=4.5J

AM