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course Phy 122
2/17 10:35pmThanks for your help. I got the lab to match the program.
I completed kinmodels 01 and 03 as directed." "Kinetic Model using Billiards Program.
Experiment kinmodel_01: The Distribution of Atomic Speeds
When the speed of the simulation is moderate it is possible to watch a specific particle (the red particle or the blue particle in the default simulation) and obtain an intuitive feeling for the relative frequencies of various speeds.
Run the simulation billiard simulation at the default settings.
Observe the simulation long enough to get a feel for the maximum velocity you are likely to see. Then estimate how much time it spends at slow (less than 1/3 of max vel.), medium (between 1/3 and 2/3 of max. vel.) and fast (more than 2/3 of max. vel.) velocities.
Express your estimates in percents of the total time spent in the three different velocity ranges.
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Slow, 20%
Medium 60%
Fast 20%
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Draw a histogram (a bar graph) of your estimates. Describe your histogram in your writeup.
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The histogram would be a crude bell curve - large middle and smaller tails, but since we have only three sets, it would be a very blocky bell curve.
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Now suppose you had estimated the percent of time spent in each of 10 velocity ranges (i.e., from 0 to .1 of max. vel., .1 to .2 of max. vel., etc, up to max. vel.). From your previous estimates, without further viewing the simulation, make a reasonably consistent estimate of the proportion of time spent in each of these ranges.
Sketch a histogram of your estimates and describe the graph in your writeup.
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Buy using the 10 percent vs 1/3 catagories our histogram would smooth out a bit and start to look even more like a nice bell curve.
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Sketch the smooth curve you think best represents the distribution, with the curve being highest at the most likely speed, near the horizontal axis for speeds you very seldom observe. According to your sketch, which speed is the most likely? What percent of the area under your curve corresponds to speeds within one unit of your most likely speed (e.g., if your most likely speed was 3, you would estimate the area under the curve between speed 3 - 1 = 2 and speed 3 + 1 = 4). For what speed(s) is the curve half as high as the maximum? For what speed(s) is it half this high?
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Most likely speed is 6.
About 50% would be within one unit.
Speeds 2 and 9 would be about half as high.
An then speeds 1 and 10 would be about half as high again
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Watch the green particle for long enough to estimate the percent of time it spends at speeds more than 2 units greater than the most likely speed, but not more than 4 units greater.
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About 15%
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What percent of the time do you estimate that the green particle is moving at less than half its most likely speed?
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About 15%
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Watch the number corresponding to the speed of the green particle.
Close your eyes for a few seconds at a time and open them suddenly, and each time write down the velocity of the particle as you see it immediately after your eyes open. Record about 100 velocities in this manner.
Tally your velocities to see how many of the 100 velocities were 0, how many were 1, how many were 2, etc.
Construct a histogram of your results and compare to the histograms you predicted earlier.
The results were far from as smooth as I'd imagined they be. 4 was the most common speed at 18% . Even if I were to apply a smooth curve, it would show a curve biased to the left - as in the slower speeds. Speeds in the fast half (7-13) made up only 24 % total.
Experiment kinmodel_03: Equipartition of energy and the direction of disorder to (increasing or decreasing)
ALTERNATIVE
Start the program using default values. Let it run for several seconds, then start observing the green particle. Keep track of whether it is moving more in the x or more in the y direction. Just say to yourself 'x x x y y y y y x x y x y y y ... ', according to what you see. Do this at a steady but comfortable pace. Continue this for a minute or so.
Then take a pencil and paper, or alternatively open a text editor in a separate window, and start writing down or typing your x and y observations. I just did this and in about a minute or two I got the following: xxyyyyxyyxxyxyyxxyxxxyyyxxyyxxyyxyxxyyyxyyyxyyxy. I haven't done this before and found this a little confusing. Every time the particle got hit I wanted to type a letter right away, but I hadn't had time to figure out in what direction it was headed. With practice I began to get over that. You will experience different glitches in the process, but with a few minutes of practice you'll be able to do a reasonably good job. I suspect I also had some tendency to type one of the letters in preference to the other (e.g., x in preference to y, or maybe y in preference to x). I don't recommend fighting this sort of tendency but just noticing it and gently trying to improve. I didn't do this with pencil and paper, and it would be interesting to see if the tendencies are the same when writing as opposed to typing. However that's not our purpose here.
At whatever pace you prefer, write or type about 50 observations of x or y. List them here.
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xxxyyyyxxyyyxxxxyyxxxyyxxxyxyxxxyxyyyyxxxyxxxxyxyy
That's 28 X and 22 Y
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Now notice the KEx and KEy values represented toward the right-hand part of the program's window, just a little ways below the middle of the screen. KEx represents the total x component of the kinetic energies of all the particles and KEy the total y component.
Using the Pause and Restart buttons, stop and start the program and with each stop record the KEx and KEy. After each observation quickly hit 'Restart' then 'Pause', and record another. Record about 50 observations.
Having recorded the 50 KEx and KEy values, write 'x' next to each pair for which the x value is greater, 'y' next to each pair for which the y value is greater. List your x's and y's in sequence here (don't list your values for the KE).
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yyxxxyxxxyxxxyxyxxxxyyyyyyxxyyyxxyyxxxxyxxxxxyyyxx
29 X and 21 Y
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What is the greatest KEx value you observed and what is the least?
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1467 is the greatest
804 is the least
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What is the greatest KEy value you observed and what is the least?
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1416 is the greatest
847 is the least
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On a 50-trial sample of a normal distribution, the mean would be expected to occur about halfway between the least and greatest values observed, and the expected standard deviation would be very roughly 1/5 of the difference between the least and greatest values. According to this (very approximate) rule, what would be the mean and standard deviation of your KEx values, and what would be the mean and standard deviation of your KEy values?
Mean KEx = 1135.5
STD KEx = 132.6
Mean KEy = 1131.5
STD KEy = 113.8
Do you think the mean KEx value differs significantly from the mean KEy value? There is a difference. By 'significantly', we mean a difference that seems greater than what would naturally occur by chance statistical variations.
I would say that the means are not significantly different.
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&#Very good data and responses. Let me know if you have questions. &#