Question

Elastic and Inelastic collisions? Please help with interpreting data!

Answer 1

http://i.imgur.com/c5pOIe8.png & http://i.imgur.com/zdxfXLE.png

Any help at all would be appreciated! I have been stuck on this for over a day now and it's starting to get me a little flustered.
I mean, I know how to figure out the final velocity of entangled masses or just one object after a collision, but how do I do it with this data? I'm really lost. What does Vx, Vy mean and how do we use distance to determine that? I could provide a background description on the assignment if that would help!

Answer 2

Here is the prompt for the assignment:
Sitting in a parking lot you witness a minor, but still noteworthy collision between two cars. You remembered studying collisions and momentum in class and wondered, "Is momentum really conserved in collisions?" It didn't seem like it was in the real world so you made the hypothesis, "Momentum is not conserved in all collisions. Collisions with less elasticity will lose more momentum than collisions with higher elasticity."

To test your hypothesis you used a simulation to gather data for two colliding objects. You looked at both linear (straight line) and nonlinear collisions for three different values of elasticity; 100% elastic, 50% elastic, and 0% elastic. The data from your trials is shown in the data sets.

You are to use the data as your basis to show the degree of momentum conservation and whether your hypothesis is validated or not. If it is not, then reformulate your hypothesis.

What does 100% or 50% elasticity mean? I thought there were only Perfectly Inelastic, Elastic or in between, but I never found a way to measure them?

Answer 3

Or measure elasticity, I should say. . . I'm just confused right now.

Answer 4

A 100% elastic collision has the kinetic energy conserved.
A 0% elastic collision, 100% inelastic, has the two bodies merge as one,
with a loss of kinetic energy turned into heat. 50% elastic? Not sure of definition. Google?

Answer 5

I haven't seen elasticity used in a context like this, and I couldn't find one on the web. So here's what I assume:

An elastic collision conserves all kinetic energy. So, a more elastic collision is more conservation. So, if I want to define an elasticity percentage, I'd assume that a certain percentage of the energy is conserved. And so 0% means none is conserved, and 50% means half is conserved.

Answer 6

I've only seen elasticity when talking about an object regaining its shape... And that's only when looking up a definition for elasticity. I can't work with it.


I'll just say what I'm thinking as I look at this....

I think we should look at your made up trials. We should check to see the kinetic energy before and after, and you should notice that they are different like \(E_{K\text{, before}}=\gamma E_{K\text{, after}}\) where \(\gamma\) is elasticity. Does that make sense? So \(\gamma=1\) is perfectly elastic, \(\gamma=0.5\) is 50% elastic, and \(\gamma=0\) is perfectly inelastic.

But what we really care to see is the conservation of momentum, so you calculate momentum before and after. They should be about the same.

And you must keep in mind your hypothesis, which I read is incorrect.
"Momentum is not conserved in all collisions. Collisions with less elasticity will lose more momentum than collisions with higher elasticity."
To demonstrate that this is possibly true, the 0 elasticity collisions should lose the most momentum. I guess we can look at percentages again, like, momentum after is 100% of the momentum before. The 100% elasticity should lose the least momentum, according to the hypothesis.

So you need to make the calculations for momentum before and after, and... What I would do is look at the before:after ratio for momentum for each trial. Then find the average of the 0% elasticity, the average of the 50%, and then of the 100%. Then you should see if there is the trend of higher elasticity\(\rightarrow\)more momentum conserved.

That will be false, so you state your new hypothesis. Probably that momentum is conserved.

Fun fact, experimentally it's not cool to use this data to back up the hypothesis based on this data. You'd get as many other kinds of data as you can to test the new hypothesis. Otherwise, it's circular reasoning.

Answer 7

Momentum should be conserved. Check the energy loss. Perhaps that will explain "50% elasticity."

Answer 8

Oh!

\(\huge\sf\color{#00AA33}{\text{Reading the Data}}\)
So!
I'm looking at the attached picture.
The balls are identified by a unique color and number. In the data part, the row contains information about the specified ball at that time. The left side is "before" and so each section to the right is the "after."
The elasticity is noted at the bottom of each, so you can group them together.
Vx is \(v_x\), the velocity in the \(x\) direction.
Vy is \(v_y\), the velocity in the \(y\) direction.
Based on the attached picture, positive \(x\) increase is in the right direction \(\rightarrow\).
Also, positive \(y\) increase is in the up direction \(\uparrow\).

Answer 9

Also, trials are separated by dashed lines.


The first trial gives position. I don't think this is important. But the fact that there is only one velocity makes me think it's the linear collision that was mentioned. (Linear :: 1 dimension)

Answer 10

There are other linear collisions.. I said "the," which is misleading.

So I looked at one example! A linear collision with 0.5 elasticity. I was sloppy with my calculation (used the windows calculator and wrote nothing down).
If I did it correctly though, using my \(E_{K\text{, before}}=\gamma E_{K\text{, after}}\) explanation of elacticity (\(\gamma\)), I got \(\gamma\approx .63\) or something like that.

Answer 11

I don't think the elasticity is important though, other than for grouping trials together.

Answer 12

\(\sf\huge\color{orange}{My\ Suggestion}\)
\(\sf\large\color{#00AA33}{Concisely}\)
Find the momentum in each case.
For each trial, find the percentage of \(\dfrac{\text{momentum after}}{\text{momentum before}}\).
Group them by elasticity and find each group's average.
Look at your results, and see if your hypothesis looks alright, still.

Hopefully you don't have to account for error!

Answer 13

Good luck!

Answer 14

Thanks so much for your willingness to help! Except I had already figured it out before hand. :-) I think I may have did it right, since I drew the same conclusion you did. But I did notice that the hypothesis was on track. The higher the elasticity, the less momentum that is lost. The less the elasticity, the more momentum that is lost!

Answer 15

I think I did it right.. If not would it be okay to contact you for help on revisions? I already submitted my assignment and am currently awaiting feedback. :-) I would greatly appreciate it!

Answer 16

Sure! I didn't do it myself, but if there are errors I can look through it again! I'm glad you figured it out! :)