course Phy 202
rsh220@email.vccs.edu Bob.S.Hamilton@kcc.com
Preliminary Questions:Watch the KEx and KEy values as they change with each collision, representing the total x and y kinetic energies of the particles.
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• Watching the KE(x) and KE(y) the initial observation is that the KE(x) is greater than the KE(y). However, after a very short period of time, the system begins to oscillate and the KE(x) or KE(y) can be greater at any given time interval.
Watch the 'red' particle for a couple of minutes, estimating the average time between its collisions and its average speed (one of the speeds given near the top of the screen corresponds to that of the 'red' particle--which is it?).
• When watching the red particle, the average time between collisions is estimated to be approximately 750 milliseconds. This was determined due to the longest length of time between collisions appearing to be approximately 2 seconds, however, several collisions occurred consecutively, with very little time between occurrences.
• Observation of the red particle velocity indicator, the indicator to the left at the top, showed a maximum value of 12. However, this value occurs least often for the shortest period of time. The smaller values of velocity, 1-4, occur second most for a larger percentage of the time. The middle values, 5-8, occur most often and for the longest periods of time. After observing the meter over a long time interval, it was determined that the average velocity was approximately 5.
Watch the 'blue' particle, and speculate on what property of this particle is different from that of the other particles.
• The blue particle appears to have a mass greater than the other particles. This is evident by the velocity the blue particle maintains with respect to the faster, lighter particles around it, and the impact of collisions on the blue particle.
Watch as the 'red' particle sometimes turns yellow. What causes this? What property does the particle have when it is yellow?
• The transfer of energy causes the particle to turn yellow, and it appears that the yellow indicates that the particle is at the maximum levels of velocity, therefore, it has been accelerated.
Actually the yellow indicates velocities in a certain range. The range is a bit above the average energy, so the yellow typically appears after a collision. If the velocity is too great the particle won't be yellow; however a particle moving this fast will be hard to see so this won't necessarily be apparent.
What might the graphs represented at the right of the screen represent?
• The red graph appears to represent the velocity of the particle, while the white graph appears to represent the energy transfer, or acceleration curve, of the particle. The longer the simulation runs, the more the graphs appear to more uniform.
some graphs represent the velocity distribution (the graph is higher for velocities which occur more frequently), while some represent the energy distribution (similar at first glance, though energy is proportional to squared velocity).
Experiment kinmodel_03: Equipartition of energy and the direction of disorder to (increasing or decreasing)
Observe the first several seconds of the simulation at the 'slow' default speed. You will see how the particles initially are all moving in or very close to the x direction, with little or no y component. Note the x and y kinetic energies, displayed near the top of the screen.
• In the initial stages of the simulation, KE(x) is maximum and the KE(y) is minimum.
Observe what happens to the directions of motion of the particles as they start colliding.
• As the simulation continues to run, the motion and energy level components become more random..
Observe what happens to the x and y kinetic energies.
• Initially, the KE(x) is maximum, and KE(y) is minimum. As the simulation progresses, the KE(y) becomes greater than the KE(x) component.
Is the system more organized at the beginning of the simulation or after a couple of minutes?
• The system is more organized and uniform at the beginning of the simulation. As the particles begin to collide, the direction, organization and uniformity become more undefined.
If the x and y kinetic energies were averaged for 100 years, starting a few minutes after the simulation began, which do you think would be greater?
• I believe that if KE(x) and KE(y) were averaged over 100 years the final average for both would be essentially the same. After watching the simulation and the varying energy levels, it would appear that over time they would average, or essentially cancel out.
Run the simulation in this manner several times, and each time determine how long it takes before the total y kinetic energy is first greater than the total x kinetic energy. Report your results.
Attempt Time Interval
1st 53 seconds
2nd 48 seconds
3rd 24 seconds
4th 30 seconds
5th 84 seconds
6th 16 seconds
7th 35 seconds
8th 17 seconds
9th 55 seconds
10th 25 seconds
Now take some data:
Running at the fastest default speed, stop the simulation with the pause/break key every few seconds, keeping your eyes closed for at least 2 seconds before stopping the motion.
Write down the x and y kinetic energies each time.
Pause/Break KE(x) KE(y)
1 384.3 407.7
2 331.8 453.6
3 394.7 386.3
4 217.5 526.1
5 392.4 435.4
6 484.4 281.1
7 335.5 393.1
8 432.7 393.6
9 374.6 448.1
10 494.5 365.6
11 417.5 421.6
12 504.8 357.7
13 477.6 371.5
14 452.3 373
15 358 500.8
16 334.4 497.1
17 449.5 408.8
18 454.4 412.9
19 358.9 507.9
20 424.6 433.8
21 403.7 406.7
22 472.8 291.1
23 384.8 414.3
24 528.3 265.3
25 450.6 399.3
26 438.7 461.2
27 491.9 375.4
28 441.8 408.8
29 203.2 608.9
30 401.7 454.2
Average 409.7 415.4
Do you believe the difference in the averages is significant, in that the direction that has the higher average will always tend to have the higher average every time the simulation is run?
• No, I believe that the difference between averages is insignificant and the higher, average energy could vary from simulation to simulation.
Good. The difference is small enough compared to the standard deviation of the sample that the difference is statistically insignificant.