Home Page Textbooks Physics: Principles and Problems Section 1.2: Measurement

Physics: Principles and Problems

9th Edition

Elliott, Haase, Harper, Herzog, Margaret Zorn, Nelson, Schuler, Zitzewitz

ISBN: 9780078458132

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Section 1.2: Measurement

Exercise 18

Solution 1

Solution 2

Step 1

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The reason why some rulers doesn’t start their counts, is that as the ruler is used more and more the edges could suffer some damage leading to the deformation of zero mark in the ruler, hence affecting the user to precisely define the position of the zero mark, thus making the user is reading inaccurate.

To clarify more, the useق for example wants to measure the length of a pen cap which is 3 cm long $textit{but underline{textbf{he can’t}} measure the pen cap length textbf{accurately}}$ because the end of his ruler is worn out, thus $textit{measuring the pen cap length textbf{with a value different from the actual value}}$.

Thus a tiny space is left before zero count to make it less probable that the accuracy of the ruler gets affected due to the worn out or faded zero mark, thus enhancing the accuracy of measurement as overall.

Result

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Overall, It increases the accuracy of the ruler. Where it makes less probable that the zero mark would be deformed or worn out hence decreasing the inaccuracy of measurement.

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The ruler may be damaged during use. If the mark was at the very end, it would be much easier to erase, which would reduce the accuracy of the measurement. By moving the zero mark, this problem is reduced and the accuracy is preserved.

Result

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It is done to protect markings

Exercise 19

Solution 1

Solution 2

Step 1

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A micrometer can measure lengths up to the nearest 0.01 mm. Since the micrometer can measure values in smaller steps, we can say that the micrometer is **more precise** as compared to the meter stick.

However, since the micrometer is bent, it means that it cannot measure the actual lengths properly. Hence, we can say that the micrometer is **less accurate** as compared to the meter stick.

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The micrometer would be *more precise* because it is capable of measuring to a much smaller and exact degree.

However, this micrometer will *not be more accurate* because it is bent and it will be off in the precise measurement it provides compared to the meter stick.

Exercise 20

Solution 1

Solution 2

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Parallax, which is a measurement difference in what you see based on your position, does not affect the precision of measurements you make. Precision is based completely on the tool that you’re using, NOT how you read it.

Result

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No, it does not.

Step 1

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Parallax is generally defined as the difference in observation when an object is viewed from different positions. When trying to measure the length or width of an object, its perceived size does not change based on position. Thus, if we have a measuring device like a ruler with a certain precision of measurement, an object viewed in parallax will still have the same size and will retain the precision of the measurement.

Exercise 21

Solution 1

Solution 2

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The height given to you is 182 cm, which is accurate only to the nearest centimeter. The precision of measurement is half of smallest possible division. Thus, the height is 182 cm, but it can actually be 0.5 cm less than or greater than that.

Result

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It means he’s between 181.5 and 182.5 cm.

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The measured height is 182 cm. When measuring using a certain instrument, there will always be a precision level. In this case, your friend is certain up to the nearest 1 cm. If we consider a measuring instrument with a precision of 1 cm, it means that the readings can be anywhere around 0.5 cm less than up to 0.5 cm greater than 182 cm, or from 181.5 cm to 182.5 cm to account for the precision error.

Exercise 22

Step 1

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$textbf{underline{textit{Solution}}}$

Step 2

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The volume of the box knowing the length, width and the height of the box is given by the following formula
[ V = l times wtimes h tag{1}]

enumerate[bfseries (a)]
item Knowing that the length of the box is 18.1 cm, and the width of the box is 19.2 cm, and the height of the box is 20.3 cm, thus using equation (1) the volume of the box is
begin{align*}
V&= 18.1 times 19.2 times 20.3 \
&= 7054.66 ~ rm{cm}^3
intertext{But, since the measured lengths have only 3 significant number, hence the product of these 3 numbers must have only 3 significant number, therefor the volume of the box rounded to 3 significant figures is}
&= fbox{$7050 ~ rm{cm}^3$}
end{align*}

Step 3

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enumerate[bfseries (b)]
item The precision of the length is to the nearest 0.1 cm or 1 mm, while the precision of the volume is to the nearest 10 cm$^3$ where the volume from part (b) is rounded to 3 significant figures thus it is rounded to the nearest 10 cm$^3$.

Step 4

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enumerate[bfseries (c)]
item The height of 12 stack of boxes knowing that one box is 20.3 cm height is
begin{align*}
text{Tall} &= 12 times 20.3 \
&= fbox{$243.6 ~ rm{cm}$}
intertext{textbf{underline{textit{note:}}}: It is like adding 20.3 cm 12 times, thus the final answer must have at least one digit after the decimal thus the final answer is not rounded as it only have 1 significant figures after the digit.}
end{align*}

Step 5

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enumerate[bfseries (d)]
item The precision of the measurement of one box is length is to the nearest 1 mm, the precision of the height of the 12 box is the same as 1 mm, where in addition the final answer must have the same number of significant figures after the digit as before therefor in both cases they have 1 significant figures after the digit, therefor both of measurements are to the nearest mm.

Result

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enumerate[bfseries (a)]
item 7050 cm$^3$.
item To the nearest 1 mm, and to the nearest 10 cm$^3$.
item 243.6 cm.
item Both to the nearest 1 mm.

Exercise 23

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The time was measured using a clock with a precision of 0.1s, but the average time computed was 65.414s. However, the average time computation is not supposed to exceed the possible precision of the clock! The precision of the result should be limited to the least precise measurement in the experiment.

If the average time was 65.4s, the result would be more acceptable.

Result

2 of 2

Not much confidence.

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Section 1.2: Measurement

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