Question regarding inelastic/elastic collision.

[jfnn]

Homework Statement

[/B]
Hi,

I have a quick question regarding elastic and inelastic collisions. I preformed an experiment in my house with two large, heavy marbles. I rolled one horizontally towards a stationary one, recorded a video of the collision. I uploaded the video to Tracker software, obtained motion graphs for each, and calculated the horizontal and vertical velocities. I then used pythagoreans theorem to find the scatter angle. I got 28 got marble one and 31 for marble two.

My question is, after plugging these values with the velocity obtained into the conservation of momentum equation, I see that momentum is conserved, which is a good thing.

However, how can I tell if the collision is elastic or not? I tried looking at the relationship between the kinetic energy and found that it was NOT constant. If it was not constant, would that be enough to say the collision was inelastic?

I also add those two angles, which do not add up to 90 degrees. For an elastic collision, the angles should add up to 90 degrees for two identical masses; however, it does not, it is not even close! Is this further evidence to show that the collision is inelastic?

Does it make sense for the collision to be elastic AT ALL? Like I did this experiment on the hardwood floor in my house, clearly the KE could not be conserved because energy left the system through the friction force and dissipated as heat. Therefore, energy was lost and not constant. Would it be possible to have an elastic collision at all in this situation?

Furthermore: Could there be enough experimental error that my values just deviate so much that the collision should be elastic instead of inelastic? Is my logic wrong?

Thank you so much for your help,
J

Homework Equations

[/B]
p=mv

KEi=KEf

The Attempt at a Solution

Mentioned above.[/B]

 

[jfnn]

Homework Statement

[/B]
Hi,

I have a quick question regarding elastic and inelastic collisions. I preformed an experiment in my house with two large, heavy marbles. I rolled one horizontally towards a stationary one, recorded a video of the collision. I uploaded the video to Tracker software, obtained motion graphs for each, and calculated the horizontal and vertical velocities. I then used pythagoreans theorem to find the scatter angle. I got 28 got marble one and 31 for marble two.

My question is, after plugging these values with the velocity obtained into the conservation of momentum equation, I see that momentum is conserved, which is a good thing.

However, how can I tell if the collision is elastic or not? I tried looking at the relationship between the kinetic energy and found that it was NOT constant. If it was not constant, would that be enough to say the collision was inelastic?

I also add those two angles, which do not add up to 90 degrees. For an inelastic collision, the angles should add up to 90 degrees for two identical masses; however, it does not, it is not even close! Is this further evidence to show that the collision is inelastic?

Does it make sense for the collision to be elastic AT ALL? Like I did this experiment on the hardwood floor in my house, clearly the KE could not be conserved because energy left the system through the friction force and dissipated as heat. Therefore, energy was lost and not constant. Would it be possible to have an elastic collision at all in this situation?

Thank you so much for your help,
J

Homework Equations

[/B]
p=mv

KEi=KEf

The Attempt at a Solution

Mentioned above.[/B]

QUICK EDIT: For an ELASTIC collision the angles should add up to 90 degrees!

 

[TSny]

I have a quick question regarding elastic and inelastic collisions. I preformed an experiment in my house with two large, heavy marbles. I rolled one horizontally towards a stationary one, recorded a video of the collision. I uploaded the video to Tracker software, obtained motion graphs for each, and calculated the horizontal and vertical velocities. I then used pythagoreans theorem to find the scatter angle. I got 28 got marble one and 31 for marble two.

OK. Sounds like fun!

My question is, after plugging these values with the velocity obtained into the conservation of momentum equation, I see that momentum is conserved, which is a good thing.

Yes. Momentum should be conserved if external forces can be neglected during the collision. The fact that the momentum is conserved is an indication that there was no significant impulse from external forces during the collision.

However, how can I tell if the collision is elastic or not? I tried looking at the relationship between the kinetic energy and found that it was NOT constant. If it was not constant, would that be enough to say the collision was inelastic?

Yes. By definition, total KE must be conserved in an elastic collision. However, you need to be looking at all forms of KE. The marbles are probably rolling without slipping. So, there is some rotational KE as well as translational KE. You can easily correct for that by using physics to determine how the total KE (translation plus rotation) depends on the speed. You should find that the total KE of one of the marbles is (7/10)mv². The fact that the total KE is proportional to the square of the speed would still lead to

v1_f²+ v2_f² = v1_i² (if the masses are equal ,the collision is elastic, and no extra spin is created in the collision [see below])

So, if your data is not obeying the above relation, then either the collision is not elastic or something else is going on. One thing that could be going on is that during the collision the marbles picked up some "spin" over and above the rolling rotational motion. This would also need to be included as part of the KE. But you probably didn't get any data on spin motion.

I also add those two angles, which do not add up to 90 degrees. For an elastic collision, the angles should add up to 90 degrees for two identical masses; however, it does not, it is not even close! Is this further evidence to show that the collision is inelastic?

If there is significant spinning motion generated in the collision, then I don't think the angles would need to add to 90 degrees even if there is no loss of total KE.

Does it make sense for the collision to be elastic AT ALL? Like I did this experiment on the hardwood floor in my house, clearly the KE could not be conserved because energy left the system through the friction force and dissipated as heat. Therefore, energy was lost and not constant.

There was probably not much KE lost due to friction with the floor. The fact that momentum was conserved indicates that the friction was not significant. But, even without any external forces acting on the system, it is still possible for a large percentage of the KE to be converted into heat (internal energy within the marbles). It depends on the material properties of the colliding objects. I would think that marbles would not lose a lot of KE to heat.

Would it be possible to have an elastic collision at all in this situation?

It's not possible to have a true elastic collision with real everyday objects making contact during a collision. Some heat will be generated. But, there are situations where the collisions are close to being elastic. Steel balls can have collisions that are pretty elastic. And I would think the marbles would be pretty elastic, too.

Furthermore: Could there be enough experimental error that my values just deviate so much that the collision should be elastic instead of inelastic? Is my logic wrong?

The "error" might be due to neglecting any extra spinning motion picked up in the collision. Or, the marbles just might not be very elastic. It's hard to say.