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course Phy 121

9/2 1:30 pm

ph1 query 0Most 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:

Are the discrepancies in timing on the order of 0.1 second, 0.01 second, or 0.001 second?

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The discrepancies are on the order of 0.1 second. The are all uniform at the order of 1 second. In this case all are 2. They vary at the 0.1 second level.

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To what extent do you think the discrepancies in the time intervals could be explained by each of the following:

· The lack of precision of the TIMER program. Base your answer on the precision of the TIMER program as you have experienced it. What percent of the discrepancies in timing do you think are due to this factor, and why do you think so?

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Based on the work we did with the timer, it was accurate to 0.01 so the percentage here would be relatively small to negligble. I would say 1%

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· The uncertainty associated with human triggering (uncertainty associated with an actual human finger on a computer mouse). What percent of the discrepancies in timing do you think are due to this factor, and why do you think so?

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I think this uncertainty would account for a large percentage, say 40%. I base this on my own experiences with timing. These differences are so small and human reflexes can only be but so fast and even when they are fast, they are not consistent.

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· Actual differences in the time required for the object to travel the same distance. What percent of the discrepancies in timing do you think are due to this factor, and why do you think so?

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I'll assign 10% to the the actual time. Things like uneven smoothness of the marble and variations in grain on the wood could depending on the way the marble travels could have slight effects on the speed. Since the experiment is not conducted in a vaccuum, I would assume things like a slight breeze or movement of air could affect the speed. Maybe even changes in humidity. I know humidity can really affect wood, so a slight variation in the swelling of the wooden incline could have a slight effect on the speed of the marble.

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· Differences in positioning the object prior to release. What percent of the discrepancies in timing do you think are due to this factor, and why do you think so?

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I'll asign 9% here. I think this difference is closely tied to the considerations above because the postioning of the marble will determine its exact course and what grains it will encounter in the wooden incline. I've been doing a lot of wood-working lately, so maybe grain is on my mind.

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· Human uncertainty in observing exactly when the object reached the end of the incline. What percent of the discrepancies in timing do you think are due to this factor, and why do you think so?

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Like the trigger, I would assign 40% of the descrepancy here. It is very difficult to determine when exactly a fast moving object crosses a line. This one is very much tied to the human trigger discrepancy. A decision must be made as to when the marble crosses the line and then the brain must send a message to the finger to actually click the mouse.

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Question: If you had carefully timed the ball and obtained the results given above, how confident would you be that the mean of those five intervals was within 0.1 seconds of the actual mean? (Note that the mean of the given intervals is 2.43 seconds, as rounded to three significant figures)? Briefly explain your thinking.

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I think you could be very confident since we have three significant figures in the mean of 2.43 and we are only asking for 2 significant figures in our 0.1 seconds concern.

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How confident would you be that the 2.43 second mean is within .01 second? Briefly explain your thinking.

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I think you could be very confident again to the .01 second level since you have three significant figures and the .01 still falls in that range.

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How confident would you be that the 2.43 second mean is within .03 second?

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This question forces me to think about my last answer. If I was correctly confident in .01 why bother asking about .03? However, for now I will stick with my original answer, and say that since we can be confident at the .01 level, we can be confident at the .03 level.

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There's a different level of confidence with .03 than with .01. Of course if you're 100% confident that you're within .01, then you're 100% confident of being within .03.

It would be unusual for human-triggered timing to be 100% confident at either the .01 second level or the .03-second level.

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At what level do you think you can be confident of the various degrees of uncertainty?

Do you think you could be 90% confident that the 2.43 second mean is within 0.1 second of the actual mean?

Do you think you could be 90% confident that the 2.43 second mean is within 0.01 second of the actual mean?

Do you think you could be 90% confident that the 2.43 second mean is within 0.03 second of the actual mean?

Give your three answers and briefly explain your thinking:

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I think you could be 90% confident at all the above levels. the 2.43 and all the times used to arrive at 2.43 were determined to 3 significant figures. That gets you the accuracy required in all three questions. 90% or more confident on all three.

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I doubt that 90% certainty is possible for a human-triggered timer at the .01 second uncertainty.

0.1 second, certainly. 0.3 seconds perhaps.

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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.

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The more accurate timer is the only way to address this one.

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· The uncertain precision of human triggering (uncertainty associated with an actual human finger on a computer mouse)

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Practice might improve this one, but knowing myself, I don't think I'd improve very much.

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· Actual differences in the time required for the object to travel the same distance.

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Getting a very uniform surface, perhaps a synthetic surface might help here. Sealing, and keep ing the room at a constant environment might help. A more precision oriented marble could help too.

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· Differences in positioning the object prior to release.

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Practice positioning could help, but I don't know the size of the incline and how easy it is to tell exaxt position.

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· Human uncertainty in observing exactly when the object reached the end of the incline.

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Practice might help here as well. The use of a camera with a view of the clock in the same image would help. Then a frame by frame analysis could be used to improve accuracy.

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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:

The average speed is determined by the distance travelled divided by the time required.

confidence rating #$&*: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 average velocity is found by dividing 40 cm by 5 seconds to get 8cm/s. I'm not sure how this is connected to my experience other than I've been experiencing average velocities all of my life. If I travel 50 miles in my car in 1 hour than my average velocity would be 50 mph (althoughI suppose I would need to be travelling in a straight line for this to be accurate)

confidence rating #$&*: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:

The average velocity on the first half is 20cm divided by 3 seconds or 6.67 cm/s.

The average velocity on the second half is 20 cm divided by 2 seconds or 10 cm/s.

confidence rating #$&*:3

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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:

Doubling the length will result in more than half the frequency. From my results, doubling from 7 to 14 cm gave me a corresponding 108 and 72 cycles respectively. 72/108 = .667, well above half.

Similarly, doubling 14 to 28 cm corresponds to 72 and 54 cycles respectively. 54/72 = .75, again well above half.

confidence rating #$&*:3

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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:

This is actually something that trips me up on occassion. The y coordinate is a measure of the distance from the x-axis and the x coordinate is the measure of the distance from the y axis. This is somewhat counter-inutitve so therein lies the tripping point.

Trip or not, since y is measured in distance from the x-axis, if the point is sitting on the x-axis it is zero units of distance from the the x axis and therefore has a y coordinate of zero.

Same way for the the x. X is measured in distance from the y-axis, if the point is sitting on the y-axis it is zero units of distance from the the y axis and therefore has an x coordinate of zero.

confidence rating #$&*:2 (since this often trips me up)

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As with a lot of other things most of us have to be careful about this.

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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:

The distance from the vertical axis is the length of the pendulum (since the distance from the vertical axis is what we measure on the horizantal axis - again this is something that can muddle the mind a bit) For something to cross the vertical axis would mean we were measuring something with a negative x-coordinate. This would mean something had a negative length, which the the realm of our experiment is impossible.

Therefore having the graph of actual date cross the vertical axis would mean that we made an error.

confidence rating #$&*:2

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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:

Similar to the answer above, this would mean we came up with a negative frequency or something that happened less than zero times. This again would lead us to believe we had made an error in graphing.

confidence rating #$&*:2

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Question: `qIf a ball rolls 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:

At 6 cm for every second we multiply this by 5 sec to get 30 cm between the two points.

confidence rating #$&*: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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Your solution:

I fully understand this, although I would not go through all of the steps above to get my answer.

confidence rating #$&*:3

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Nobody in their right mind would, but everyone should be able to do so, as it does become necessary on more complex problems to go through every detail very carefully.

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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 suppose what I don't understand at this point is the actual order of events I am supposed to be following in this assignment. I understood from the table of assignments that what I am doing now is supposed to come before anything else in the assignment, but now I'm asked to address something later in the assignment.

??? Do I have the order of events incorrect???

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This document should be the Query, which comes at the end of the assignment. However it does appear to be out of order.

This won't usually be a problem. I'll have to check into how this question got into this document (my doing, in any case).

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Excellent work, but be sure to see my notes about levels of certainty.

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