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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Note: The majority of student report taking less than an hour on this experiment, though a few report significantly longer times.
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 brand-new 2009 Hot Wheels Black Cadillac CTS-V as my toy car, made in Malaysia. Because my Physics textbook seemed to short in length and too heavy to support, I rolled it down my mothers' decoration book entitled, Anne McKevitt's Style Solutions, ISBN 1-4000-4610-6. The book is in good condition with even, straight ends and a smooth cover. It was propped up by three quarters, two nickels, and two dimes stacked on top of each other on one end. The Cadillac rolled very smoothly down the incline, with very little resistance, even more so than down my University Physics with modern Physics 11th Edition, ISBN0-8053-9185-1. Its acceleration increased downward, thus it increased its velocity and acceleration down the incline at an increasing rate; the CTS-V stayed its course, rolling practically straight down the path I started it from ( in the center ) at the top. I attempted each time, by using tape to mark the initial position, to roll the car down the ramp from the same position each time.
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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:
Object Measurements ( always in cm ) :
Cadillac CTS-V: Length ( L )- 11 , Width/Stance ( W )- 5, Height ( H )- 3.25
Initial-Final Length ( Distance Traveled ): 33 ( 44 - 11 )
High End of Book Height: 5.5 ( + 2.5 )
Low End of Book Height: 3.5
Supports ( Stacked Monies ) Height: 2
Supports - End Length ( Distance from Support to End ) 40
I measured the lengths using a cm ruler cut out from my lab kit. The initial to final length was the length of the book sideways minus the car's length. The heights of the book were measured from the surface of the table, as were the supports. The final measurement was from the beginning of the first quarter to the opposite end of the book. The degree of accuracy of the measurement is within 1/10 of a cm for all measurements above.
Time Trials ( Initial Set-up ): Start to Finish Times ( in seconds )
1: 2.503906 s
2: 2.238281 s
3: 2.371094 s
Ave 'dt ( First Three Trials ): 2.371094 s
My third trial appeared to be the exact average.
Time Trials ( Reverse Set-up ): Start to Finish Times ( in seconds )
4: 2.488281 s
5: 2.214844 s
6: 2.421875 s
Ave 'dt ( Second Three Trials ): 2.375000 s
Ave 'dt Overall ( All Six Trials ): 2.373047 s
Bonus: Trial 7 ( Read Response 4 & 6 Below ): 2.398438 s
Ave 'dt Overall ( All Seven Trials ): 2.376674 s
I used the TIMER program to capture the time trials. I believe the degree with which accuracy is measured using the program is within .000001 seconds, notwithstanding my error in time to respond and press the click to time event button. And with that, my error is a rather large at about .1 seconds, as seen in the variance in my results.
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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:
Original Formula:
'ds/'dt = vAve
33 cm/ 2.373047 s = 13.90617211 cm/s or about 14 cm/s.
I believe I was able to estimate the car's speed best by taking the average of the six time trials ( using more data ) consistently forward and backward on the same flat, hard table surface. The displacement was within .1 centimeters. And the time was within .000001 seconds. Coincidentally, my second time trial being exactly the same as the average of my first three, and less than .002 than my average overall, is a good contributing factor to attest my accuracy. Even using simply 2.37 seconds as the change in time, which is fairly close to the overall time it takes for the car to travel 33 cm down the incline, it is even closer to the estimated 14 cm/s at 13.92 cm/s. However, I believe I lose some accuracy when I divide to get the average because there is such a wide difference in degree of accuracy and precision, even within centimeters.
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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:
During the beginning of the timed interval, the car was moving at a velocity less than that of the overall average velocity; its initial velocity was 0 cm/s since it started at rest before I released it each trial. However, it had potential energy, gained from its position at the top of the end of the book, which it converted to mechanical energy, the energy of motion. I used a new seventh trial with a time close to the average to document its progress at the beginning of the timed interval, showcasing the results. With the added trial, the overall average increases by only .003627 s, well within my large error of .1 seconds. After .78125 seconds on trial seven , the CTS-V had traveled 3 cm, equating to an average velocity of 3.84 cm/s ( nearly 4 cm/s ). When the car reached the end of the book, it was traveling faster than the average speed I previously calculated within that small, beginning of the timed interval. It traveled from beginning to end in 2.398438 seconds total ( a little slower than the six trial average ), an overall average of 13.75 cm/s ( slightly lower than average ).
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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:
Using First Six Trials (Using Significant Figures ):
1. Initial Speed ( 0 cm/s ),2. Average Speed ( 14 cm/s ),3. Change in Speed ( approx. 28 cm/s ),4. Final Speed ( approx. 28 cm/s )
The final speed and change in speed are the same because the car presumably starts from rest, resulting in a tie. The change in speed is equal to the final speed because it is the car's overall change from its lowest speed to its greatest speed. Likewise, its final speed is double its average speed because it started from rest.
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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 car is in fact speeding up. I captured the car's displacement and time before halfway through its course, as stated in response to question four. I recorded the car's approximate displacement and corresponding time using the TIMER program and my sight on the same incline in its initial facing position as before. After .78125 seconds in trial seven, the CTS-V had ridden 3 cm, equating to an average velocity of 3.84 cm/s ( nearly 4 cm/s ). When the car reached the end of the book, it was traveling faster than the average speed I had previously calculated within those first .78125 seconds. It traveled from beginning to end in 2.398438 seconds total ( a little slower than the six trial average ), an overall average of 13.75 cm/s, which is greater than the initial average by more than three times; but, it is slightly lower than the six-trial average. Thus, it picked up its pace, its acceleration, within its time interval slower than the first six trials averaged together.
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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?
55 Minutes
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You may also include optional comments and/or questions.
#### I enjoyed this experiment using my car. Finding a book long enough for the duration of more than 2 seconds was a bit challenging. For the fourth question, it was hard to decipher what qualified as the beginning of the interval. I assumed any displacement before halfway through the entire time interval, somewhere in the realm of before 1.185 seconds. I had to do another trial, accounting for displacement in the beginning and corresponding time, after I had done those initial trials, which I had not done with the aforementioned six trials. However, the TIMER program made this entire process very simple to use.
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&#Very good responses. Let me know if you have questions. &#