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09-02-2010, 04:57 AM #1
 Class 2 Laser Join Date: Sep 2009 Location: 0,0,0 U (dimensions) Posts: 432 Rep Power: 16
Moptsp
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Pre calculus 2 class.

Well I just started college full time (doing 13 credit hours,) and I decided to take pre-calculus 2. It's basically just pre-calculus. I guess part 2 is being considered as pre-calculus + trigonometry or something.

Anyway, I have had this assignment to do with measuring a ball's height drop to it's bounce height. And then make a model for it. It's supposed to be either a power regression or a exponential regression model.
I used a little rubber ball that is probably 1 1/2" in diameter. The reason I chose a small ball is to cut out air friction for the most part. (maybe I should have kept air as a larger factor to make it less linear. read on to understand)

The reason I'm posting this is that after getting data points (15 different height drops) and plotted it out, it was almost linear. I was wondering if I was getting valid measurement points.

The way I look at it is if there was no friction at all, the ball's elasticity was perfect, the bouncing plane absorbed no energy, and gravity (or any force for that matter) was perpendicular with the bouncing plane, the function would simply be f(x) = x (linear with slope of 1). Where x could be height dropped and f(x) would be bounce height. So in other words, the ball would bounce to where it was dropped from as the height it is dropped from is it's potential energy, and it takes the same amount to return back.

Of course this is will all energy conserved within the motion of the ball. Though in reality as I get my measurements, there is friction all about it's motion, including the ball it self.

So I guess my question is, should my data be "linear" to my accuracy of calculations considering my environment?

Environment:
ball size: 1 1/2"
ball mass: not sure, but it's about equal to the mass of 5-7 large gum balls.
dropping distance min-max: 2"-75"
surface: hard finished wood (does not absorb much energy)

I was thinking if I were to scale up 2"-75" that maybe I would start to see something less "linear".
Anyway, with my environment, the ball seems to bounce ruffly at 72% it's drop height, regardless of height. This is what I believe keeps it linear.

So, am I thinking correctly here?
I no I'm totally over thinking it as my instructor really just wants us to get data points and just model it, but I would like to clarify this for myself.

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09-03-2010, 03:11 AM #2
 Class 4 Laser Join Date: Sep 2007 Location: Wisconsin Posts: 8,852 Rep Power: 1363
Cyparagon
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Re: Pre calculus 2 class.

Yes, it would be linear. After a great height, however, the peak speed would be closer and closer to terminal velocity, so it would be technically logarithmic when considering air resistance. But with most (all?) physics problems, we assume many factors to be insignificant.
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09-05-2010, 09:04 PM #3
 Class 2 Laser Join Date: Sep 2009 Location: 0,0,0 U (dimensions) Posts: 432 Rep Power: 16
Moptsp
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Join Date: Sep 2009
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Re: Pre calculus 2 class.

Ok. Thanks for the clarification, Cyparagon. I tried +rep on you, but I have to "spread" more rep first, as the forum says. Oh well, maybe another time.
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Optotronics RPL-532-260 - Avg ~294mw
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Modded 5mw-532 WickedLasers Core ~15mw - Back down to 5mw for fun

532nm Safety Glasses >2 OD ~2.6 OD, From Glenn

Defining the undefined defines a new definition of which has always been defined.

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