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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.
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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 that the steepest ramp will require the shortest time intervalof the three.
In all three cases, the ball should accelerate steadily. We know it accelerates to start with, because it begins, in all three cases, with a velocity of 0cm/s and speeds up to something greater than 0cm/s. The materials used should allow for a minimum of interference due to air resistance or friction, so the conditions are probably as close to ideal as we can get at home using everyday materials. So I see no reason why the ball won't continue to accelerate through the entire ramp.
The reason the ball starts moving is because the force of gravity is pulling it down. But as the ball begins to move, different things will happen depending on the slope of the ramp.
Take the first centimeter of the ramp's length. The ramp with the steepest slope would see the ball traveling the greatest vertical distance over the course of that first centimeter. That is, the vertical component of the ball's motion will be greatest per centimeter when the slope is steepest. I believe this will allow it to build up speed at a greater rate; less of gravity's force will be wasted on propelling it along horizontally.
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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):
I believe the time interval will decrease as slope increases.
As above, the horizontal and vertical components of each centimeter of the ball's path will differ depending on the slope. Since the main force causing the ball to move is gravity (which is acting vertically on the ball), it seems reasonable to guess that the more vertical the path, the more efficiently gravity will be able to do what gravity does, which is cause things to accelerate toward the earth. If we think of horizontal surfaces as mostly functioning to PREVENT gravity from doing this, in a sense, it stands to reason that steeper slopes = greater vertical component = more efficient ability to win over the horizontal component's ability to hold the ball up.
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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):
2.387
2.414
2.180
2.230
2.410
2.094
2.020
2.230
2.180
2.094
Timed trials with one domino under top of ramp; 5 facing left, 5 facing right. Slightly shorter intervals when facing right indicate surface may not be level.
The process involved many situations that called for precision. I realized that slight differences in the position of the base domino holding the ramp up would change the slope of the ramp. While the instructions here called for an exact position (1/2cm from the top), I realize that when doing a lab, we have many opportunities to set similar standards for what we are doing, and it's important for us to recognize that when we decide on a standard, it has to stay consistent throughout the lab.
I also found that there was a certain spot right at the starting point on the track that seemed to have a slight divot or indentation, causing the ball to catch and hestitate on certain trials. After this happened a few times, I adjusted the starting point to below the divot so it wouldn't interfere with the path of the ball at the very beginning. I think it's likely that there are similar dents at other points on the track, but that having one right at the start, before the ball has built up much momentum, causes the greatest interference.
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Good. Glitches in the motion are particularly effective near the beginning, and do need to be eliminated if possible.
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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):
1.324
1.434
1.371
1.348
1.309
1.274
1.117
1.199
1.223
1.227
Timed trials with two dominos under top of ramp; 5 facing left, 5 facing right. Again, slightly shorter intervals when facing right indicate non-level surface.
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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):
1.089
1.078
1.089
1.113
1.101
1.043
.992
.992
1.016
.980
Timed trials with three dominos under top of ramp; 5 facing left, 5 facing right. Again, slightly shorter intervals when facing right indicate non-level surface.
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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):
1.152
1.199
1.188
1.152
1.176
1.102
1.063
1.164
1.125
1.102
Timed trials with three dominos under top of ramp and CD under bottom of ramp; 5 facing left, 5 facing right.
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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):
1.090
1.188
1.176
1.176
1.176
1.016
1.078
1.106
1.043
1.016
Timed trials with three dominos under top of ramp and sheet of paper under bottom of ramp; 5 facing left, 5 facing right.
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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):
The results support my hypothesis that an increasing slope will lead to a shorter time interval from the top to the bottom of the ramp.
The ramp with the least slope (supported by one domino) resulted in an average time interval of 2.22 seconds. The ramp supported by 2 dominos resulted in an average time interval of 1.283 seconds. The ramp with the greatest slope, supported by 3 dominos, resulted in an average time interval of 1.049 seconds.
Even very slight changes in slope can effect the time interval. Taking the three-domino ramp and propping up the bottom with a CD reduces the rise of the system by about a millimeter, and thus reduces the slope slightly. This increased the travel time from an average of 1.049 seconds to an average of 1.143 seconds; so the 1-millimeter difference in vertical drop cause about a .1-second increase in travel time. Putting a sheet of paper in place of that CD gave an average travel time of 1.106 seconds, which falls in between the regular 3-domino ramp and the 3-domino-opposite-a-CD ramp. That is what we would predict, since the slope would fall in between those two as well.
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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 starts at 0 in all cases. Then, the ball accelerates at different rates depending on how far it is able to fall vertically in relation to its linear path. The greater the acceleration, the higher the velocity at the end of the path. So, finding the average velocity means adding initial velocity (always 0) to final velocity and dividing by 2. This means that the greater the slope, the higher the final velocity, and thus the higher the average velocity.
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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):
As the force of gravity starts the ball in a downward vertical motion, the ball must also move along a horizontal path in order to make progress vertically. The greater horizontal distance it must travel, the larger the proportion of gravity's force that goes toward the horizontal component of the journey, and the ball moves down vertically (which is the motion that causes it to accelerate).
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How might you verify whether your speculations are indeed valid explanations?
Your answer (start in the next line):
I need to come to a greater understanding of how different forces act on an object simultaneously. I suspect that my explanation is incomplete, and that there is some way to account, mathematically, for the force of the ramp holding the ball up.
If the ramp is indeed exerting a force, we would calculate how the ramp's force and force of gravity are working simultaneously (and in opposing directions, at least to a degree). That would allow us to quantify what is happening both vertically and horizontally.
In a lab setting, we could repeat this experiment using different length ramps, balls of different masses, a greater variety of slopes, etc., to replicate the pattern with different data sets.
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Do your data conclusively show that the disk made a difference?
Your answer (start in the next line):
Average time span for the 3-domino ramp with the low end on the surface of the counter was 1.049 seconds, with a standard deviation of .045s.
Average time span for the same ramp with the low end on the disk was 1.143 seconds, with a standard deviation of .043s.
Added up, the total standard deviation is less than the difference between the two average times.
This means that even accounting for the maximum error as defined by the standard deviation, we can be confident that the ramp with the greater slope produces consistently shorter time intervals than the ramp with smaller slope.
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Do your data conclusively show that the piece of paper made a difference?
Your answer (start in the next line):
Average time span for the same ramp with the low end on the sheet of paper was 1.106, with a standard deviation of .069s.
While the average time span with the piece of paper is longer than the average time span without it, I believe that when we take into consideration both standard deviations (which add up to a greater length of time than separates the two averages), we cannot say that the data are conclusive. At this level of hundredths of a second, the deviation from the average is too great.
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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):
Half the thickness of a CD.
My sets of trials have a fairly large standard deviation. As I've calculated it, I would not go any thinner than the CD. However, I calculated one standard deviation for the entire set of 10 trials, which include 5 left-facing and 5 right-facing. The numbers are consistently different depending on which direction you are facing. But if I calculate standard deviation for the left-facing trials as a set and the right-facing trials as a separate set, the deviation is about half as much in most cases.
So, if look at each direction as a separate data set, my numbers are more precise and any difference caused by changing slope will be more statistically significant.
This would be a way to refine the experiment: keep all other conditions as close to exactly the same as possible. Moving the entire system even an inch or two on an old kitchen counter could affect slope. I could also use a level to place the system on the most level part of the counter as possible.
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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):
I think the disk would make more of a difference to the 1-domino setup. The disk at the low end changes the slope by a greater percentage of the 1-domino slope as measured without the disk than it does with the 3-domino slope.
We can see that the average difference between the 1 domino setup and the 2 domino setup is nearly a full second in time interval, whereas the average difference between 2 and 3 dominos is about a quarter of a second. So, the same amount of change in height makes more of a difference when we are looking at lesser slopes. So, I think very thin objects like a sheet of paper would make more of a difference for the lesser slopes as well. (But, I don't think I could measure that difference any more accurately, so it would be difficult to repart with any more confidence.)
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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):
The ball's velocity changes more quickly with the 3 domino setup. Shorter travel time over the same distance means a higher average velocity, as we know. Since all velocities start at zero, that means we know that shorter travel time also means a higher final velocity.
Since acceleration is calculated by finding the change in velocity and dividing by elapsed time, and the 3-domino setup involves a GREATER change in velocity divided by a SHORTER time span, we know for sure that acceleration will be higher. That means that the velocity is changing more quickly.
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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 insightful. Good data, good analysis.
Very good work.
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