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PHY 241
Your 'initial timing experiment' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Initial Timing Experiment_labelMessages **
6/25 19:33
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Take reasonable care to get good data in this experiment. Try to do the timing as accurately as possible. Measurements of length, height, etc. should be reasonably accurate (e.g., with a meter stick or ruler you can measure to within +- 1 millimeter, but it's not necessary to try to determine fractions of a millimeter).
In this experiment you will use the TIMER program, a hardcover book, the toy car that came in your lab materials package (or, if you do not yet have the package, a cylinder or some other object that will roll along the book in a relatively straight line), and a ruler or the equivalent (if you don't have one, note the Rulers link, which is also given on the Assignments page).
· The book's cover should be straight and unbent.
· The toy car (or other object) should roll fairly smoothly.
Place the book on a flat level tabletop. You will prop one end of the book up a little bit, so that when it is released the object will roll without your assistance, gradually speeding up, from the propped-up end to the lower end. However don't prop the end up too much. It should take at least two seconds for the ball to roll down the length of the book when it is released from rest. For a typical book, a stack of two or three quarters placed under one end works well.
· Using the TIMER program determine how long it takes the ball to roll from one end of the ramp to the other, when released from rest. Once you've got the book set up, it takes only a few seconds to do a timing, so it won't take you long to time the object's motion at least three times.
· Determine how far the object travels as it rolls from its initial position (where you first click the timer) to its final position (where you click at the end of the interval). This will probably be a bit less than the length of the book, due to the length of the object itself.
· Determine how much higher one end of the book was than the other, and how far it is from the supports (e.g., the stack of quarters, or whatever you used to support one end) to the end of the book which rests on the table.
Then reverse the direction of the book on the tabletop, rotating the book and its supports (e.g., the stack of quarters) 180 degrees so that the ball will roll in exactly the opposite direction. Repeat your measurements.
In the box below describe your setup, being as specific as possible about the book used (title, ISBN) and the object being used (e.g., a can of vegetables (full or empty; should be specified) or a jar (again full or empty); anything round and smooth that will upon release roll fairly slowly down the incline), and what you used to prop the object up (be as specific as possible). Also describe how well the object rolled--did it roll smoothly, did it speed up and slow down, did it roll in a straight line or did its direction change somewhat?
your brief discussion/description/explanation:
I tried using a hardcover book, but I simply could not make it work with my setup. Either the desk is not quite level and/or the book kept ‘expanding’ so that the object rolled in a more or less diagonal fashion down the book, or it rolled width-wise rather than length-wise. After several attempts with several books I switched to using a standard Westcott 1-B meter stick (mm graduations on one side/1/8” graduations on the other side). I did not receive a car in my initial lab packet so I used the large marble that did come in the packet as the object rolled. At first, the marble rolled off the side of the meter stick, so I taped paper along the edges of the meter stick to keep the marble on the stick while rolling. The paper stuck up approximately 1/8” above the edge of the meter stick. I used small bits of model clay to level-out the meter stick to minimize the amount of times the marble hit the paper while rolling.
I elevated the meter stick with two of the dominoes that were provided in the initial lab packet. I stacked the two dominoes flat on the desk under the meter stick between the 50-55 cm markings. I then taped a paper clip to the bottom of the meter stick to stop the marble when it reached the end of the stick and to keep that end of the stick on the desk. I rolled the ball starting from the 60 cm line towards the 100 cm end of the stick, for a distance of 40 cm.
The 60 cm line was elevated above the desk approximately 21 mm above the surface of the desk; the 100 mm end of the stick was on the desk.
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In the space indicated below report your data. State exactly what was measured, how it was measured, how accurately you believe it was measured and of course what the measurements were. Try to organize your report so the reader can easily scan your data and identify any patterns or trends.
your brief discussion/description/explanation:
I recorded the time it took for the marble to roll from the 60 mm line on the meter stick to the 100 mm end of the meter stick. I used the computer “timer” application to measure those times.
The first set of recordings was taken with the meter stick sloping from left to right (high to low) on my computer desk. I positioned the marble on the meter stick so that the downslope edge of the marble was directly over the 60 mm mark on the meter stick. I ‘clicked’ the “click to time event” button on the timer at the same time I released the marble. The marble rolled down the meter stick and struck the paper clip at the end with an audible sound. I watched the marble and listened for the sound – and I attempted to ‘click’ the “click to time event” button on the timer at the instant the marble reached the end of the meter stick. I recorded the time for 10 rolls of the marble. The times were:
First set – Time (in seconds) for marble to roll 40 mm (sloping down from left to right)
2.183594
2.277344
2.261719
2.214844
2.324219
2.292969
2.246094
2.183594
2.386719
2.371094
Average = 2.27430 --> rounded to 2.274 seconds
The second set of recorded times was made in exactly the same manner as the first set of recorded times. The only difference was in the experimental setup; the meter stick was rotated 180º so that it sloped from right to left (high to low). All other aspects of the setup were unchanged from the first trial. The second set of recorded times were:
Second set – Time (in seconds) for marble to roll 40 mm (sloping down from right to left)
2.121094
2.089844
2.214844
2.105469
2.277344
2.308594
2.214844
2.324219
2.121094
2.183594
Average = 2.196094 --> rounded to 2.196 seconds
There are five elements of uncertainty in these measurements:
1) The distances involved were measured to ±0.5 mm. The distance that the marble rolled was measured by placing the marble directly on a meter stick. The height of the 60 mm mark was measured using a standard ruler marked off in mm graduations.
2) The timer is accurate to ±0.001 seconds, so the time measurements should be rounded to that value when used in calculations. Of the five elements of uncertainty, this is probably the most accurate.
3) The release of the ball and the ‘clicking’ of the timer button may not be as simultaneous as desired. So, of the events of this lab having to do with time, this element of uncertainty is certainly less accurate than the timer, but is probably more accurate than the next element. There is no way (that I know of) to accurately quantitatively estimate the amount of uncertainty introduced by this element.
4) The coordination of the click of the timer and the termination of the roll of the marble is certainly the least accurate measurement in this lab. Hopefully, the variance in the two events does not introduce an error of more than ±0.1 second, but I’m not sure how to accurately quantitatively estimate the amount of uncertainty introduced by this element.
5) Variations in the times it takes the ball to roll down the meter stick. This could be affected by the small depressions that mark the millimeters, variations in the number of times the marble hits the paper ‘boundary’ on either side of the stick, variation in the initial positioning of the marble, and other things.
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Very good.
You could get a good idea of the uncertainty in the actual use of the TIMER by timing a random sequence of pairs of events, each pair with a known time interval, and comparing results. That would digress a bit from the physics, touching on psychology, neurology and other areas, and we aren't going to do it here. But it is possible to get some pretty good bounds on those uncertanties.
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Using your data determine how fast the object was moving, on the average, as it rolled down the incline. Estimate how accurately you believe you were able to determine the object's average speed, and give the best reasons you can for your estimate of the accuracy.
your brief discussion/description/explanation:
The first set of measurements can be used to estimate the average speed of the marble as 40.0 mm/2.274 seconds = 17.590 mm/sec. Since the least accurate measurement is ±0.1 (an estimate of the error introduced by the inaccuracy of not simultaneously clicking the timer as the marble ends its roll), then I’ll estimate the average speed to be 17.6 mm/sec.
The second set of measurements can be used to estimate the average speed of the marble as 40.0 mm/2.196 seconds = 18.215 mm/sec. Since the least accurate measurement is ±0.1, then I’ll estimate the average speed to be 18.2 mm/sec.
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How fast was the object moving at the beginning of the timed interval?
According to your previous calculation, what was its average speed during this interval?
Do you think the object, when it reached the lower end of the book, was moving at a speed greater or less than the average speed you calculated?
your brief discussion/description/explanation:
The marble was stationary (v = 0) at the beginning of the timed interval.
The estimates of the average speed were: 17.6 mm/sec for the first set of trials, and 18.2 mm/sec for the second set of trials.
Since the initial speed of all trials was zero, the average speeds are one-half the final speeds. I’d say that the final speed was greater than the average speed.
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The assumption being of course that the acceleration is uniform, which has not been established but which is a reasonable tentative assumption.
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List the following in order, from least to greatest. Indicate 'ties': The object's initial speed, its final speed, its average speed, and the change in its speed as it rolled from one end of the book to the other.
your brief discussion/description/explanation:
First set:
Initial speed Average speed Final speed Change in speed
0 16.8 33.5 33.5
0 16.9 33.7 33.7
0 17.2 34.4 34.4
0 17.4 34.9 34.9
0 17.6 35.1 35.1
0 17.7 35.4 35.4
0 17.8 35.6 35.6
0 18.1 36.1 36.1
0 18.3 (tie) 36.6 36.6
0 18.3 (tie) 36.6 36.6
Second set:
Initial speed Average speed Final speed Change in speed
0 17.2 34.4 34.4
0 17.3 34.7 34.7
0 17.6 35.1 35.1
0 18.1 (tie) 36.1 36.1
0 18.1 (tie) 36.1 36.1
0 18.3 36.6 36.6
0 18.9 (tie) 37.7 37.7
0 18.9 (tie) 37.7 37.7
0 19.0 38.0 38.0
0 19.1 38.3 38.3
(Note: all speeds in mm/sec)
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Devise and conduct an experiment to determine whether or not the object is speeding up as it rolls down the incline. If you have set the experiment up as indicated, it should seem pretty obvious that the object is in fact speeding up. But figure out a way to use actual measurements to support your belief.
Explain how you designed and conducted your experiment, give your data and explain how your data support your conclusions.
your brief discussion/description/explanation:
The setup would remain the same; implementation would change slightly. I’d record the time it takes for the marble to reach the 20 mm mark, and then record the time it takes the marble to travel from the 20 mm mark to the 40 mm mark. The revised experiment simply requires three ‘clicks’ of the timer button instead of the two ‘clicks’ of the original experiment. One would ‘click’ the timer as the marble started – click again when the marble reached the 20 mm (half-way) point, and then finally when the marble reached the end of the roll at the 100 mm mark.
Calculate the average speed during the first half of the roll and compare that to the calculated speed for the second half of the roll.
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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?
About 2 hours – most of the first hour was trying to set up the book (which ultimately failed) and then constructing the revised experimental setup. It took about an hour to make the subsequent measurements. I used Excel for the calculations.
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You may also include optional comments and/or questions.
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&#This lab submittion looks good. See my notes. Let me know if you have any questions.
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