Phy 231
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.
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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 withing +- 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 an 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 used Sears and Zemanskys University Physics 12th Edition as the ramp in this experiment. And the object I used to roll down the book was the toy car that came in my lab kit. The object rolled pretty well on most of the trials, but a couple times it got stuck at the top and never started rolling. Once it started moving, however, it rolled smoothly down the rest of the book. The car sped up as it reached the end of the book and it rolled in a straight line.
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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:
Positive slanted book (taller on the right):
Trial Time (s)
1 3.97
2 3.38
3 3.72
Distance of travel: 24.5 cm
Height difference in ends of book: 0.8 cm
Distance from end to support: 28.2 cm
Negative slanted book (taller on left);
Trial Time (s)
1 3.47
2 3.18
3 3.38
Distance of travel: 24.5 cm
Height difference in ends of book: 0.8 cm
Distance from end to support: 28.2 cm
I measured this data using a ruler marked in centimeters. The measurements are to within 1 millimeter (+/- 1 mm).
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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:
Average time: (3.97 + 3.38 + 3.72 + 3.47 + 3.18 + 3.38)/6 = 3.52 s
Average speed: 24.5/3.52 = 6.96 cm/s
I believe these measurements are within +/- 1 millimeter and +/- 1/100 of a second. I can only be this accurate on the length measurements because the ruler I am using is marked in millimeters, so I cannot determine fractions of a millimeter. I think the timing is accurate to 1/100 of a second because the timer measures out this far and only this far.
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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:
At the very beginning of the interval, the speed of the object was 0, which means its average speed over this first interval would be 0.
The first instant doesn't constitute an interval. You need two different instants to make an interval. Any interval that begins with the release of this object from rest will cover some nonzero distance in a nonzero time interval, so the average velocity over any such interval will not be zero.
When the object reached the lower end of the book, I think it was moving a speed greater than the average speed calculated because since there are speeds lower than the calculated average (for example, 0), there also must be speeds greater than the calculated average.
Your reasoning is very good, but the average velocity over any interval between release and the end of the ramp will be something other than 0.
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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:
initial speed, average speed, tie: final speed and change in speed
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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:
To determine whether or not the car is speeding up as it rolls down the book, I wanted to split the length of the book into two equal intervals and compare the speeds from each. Since the book is 28.2 cm long, each interval will be 14.1 cm long. To determine speeds for each interval, I will time the car as it rolls down the book and take a time measurement at the halfway mark and then at the end. I will use these times combined with the travelled distance to find the speeds.
Trial 1st Half Time End Time 2nd Half Time
1 1.69 2.47 2.47 1.69 = 0.78
2 1.81 2.58 2.58 1.81 = 0.77
3 1.88 3.21 3.21 1.88 = 1.33
Distance of each interval: 14.1 cm
Average 1st half time: (1.69 + 1.81 + 1.88)/3 = 1.79 s
Average 2nd half time: (0.78 + 0.77 + 1.33)/3 = 0.96 s
Average speed for 1st half: 14.1/1.79 = 7.88 cm/s
Average speed for 2nd half: 14.1/0.96 = 14.7 cm/s
This data supports the conclusion that the car speeds up as it goes down the slope because the average speed during the second interval (14.7 cm/s) is much greater than the speed in the first interval (7.88 cm/s) indicating an increase in speed.
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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 1 hour.
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You may also include optional comments and/or questions.
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Good work, good reasoning throughout. See my note on the terminology of 'interval'.