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Phy 231
Your 'ball down ramp' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Ball Down Ramp_labelMessages **
This lab answered many questions i had related to slope that i had previously. This lab helped me understand concepts that previously eluded me in previous classes. In particular it was the 'ds of each different slope. I now see that the distance traveled remains the same throughout.
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A ball is timed as it rolls from rest to the end of a ramp. The slope of the ramp is varied. Preliminary conclusions are drawn about the motion and the effect of
ramp slope. A subsequent lab exercise uses the data from this lab to reach additional conclusions.
Most students report completion times between 45 minutes and 75 minutes hour, with a few reporting times as short as 25 minutes or as long as 2 hours. Median time of
completion is around 1 hour.
Timing Ball down Ramp
The picture below shows a ball near the end of a grooved steel track (this steel track is a piece of 'shelf standard'); the shelf standard is supported by a stack of
two dominoes. Your lab materials package contains two pieces of shelf standard; the shelf standard shown in the figure is white, but the one in your kit might be
colored black, gold, silver or any of a variety of other colors.
If a ball rolls from an initial state of rest down three ramps with different slopes, the same distance along the ramp each time, do you think the time required to
roll the length of the ramp will be greatest or least for the steepest ramp, or will the interval on the steepest ramp be neither the greatest nor the least? Explain
why you think you have correctly predicted the behavior of the system.
Your answer (start in the next line):
I believe the time required to travel down the steepest ramp will be the least. This is due to that there is more rise and less run in a steeper sloped system resulting in a larger acceleration, covering the same distance in a smaller time interval.
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If we write down the slopes from least to greatest, next to the time intervals observed for those slopes, would you expect the time intervals to be increasing or
decreasing, or do you think there would be no clear pattern? Explain why you think you have correctly described the behavior of the numbers in the table.
Your answer (start in the next line):
With the slopes from least to greatest, next to the time intervals for those slopes, the time intervals would be decreasing. This is due to the increases in slopes resulting in greater accelerations with every increase. The greater accelerations would cause the system to reach the end at a faster rate.
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Set up the shelf standard ramp on a reasonably level table, using a piece of 30-cm shelf standard and a single domino under the high end of the ramp. Position the
dominoes so that the last .5 cm of the ramp extends beyond the point where the ramp contacts the domino,.and do the same in all subsequent setups.
Set the bracket on the table, touching the lower end of the ramp so that a ball rolling down the ramp will strike the bracket..
Mark a point about 3 cm below the top end of the ramp. Place a domino on the ramp to its high end is at this point, and place the ball just above the domino, so the
domino is holding it back. Quickly pull the domino away from the ball so the ball begins to roll freely down the ramp. Allow the ball to roll until it strikes the
bracket.
The bracket will probably move a little bit. Reset it at the end of the ramp.
Determine how far the ball rolled from release until it struck the bracket.
Now repeat, but this time use the TIMER. The first click will occur at the instant you release the ball, the second at the instant the ball strikes the bracket.
Practice until you are as sure as you can be that you are clicking and pulling back the domino at the same instant, and that your second click is simultaneous with the
ball striking the bracket.
When you are ready, do 5 trials 'for real' and record your time intervals.
Then reverse the system--without otherwise changing the position of the ramp, place the domino under the left end and position the bracket at the right end.
Time 5 trials with the ramp in this position.
In the space below, give the time interval for each trial, rounded to the nearest .001 second. Give 1 trial on each line, so that you will have a total of 10 lines,
the first 5 lines for the first system, then 5 lines for the second system.
Beginning in 11th line give a short narrative description of what your data means and how it was collected.
Also describe what you were thinking, relevant to physics and the experiment, during the process of setting up the system and performing the trials.
Your answer (start in the next line):
1.762
1.637
1.703
1.691
1.879
1.660
1.703
1.953
1.762
1.707
The data above is the time in seconds for the ball to roll down the hypotenuse of my 27.55 cm ramp. This ramp was elevated by one domino on the end and the ball was released from a set point and rolled until it struck an object attached to a bell, signaling the end of the run. This was done for five trials , then the system was rotated for a second of five identical trials.
I thought that this was an example of acceleration, with the ball starting from rest and accelerating down to an end point. I thought that gravity pulled the ball down the ramp and that the acceleration was uniform.
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Now place two dominoes under the right end and repeat the process, obtaining the time interval for each of 5 trials.
Then place the two dominoes under the left end and repeat once more.
Enter your 10 time intervals using the same format as before.
Your answer (start in the next line):
1.211
1.238
1.242
1.230
1.266
1.211
1.339
1.195
1.172
1.281
Time in seconds for ball to travel down ramp 2 dominoes high. the hypotenuse was again 27.55 cm.
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Repeat the preceding using 3 dominoes instead of 2. Enter your 10 time intervals using the same format as before.
Your answer (start in the next line):
1.016
0.910
0.914
0.965
1.023
1.004
1.004
0.906
0.922
0.977
Time in seconds for ball to travel down ramp with three dominoes.
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Repeat the preceding again, still using the 3 domino setup, but this time place a CD or a DVD disk (or something of roughly similar thickness) on the 'low' end of the ramp. You need time only 5 intervals, but if you prefer you may use 10. Enter your 5 (or 10) time intervals using the same format as before.
Your answer (start in the next line):
1.020
0.984
1.063
1.016
1.172
Time in seconds for ball to travel with 3 dominoes on higher end and cd on lower end.
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Repeat the preceding one last time, still using the 3 domino setup, but remove the disk and replace it with a piece of paper. You need time only 5 intervals, but if
you prefer you may use 10. Enter your 5 (or 10) time intervals using the same format as before.
Your answer (start in the next line):
0.984
1.039
1.047
1.078
1.043
Time in seconds for ball to travel with three dominoes on higher end, and a sheet of paper on the lower end.
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Do your results support or fail to support the hypotheses you stated in the first two questions, regarding the relationship between time intervals and slopes?
Explain.
Your answer (start in the next line):
My results support my hypothesis I stated which was that with a starting higher elevation, the faster the ball would take to travel down the ramp. It was clear when there was abrupt changes in starting elevations with the stacking of dominoes, but not as clear when there was only a small change in elevation as with the cd, and sheet of paper on lower end, but there was still a small difference which supports my hypothesis.
So the greater the angle of the ramp, the faster the acceleration, and the shorter the time interval for the ball to travel down the same distance of ramp.
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How do you think the average velocity of the ball is related to the slope of the ramp? Explain in as much detail as possible.
Your answer (start in the next line):
Average velocity is the change in distance over the change in time. So as the slope of the angle is increased, the average velocity of the ball also increases.
Using random sets of data from the three domino systems we can calculate average velocity for each system.
V_ave = 'ds / 'dt = 27.55 cm / 1.703 sec = 16.17 cm/s = one domino elevation
v_ave = 'ds /'dt = 27.55 cm / 1.230 sec = 22.40 cm/s = two domino elevation
v_ave = 'ds /'dt = 27.55 cm / 1.004 sec = 27.44 cm/s = three domino elevation
Final answer = yes, average velocity is related to the slope of the ramp. As the rise increases, the run (time intervals) decreases.
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Speculate on what it is that causes the average velocity on these ramps to change with slope.
Your answer (start in the next line):
The change in initial height is what causes the average velocity of the system to increase. As the slope increases, the time to cover the same distance decreases.
V_ave = 'ds / 'dt
'ds is constant at 27.55 cm
'dt is variable with the angle of elevation, the higher the elevation, the shorter the time.
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How might you verify whether your speculations are indeed valid explanations?
Your answer (start in the next line):
In the extreme case, I could use two sample points from the three dominoes to cd, and the three dominoes to sheet of paper to validate my hypothesis. In this case I will use the average time of both system
cd system time average = sum of times / (1 less of number of times) = 5.255 sec / 4 = 1.314 s
cd system v_ave = 27.55 cm / 1.314 s = 20.97 cm/s
paper system time average = sum of times / (1 less of number of times) = 1.298 s
paper system time average = 27.55 cm / 1.298 s = 21.22 cm/s
So as the average data shows, from the two runs in which elevation difference was only a few millimeters, there is a noticeable difference in average velocities with the differences in height. The higher the starting point, the faster the higher the average velocity.
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Do your data conclusively show that the disk made a difference?
Your answer (start in the next line):
3 Dominoes to floor time average = sum of times / (1 less of number of times) = 4.825s / 4 = 1.206 s
vAve for above system = 27.55 cm / 1.206 s = 22.84 cm/s
3 dominoes to cd (less angle) time average = sum of times / (1 less of number of times) = 5.255 s / 4 = 1.314 s
vAve for above system = 27.55 cm / 1.314 s = 20.97 cm/s
so less angle equals less velocity
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Do your data conclusively show that the piece of paper made a difference?
Your answer (start in the next line):
3 dominoes to cd (less angle) time average = sum of times / (1 less of number of times) = 5.255 s / 4 = 1.314 s
vAve for above system = 27.55 cm / 1.314 s = 20.97 cm/s
3 dominoes to paper system time average = sum of times / (1 less of number of times) = 1.298 s
3 dominoes paper system velocity average = 7.55 cm / 1.298 s = 21.22 cm/s
The above shows that even with a slight increase in slope angle, the average velocity also increases.
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Imagine that someone is placing different objects below the 'low' end of the ramp, and you are timing the ball. Assume that somehow the object placed below the 'low'
end is hidden from you in a way that does not interfere with the timing process. Compared to the thickness of the DVD, how thin would the object have to be before you
would be unable, using the TIMER, to observe a difference in times down the ramp?
Answer this question in the first line below. Express your answer in multiples or fractions of the thickness of a disk.
Starting in the second line, explain how you came to your conclusion, based on the results you obtained in this experiment. Also discuss how you could modify or
refine the experiment, still using the TIMER, to distinguish the effect of the thinnest possible object placed under the 'low end.
Your answer (start in the next line):
I think using the process of finding average times as in previous questions, as long as there were the same amount of runs for each system, The change would be less than 1 millimeter. I think that it could be accurate to 0.25 millimeters, or 1/4 of a millimeter in difference. A little bold, but if all things were equal, I think it
could be done.
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Had you placed the disk below the 'low' end of the ramp in a 1-domino setup, do you think the difference in times would have been greater or less? Do you think you
would be better able distinguish the presence of a thinner object using the 1-domino setup, or the 3-domino setup? Explain your reasoning below:
Your answer (start in the next line):
Differences in times would be greater. There would be less of a angle of slope, this would result in a longer period of time to cover the same distance.
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Does the ball's velocity change more or less quickly with the 3-domino setup or the 1-domino setup? Explain as best you can how you could use your results to support
your answer.
Your answer (start in the next line):
'dv = vf -v0
vave = (v0 +vf) / 2, with v0 = 0
vf = 2*vave
vf 3 domino setup = 2 * 22.84 cm /s = 45.68 cm /s
'dv 3 domino setup = 45.68 cm /s
vf 1 domino setup = 2 * Vave(1 domino) = 2 * 16.17 cm /s = 32.34 cm/s
'dv = 32.34 cm/s
'dv is greater in the three domino setup than it is in the one domino setup.
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Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can,
understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
Approximately how long did it take you to complete this experiment?
Your answer (start in the next line):
2 hours
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&#Very good data and responses. Let me know if you have questions. &#