Query ast 1

course Phy 202

्z퉲Kassignment #001

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001.

Physics II

07-13-2007

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12:12:40

Most queries in this course will ask you questions about class notes,

readings, text problems and experiments. Since the first two assignments

have been experiments, the first two queries are related to the

experiments. 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.

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RESPONSE -->

ok

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12:12:59

Suppose you measure the length of a pencil. You use both a triply-reduced

ruler and the original ruler itself, and you make your measurements

accurate to the smallest mark on each. You then multiply the reading on

the triply-reduced ruler by the appropriate scale factor. Which result is

likely to be closer to the actual length of the pencil? What factors do

you have to consider in order to answer this question and how do they

weigh into your final answer?

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RESPONSE -->

I think that the measured obtained by using the original ruler will be

more accurate because even using the triply-reduced ruler will not be

nearly as accurate, I would think, due to the optical distortion.

Considering, that distortion, the scaling doesn't really matter because

the markings are not accurate enough. The original ruler doesn't need to

be scaled nor does it have the optical distortion as the triply-reduced

one does from the copying process.

confidence assessment: 2

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12:13:15

Answer the same question as before, except assume that the triply-reduced

ruler has no optical distortion and you know the scale factor accurate to

4 significant figures.

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RESPONSE -->

Ok, in this situation. I would assume that either ruler would suffice. I

mean I'd still use the original to cut out having to do the work with the

scaling, but seeing as how the scale factor is accurate to 4 sig figs, I

don't see why it wouldn't be acceptable to use and rely on its accuracy.

confidence assessment: 2

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12:14:44

Suppose you are to measure the length of a rubber band whose original

length is around 10 cm, measuring once while the rubber band supports the

weight of a small apple and again when it supports the weight of two small

apples. You are asked to report as accurately as possible the difference

in the two lengths, which is somewhere between 1 cm and 2 cm. You have

available the singly-reduced copy and the triply-reduced copy, and your

data from the optical distortion experiment. Which ruler will be likely

to give you the more accurate difference in the lengths? Explain what

factors you considered and how they influence your final answer.

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RESPONSE -->

I would say the singly-reduced ruler because the triply-reduced ruler

seems to have triple the distortion. If we are supposed to be as accurate

as possibly I would bank on the ruler who has been manipulated the least.

The singly-reduced ruler's measurements most closely coincide with a

regular ruler. And the is more room for measurement error if we use the

triply reduced ruler because we'd have to multiply by the scale factor

which may not be accurate either.

confidence assessment: 2

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12:23:04

Later in the course you will observe how the depth of water in a uniform

cylinder changes as a function of time, when water flows from a hole near

the bottom of the cylinder. Suppose these measurements are made by taping

a triply-reduced ruler to the side of a transparent cylinder, and

observing the depth of the water at regular 3-second intervals. {}{}The

resulting data would consist of a table of water depth vs. clock times,

with clock times 0, 3, 6, 9, 12, ... seconds. As depth decreases the

water flows from the hole more and more slowly, so the depth changes less

and less quickly with respect to clock time. {}{}Experimental

uncertainties would occur due to the optical distortion of the copied

rulers, due to the the spacing between marks on the rulers, due to

limitations on your ability to read the ruler (your eyes are only so

good), due to timing errors, and due to other possible factors.

{}{}Suppose that depth changes vary from 5 cm to 2 cm over the first six

3-second intervals. {}{}Assume also that the timing was very precise, so

that there were no significant uncertainties due to timing. Based on what

you have learned in experiments done in Assignments 0 and 1, without doing

extensive mathematical analysis, estimate how much uncertainty would be

expected in the observed depths, and briefly explain the basis for your

estimates. Speculate also on how much uncertainty would result in

first-difference calculations done with the depth vs. clock time data, and

how much in second-difference calculations. {}{}How would these

uncertainties affect a graph of first difference vs. midpoint clock time,

and on a graph of second difference vs. midpoint clock time? {}How

reliably do you think the first-difference graph would predict the actual

behavior of the first difference? {}Answer the same for the

second-difference graph. {}{}What do you think the first difference tells

you about the system? What about the second difference?

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RESPONSE -->

I think there would be a lot of uncertainty. I don't know a numerical

guestimate of how much, but since I know that the triply-reduced ruler is

very off and the distortion seems to increase as you continue measuring.

with each measurement taken as the water depth decreases, the more

inaccurate your reading will be.

The first difference calculations, I don't think, will add on that much

more uncertainty, but the graph of the results will more than likely show

those uncertainties obtained by the ruler. The second-difference

calculations will magnify the uncertainties and will probably magnify them

to a point where the trend on the graph isn't nearly as noticable as it

was at first, just like in the experiment we did previously. Each time the

difference quotient is done, the more magnified the uncertainties become.

I think the first difference graph will predict the actual behavior

pretty well because the uncertainties shouldn't be as evident yet.

However, for the second difference, I do not expect the graph to be

reliable at all. The uncertainties will prevent a clear trend from being

evident.

The first difference will tell us the velocity and the second will tell us

the acceleration.

confidence assessment: 2

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12:25:25

Suppose the actual second-difference behavior of the depth vs. clock time

is in fact linear. How nearly do you think you could estimate the slope

of that graph from data taken as indicated above (e.g., within 1% of the

correct slope, within 10%, within 30%, or would no slope be apparent in

the second-difference graph)? Again no extensive analysis is expected,

but give a brief synopsis of how you considered various effects in

arriving at your estimate.

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RESPONSE -->

I don't think there will be an apparent trend for the second difference

graph.

If there happened to be one, however, I would say within 30% because there

is so much uncertainty. If the uncertainties were reduced by 1/3 like they

were in the previous experiment I'd be able to say 10%.

confidence assessment: 2

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"

Your answers to these questions are very good. You might find later in the course that you will think more about these issues and some of your conclusions might change, but everything you say here constitutes a reasonable hypothesis.

The main thing I look for here is clear thinking, good expression and reasonable conclusions. Your answers provide all of this.