Most queries in this course will ask you questions about class notes, readings, text problems and experiments. Since the first two assignments have been lab-related, the first two queries are related to the those exercises. While the remaining queries in this course are in question-answer format, the first two will be in the form of open-ended questions. Interpret these questions and answer them as best you can.
Different first-semester courses address the issues of experimental precision, experimental error, reporting of results and analysis in different ways and at different levels. One purpose of these initial lab exercises is to familiarize your instructor with your work and you with the instructor 's expectations.
Comment on your experience with the three lab exercises you encountered in this assignment or in recent assignments.
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Question: This question, related to the use of the TIMER program in an experimental situation, is posed in terms of a familiar first-semester system.
Suppose you use a computer timer to time a steel ball 1 inch in diameter rolling down a straight wooden incline about 50 cm long. If the computer timer indicates that on five trials the times of an object down an incline are 2.42sec, 2.56 sec, 2.38 sec, 2.47 sec and 2.31 sec, then to what extent do you think the discrepancies could be explained by each of the following:
• The lack of precision of the TIMER program.
To what extent to you think the discrepancies are explained by this factor?
Your answer: I don't think the discrepancies are explained by the timer because the timer is reliable to about the hundredth decimal place. Since these vary in the tenth decimal place, it seems to be some other factor at work.
• The uncertain precision of human triggering (uncertainty associated with an actual human finger on a computer mouse)
To what extent to you think the discrepancies are explained by this factor?
Your answer: I don't think human triggering is the problem either, a human can trigger his finger very quickly. But I do think human error is the biggest factor.
• Actual differences in the time required for the object to travel the same distance.
To what extent to you think the discrepancies are explained by this factor?
Your answer: I don't think the discrepancy is explained by this factor. The object moves from point A to point B and as long as the object's inclined is not change, the object's path should not change either.
• Differences in positioning the object prior to release.
To what extent to you think the discrepancies are explained by this factor?
Your answer: This may explain the discrepancy because it is hard to tell where exactly you placed the ball and to place it in the same spot consistently.
• Human uncertainty in observing exactly when the object reached the end of the incline.
To what extent to you think the discrepancies are explained by this factor?
Your answer: This would be my guess as to the one most reliable of the discrepancy. It is hard to tell when the object officially passes the finish line. This is hard to do consistently.
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Question: How much uncertainty do you think each of the following would actually contribute to the uncertainty in timing a number of trials for the ball-down-an-incline lab?
• The lack of precision of the TIMER program.
To what extent to you think this factor would contribute to the uncertainty?
Your answer: Not much, the TIMER would be more consistent then human actions.
• The uncertain precision of human triggering (uncertainty associated with an actual human finger on a computer mouse)
To what extent to you think this factor would contribute to the uncertainty?
Your answer: Deciding when to trigger should provide for the most uncertainty.
• Actual differences in the time required for the object to travel the same distance.
To what extent to you think this factor would contribute to the uncertainty?
Your answer: The gravity and friction should remain constant, along with the incline. This should be relatively constant and there shouldn't be much uncertainty here.
• Differences in positioning the object prior to release.
To what extent to you think this factor would contribute to the uncertainty?
Your answer: Any human action involved should provide for the most uncertainty since it is hard to place it in the exact same spot.
• Human uncertainty in observing exactly when the object reached the end of the incline.
To what extent to you think this factor would contribute to the uncertainty?
Your answer: Again, this would provide for the most uncertainty. It's hard to consistently see where and when it ends.
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Question: What, if anything, could you do about the uncertainty due to each of the following? Address each specifically.
• The lack of precision of the TIMER program.
What do you think you could do about the uncertainty due to this factor?
Your answer: You couldn't do much other than to use a different TIMER program. As long as you get consistency from it, it shouldn't be a problem.
• The uncertain precision of human triggering (uncertainty associated with an actual human finger on a computer mouse)
What do you think you could do about the uncertainty due to this factor?
Your answer: You could use many people, instead of one person, and use the average of these samples. This would help reduce the impact of a slow or fast trigger.
• Actual differences in the time required for the object to travel the same distance.
What do you think you could do about the uncertainty due to this factor?
Your answer: Make sure the board has not moved before each repetition.
• Differences in positioning the object prior to release.
What do you think you could do about the uncertainty due to this factor?
Your answer: You can mark the exact spot to release the ball.
• Human uncertainty in observing exactly when the object reached the end of the incline.
What do you think you could do about the uncertainty due to this factor?
Your answer: You could use many people, rather than one person, and find the average times. This would help reduce the impact of a slow or fast run.
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Question: If, as in the object-down-an-incline experiment, you know the distance an object rolls down an incline and the time required, explain how you will use this information to find the object 's average speed on the incline.
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Your solution: To find the average speed, you should divide the distance the object rolls by the time it took. This will give you the average speed. Velocity = Distance / Time
Confidence Assessment: 3
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Question: If an object travels 40 centimeters down an incline in 5 seconds then what is its average velocity on the incline? Explain how your answer is connected to your experience.
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Your solution: The object would travel at 8cm/second. This is because it traveled 40 cm in 5 seconds. 40 / 5 = 8.
Confidence Assessment: 3
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Question: If the same object requires 3 second to reach the halfway point, what is its average velocity on the first half of the incline and what is its average velocity on the second half?
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Your solution: If it took 3 seconds to reach the halfway point, that means it took 3 seconds to go 20 cm. 20 divided by 3 is equal to 6.67 cm / second. This would mean that the average velocity on the second half is 10 cm/ second. The second half is also 20 cm long and it would only take the remaining 2 seconds to clear this. That means 20/2 = 10cm/second.
Confidence Assessment: 2, This is an interesting one considering that 10cm/second and 6.67 cm/second do not average out to 8cm/second. However, the math seems like it should add up.
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Question: `qAccording to the results of your introductory pendulum experiment, do you think doubling the length of the pendulum will result in half the frequency (frequency can be thought of as the number of cycles per minute), more than half or less than half?
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Your solution: I'm not sure if the frequency will double exactly, but it would increase the distance the pendulum would have to swing meaning that the frequency will decrease.
Confidence Assessment: 2. I don't know exactly what the distance:time ratio is for the path of a pendulum.
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Question: `qNote that for a graph of y vs. x, a point on the x axis has y coordinate zero and a point on the y axis has x coordinate zero. In your own words explain why this is so.
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Your solution: If the x coordinate was greater than zero, then that would be the distance away from the y-axis and vice versa.
Confidence Assessment: 3
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Question: `qOn a graph of frequency vs. pendulum length (where frequency is on the vertical axis and length on the horizontal), what would it mean for the graph to intersect the vertical axis (i.e., what would it mean, in terms of the pendulum and its behavior, if the line or curve representing frequency vs. length goes through the vertical axis)? What would this tell you about the length and frequency of the pendulum?
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Your solution: If the graph were to intersect the vertical y-axis, that would mean the length of the the pendulum would be negative and the graph would go into the second or third quadrant.
Confidence Assessment: 1, I'm not sure as to what the question asks or if it even makes sense.
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Question: `qOn a graph of frequency vs. pendulum length, what would it mean for the graph to intersect the horizontal axis (i.e., what would it mean, in terms of the pendulum and its behavior, if the line or curve representing frequency vs. length goes through the horizontal axis)? What would this tell you about the length and frequency of the pendulum?
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Your solution: This would mean that the frequency becomes negative if it were to intersect the x-axis.
Confidence Assessment: 3
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Question: `qIf a ball rolls down between two points with an average velocity of 6 cm / sec, and if it takes 5 sec between the points, then how far apart are the points?
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Your solution: The points would be 30 cm apart. This is because it takes 5 seconds and 6cm/second. 5*6 = 30.
Confidence Assessment: 3
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Given Solution:
`aOn the average the ball moves 6 centimeters every second, so in 5 seconds it will move 30 cm.
The formal calculation goes like this:
• We know that vAve = `ds / `dt, where vAve is ave velocity, `ds is displacement and `dt is the time interval.
• It follows by algebraic rearrangement that `ds = vAve * `dt.
• We are told that vAve = 6 cm / sec and `dt = 5 sec. It therefore follows that
• `ds = 6 cm / sec * 5 sec = 30 (cm / sec) * sec = 30 cm.
The details of the algebraic rearrangement are as follows:
• vAve = `ds / `dt. We multiply both sides of the equation by `dt:
• vAve * `dt = `ds / `dt * `dt. We simplify to obtain
• vAve * `dt = `ds, which we then write as{}`ds = vAve *`dt
Be sure to address anything you do not fully understand in your self-critique.
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Question: `qYou were asked to read the text and some of the problems at the end of the section. Tell your instructor about something in the text you understood up to a point but didn't understand fully. Explain what you did understand, and ask the best question you can about what you didn't understand.
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Your solution: I understood the Chapter1 text since it seemed like a review from previous math classes and physics classes I've taken in the past. I just got done studying vector geometry so a lot of it was review.
Confidence Assessment: 3
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Question: `qTell your instructor about something in the problems you understand up to a point but don't fully understand. Explain what you did understand, and ask the best question you can about what you didn't understand.
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Your solution: I haven't had any significant problems with the questions yet.
SOME COMMON QUESTIONS:
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QUESTION: I didn’t understand how to calculate uncertainty for a number such as 1.34. When given examples we had problems such as 1.34 ±0.5 and with that we had a formula (0.5/1.34)*100. So I do not understand how to compute uncertainty when no estimated uncertainty is given.
INSTRUCTOR RESPONSE:
The +- number is the uncertainty in the measurement.
The percent uncertainty is the uncertainty, expressed as a percent of the number being observed.
So the question in this case is simply, 'what percent of 1.34 is 0.5?'.
• 0.5 / 1.34 = .037, approximately. So 0.5 is .037 of 1.34.
• .037 is the same as 3.7%.
I recommend understanding the principles of ratio, proportion and percent as opposed to using a formula. These principles are part of the standard school curriculum, though it does not appear that these concepts have been well mastered by the majority of students who have completed the curriculum. However most students who have the prerequisites for this course do fine with these ideas, after a little review. It will in the long run save you time to do so.
There are numerous Web resources available for understanding these concepts. You should check out these resources and let me know if you have questions.
Please feel free to include additional comments or questions:
your thinking on these questions is very good