course Phys 202
I went ahead and did 3 although I didn't have my directions yet. If I need to go back and do something different I will.
Billiards Experiment # 3Experiment 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.
• Observe what happens to the directions of motion of the particles as they start colliding.
• Observe what happens to the x and y kinetic energies.
• Is the system more organized at the beginning of the simulation or after a couple of minutes?
• 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?
The system is more organized at the beginning of the simulation, than after a couple of minutes. I think the x and y kinetic energies averaged for 100 years would equate out the two kinetic energies. They would be equal.
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.
1: 50 seconds
2: 1 minute 5 seconds
3: 45 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.
• Do this at least 30 times.
• Find the average of all your x and all your y kinetic energies.
• 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?
233.3 465.7
386 335.3
312.3 509.5
339 411.5
360 379.2
423.7 349.5
397.6 378.9
428.1 310
343.3 405.3
459.7 289.8
379.5 355.8
514.7 188.7
409.1 362.9
437 264.9
255.4 517.7
464.6 308.5
295.8 460.4
487.5 286.3
259.6 507.4
202.3 560.1
366 438.7
443.5 313.3
446.6 290.9
328.8 427.4
442.6 329
336 295.6
239.2 522.9
453.2 301.3
399 328.8
320.1 368.7
These were my x and y values (x in first column)
KEx average: 372.1167
KEy average: 375.4667
I believe the difference in the averages is not significant.
Good.
If the individual results have a standard deviation of, say, 50 then we would expect 30-trial means to differ by about 50 / sqrt(6), so a difference of about 3 would indeed be insignificant.