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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.
** Initial Timing Experiment_labelMessages **
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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 a hardcover children's book called Somewhere in the World Right Now. I picked this because the cover is large, and the book is not very thick or heavy (so I figured it would be easier to make sure its position was consistent). The entire length of the cover is 28.6 cm.
The book is propped up on three nickels lined up with the top edge of the book.
The rolling object is one of my kids' toy cars. The length of the car, from the front bumper to the back of the back wheels, is 5.9 cm. I consider the starting point the position of the front bumper at the top of the book. (I lined up the back of the back wheels with the very top of the book, so the front bumper is 5.9 cm closer to the bottom of the book at the moment of release). The end point is the very bottom of the book. I put a small box up against the bottom edge of the book so that I could click the timer when I see the car make contact with the box, which I think is more accurate than just watching for the precise moment it sails off the edge.
The car rolled smoothly. On most of the readings, it appeared to speed up consistently (though slightly). On two readings (the longest time intervals), it actually appeared to slow down towards the end.
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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 estimate all distance readings to be accurate within .1cm
I estimate all time readings to be accurate within .25s
I did many practice rolls to get the hang of clicking the timer with one hand at the precise moment I released the car with the other hand, and then clicking the timer again at the precise moment I observed the front of the car making contact with the box at the bottom of the incline.
I believe the accuracy of my timing improved a lot with practice, but I am still only confident of getting it right within a quarter-second or so, which puts my margin of error, realistically, at around 10%.
First set of readings: rolling from right to left
Distance car rolls (front bumper at release point to front bumper at box): 22.5 cm
Height of starting point: 1.2 cm
Height of ending point: .8cm
Distance from supports to low end: 26.4 cm
Time of first roll: 2.203125 s
Time of second roll: 2.03125 s
Time of third roll: 2.078125 s
Time of fourth roll: 2.117188 s
Time of fifth roll: 2.144531 s
Average of five right-to-left rolls: 2.1148438 s
Second set of readings: rolling from left to right
Distance car rolls (front bumper at release point to front bumper at box): 22.5 cm
Height of starting point: 1.2 cm
Height of ending point: .8cm
Distance from supports to low end: 26.4 cm
Time of first roll: 2.019531 s
Time of second roll: 2.4375 s
Time of third roll: 2.425781 s
Time of fourth roll: 2.226563 s
Time of fifth roll: 2.007813 s
Average of five left-to-right rolls: 2.2234376 s
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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:
As I stated above, I believe my time readings may only be accurate within a quarter-second. They vary by over .4 seconds (difference between shortest roll and longest roll). There are of course other differences. The second set of rolls took longer on average, and this may have to do with how level my kitchen counter is- or isn't.
But using the data I have, I can calculate the average time duration over over the course of all 10 recorded rolls by adding them all up and dividing by 10. This gives me an average time duration of 2.1691407 seconds.
To find average velocity, I divide distance traveled by average elapsed time.
So, 22.5 cm/ 2.1691407 = 10.373 cm/s, or .10373 m/s.
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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 beginning of each timed interval, the car was at rest, so its velocity was 0cm/s.
Its average velocity was .10373 m/s.
For almost all of the readings, the car appeared to move faster and faster as it got closer to the end of the book. For the longest readings, the car appeared to slow down towards the end. I believe that in ideal conditions, the car would always be accelerating due to the force of gravity. But, friction or some slight inconsistency on the surface of the book cover or one of the wheels could have created enough resistance to interfere with that principal and cause the car to accelerate less than it otherwise would, or to stop accelerating entirely and in fact slow down.
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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:
This applies to all but the two rolls that appeared to slow down at the very end.
Least: initial speed
Then: average speed
Greatest: (tie) final speed, 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:
First, I'm going to add an extra nickel. I think that if the car builds up a little more speed initially, it will be less likely to encounter enough friction or other resistance to interfere with the acceleration at the end. I'm also going to rotate the book back to the right-to-left orientation, which gave me more consistent results.
Next, I'm going to measure the midpoint of the car's total distance traveled and mark it with a piece of tape so that I can observe when it crosses that line, which I'll call A. I'll call the endpoint B. (The tape is just at the edge, where I'll be observing. The car won't actually roll over the tape.)
To get the midpoint, I take the 22.5 cm I know to be the total distance and divide by two to get 11.25, then measure up from the bottom of the book
I will take a series of readings, this time marking the time at both A and B. .
elapsed time from start to A elapsed time from A to B
1st roll 1.46875 s .7851563 s
2nd roll 1.140625 s .6484375 s
3rd roll 1.175781 s .7617188 s
4th roll 1.320313 s .6132818 s
5th roll 1.324219 s .6835938 s
Average 1.2859376 s .69804617 s
From these readings we can determine that for an equivalent distance traveled (11.25 cm), the first set of readings gave us consistently and measurably shorter time intervals.
We can use these time readings to determine average velocity before the midpoint and average velocity after the midpoint.
Getting to the midpoint took, on average, about 1.286 s. Getting from the midpoint to the end took, on average, .6980 s.
If we divide 11.25 cm (the distance traveled in both cases) by those average time intervals, we will get average velocity.
11.25cm/1.286s = 8.748 cm/s or .08748 m/s.
11.25cm/.698s = 16.117 cm/s or .16117 m/s.
That means that the average speed increases not just once when the car starts rolling, but throughout the entire journey from top to bottom.
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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?
90 minutes.
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Excellent work.
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