Where does kinetic energy go in inelastic collision?

[cmkluza]

I'm having a bit of trouble conceptualizing this. I've looked all over the Internet, and I've been seeing that in completely inelastic collisions the reason that kinetic energy is not conserved is because energy goes into deformation, sound, propelling shrapnel, and especially heat (among other things).

I did an experiment with PAScars (which became attached by Velcro upon collision) on a PAStrack, and it was noted that approximately 70% of kinetic energy was lost in the system.

At this scale, there's obviously no large deformation of the materials, not a lot of sound or shrapnel propelled out of the system. I can't imagine that the collision of two PAScars buffered by Velcro loses 70% of the energy to heat.

Can anyone help me understand this concept?

 

[Aaron Crowl]

The sound you hear from a collision represents a substantial amount of energy. Consider this: The sound radiated out from the collision in all directions. Your ears only picked up a small fraction of that sound energy at some distance.

What was your figure for lost energy?

 

[cmkluza]

The sound you hear from a collision represents a substantial amount of energy. Consider this: The sound radiated out from the collision in all directions. Your ears only picked up a small fraction of that sound energy at some distance.

What was your figure for lost energy?

Approximately 70% of the kinetic energy was lost (transformed into other forms). More concretely, my numbers were ~55.6 J before and ~26.6 J after. I suppose I've never thought of the energy necessary to produce a sound, and especially since there wasn't much of a sound in this situation (dampened by Velcro), I didn't consider it to be a substantial portion of the energy in the system.

Thanks for the insight, I'll have to look up more on sound.

 

[Dale]

You may also want to determine how much temperature increase you would expect if all 29 J were converted to heat, and how quickly that heat would dissipate.

 

[cmkluza]

The sound you hear from a collision represents a substantial amount of energy. Consider this: The sound radiated out from the collision in all directions. Your ears only picked up a small fraction of that sound energy at some distance.

What was your figure for lost energy?

Sorry to bug you with a slightly off-topic question, but I'm pretty bewildered now. What is different about elastic and inelastic collisions that allows for kinetic energy to be transformed to other forms in inelastic, but not elastic?

It's known that, ideally, kinetic energy will be conserved in a system for elastic collisions. In the experiment with PAScars, there was certainly a collision - contact that produced sound, and likely heat and slight deformation of the two PAScars. I am utterly lost on how (theoretically), none of the kinetic energy should be transformed into other forms of energy in elastic collisions, when seemingly similar interactions take place between two objects involved in an inelastic collision.

Could you, or anyone else that comes by this post, help me get over this conceptual block? I honestly can't conceptualize the difference between elastic and inelastic collisions (in the context of my PAScar experiment) at all right now.

 

[pixel]

Could you, or anyone else that comes by this post, help me get over this conceptual block? I honestly can't conceptualize the difference between elastic and inelastic collisions (in the context of my PAScar experiment) at all right now.

From http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html :

For macroscopic objects which come into contact in a collision, there is always some dissipation and they are never perfectly elastic. Collisions between hard steel balls as in the swinging balls apparatus are nearly elastic.

"Collisions" in which the objects do not touch each other, such as Rutherford scattering or the slingshot orbit of a satellite off a planet, are elastic collisions. In atomic or nuclear scattering, the collisions are typically elastic because the repulsive Coulomb force keeps the particles out of contact with each other.

 

[cmkluza]

From http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html :

For macroscopic objects which come into contact in a collision, there is always some dissipation and they are never perfectly elastic. Collisions between hard steel balls as in the swinging balls apparatus are nearly elastic.

"Collisions" in which the objects do not touch each other, such as Rutherford scattering or the slingshot orbit of a satellite off a planet, are elastic collisions. In atomic or nuclear scattering, the collisions are typically elastic because the repulsive Coulomb force keeps the particles out of contact with each other.

Thanks for the clarification. I think I was getting confused between the physical idealization of elastic collisions and the physical reality of elastic collisions. So, while this experiment might have been set up to measure elastic collisions, they're merely "mostly" elastic collisions.

However, I'm still slightly lost when looking at my results. There's no doubt that significantly more kinetic energy is dissipated, even in my experiment with the PAScars, for inelastic collisions than elastic collisions. We've identified now that in both situations there is loss of kinetic energy, since they're not perfectly elastic, but why is there such a large disparity in the energy dissipated? I still can't pinpoint that concept down.

 

[Aaron Crowl]

It's known that, ideally, kinetic energy will be conserved in a system for elastic collisions.

You seem to be getting this concept so that's a good start.

Modeling what happens when nearly-rigid bodies collide could become complex very quickly. For that matter, modeling elastic collisions would be difficult too. Let's try a simple approach first.

When two objects collide shock-waves will travel through the objects. The composition and geometry of the objects will determine how those waves behave.

Does that make sense? I think it works for our purposes.

If you really want to get into it I think we would need to set up some partial differential equations. Then we could use finite element analysis to solve for a scalar density field. That would get to the bottom of how the sound is created. I'm sure there is a software package out there that could do all of this for us. Maybe there is a free one.

There may be a more elegant method to describe the sound generation but it's beyond me.

 

[pixel]

However, I'm still slightly lost when looking at my results.

Can you provide some more detail about your experiment and how you measured the kinetic energy?

You're saying the cars became attached. Did they continue to move together?

 

[jbriggs444]

I did an experiment with PAScars (which became attached by Velcro upon collision) on a PAStrack, and it was noted that approximately 70% of kinetic energy was lost in the system.

I think that the 70% figure is misleading. A more accurate figure would be 100%.

If the cars remain attached and are (because they are on a PAStrack) not free to rotate then the remaining kinetic energy is due to the two car's combined mass moving at their shared velocity. Conservation of momentum requires that this energy remain. It can never be dissipated, ignoring friction with the air and with the track.

If we shift a frame of reference where the combined center of mass of the two cars is at rest then this final kinetic energy is zero. 100% of the car's initial kinetic energy (as measured in this frame) has been converted to heat, sound and permanent deformation.

The energy converted to sound will be negligible. For re-usable cars, the energy converted to permanent deformation will be negligible. Essentially 100% of the initial kinetic energy in the cars relative motion (i.e. as determined in the center of mass frame) will be converted to heat.

 

[nasu]

Why do you think that the percentage is more "accurate" when calculated in the center of mass frame?
In other frames it has different values. Are these less accurate?

 

[jbriggs444]

Why do you think that the percentage is more "accurate" when calculated in the center of mass frame?
In other frames it has different values. Are these less accurate?

Possibly not the best word choice. Still, I would expect that 70% has one sig fig while the 100% would likely be good for two.

 

[sophiecentaur]

but why is there such a large disparity in the energy dissipated? I still can't pinpoint that concept down.

You seem to be finding an 'intuitive inconsistency' here. Mechanical and thermal energy are different beasts. If you consider how much an increase in kinetic energy from zero to 100J represents for a 1kg lump of steel and then what temperature rise that 100J of 'heat energy' would produce. Do the sums and you will find that your 100J of added KE is readily appreciable (to the eye) but that the temperature rise is hardly noticeable (to the touch). Lost mechanical energy is often almost unnoticeable. - except in extreme cases like applying the brakes on a vehicle.