# Length Mass and Density Lab Report

Table of Contents

1 – Introduction ……………………………………………........…. Page 3

2 – Theory ………………………………………………………...... Page 3

3 – Experimental Procedure and Results …...………………..…. Page 6

4 – Discussion ………………….……………………….....….…… Page 9

5 – Conclusion ………………………………………….....…….... Page 9

6 – Bibliography …………………………………………......… Page 10 1- Introduction

The purpose of this experiment is to learn how use a variety of tools that will aid in the gathering of data. This data is then used to calculate different measurements including, volume and density. The experiment will also further understanding of measurement errors using the data collected. 2 – Theory

Along with the use of tools for basic measurements this laboratory practice introduces the students to the use of significant figures and some error analysis. Some basic calculations of volume, area and density will be used too. 2.1 - Significant Figures and Error Analysis

Significant figures are the digits required to express a number to the same accuracy as the measurement it represents. There are several rules for counting significant figures; such as, the nonzero integers are always counted, zeroes can be leading, captive and trailing. Leading zeroes are any zeroes that come before the nonzero numbers. Captive zeroes are the zeroes that can be found between nonzero numbers. Trailing zeroes are the zeroes that would follow the nonzero numbers. Example of Leading Zeroes:

0.0045, or 4.5 x 10-3, this number has two significant numbers. Example of Captive Zeroes:

8.0015, this number has five significant numbers.

Examples of Trailing Zeroes:

2000 or 2 x 103, this number has only one significant figure; however, if it is written as 2000.0, this number would have five significant figures. Frequently, the result of an experiment will not be measured directly. Rather, it will be calculated from several measured physical quantities (each of which has a mean value and an error). What is the resulting error in the final result of such an experiment? For instance, what is the error in Z = A + B where A and B are two measured quantities with errors Δa and Δb respectively? It is useful to define at this point the definition of percent error: The percent error is the error in a measurement divided by the size of the measurement: %error of A = (Δa / A)*100 (1)

If the variables are independent then sometimes the error in one variable will happen to cancel out some of the error in the other and so, on the average, the error in Z will be less than the sum of the errors in its parts. A reasonable way to try to take this into account is to treat the perturbations in Z produced by perturbations in its parts as if they were "perpendicular" and added according to the Pythagorean theorem, ￼ (2)

Obs. With some limitations we can assume that ÄZ = Äa + Äb (for addition and subtraction). That is, if A = (100±3) and B = (6±4) then Z = (106±5) since￼. However, if Z = AB (or Z = A/B) then,

￼ (3)

The fractional error in Z is the square root of the sum of the squares of the fractional errors in its parts. (You should be able to verify that the result is the same for division as it is for multiplication.) For example, ￼

2.2 – Measurement Techniques

All measurements involving human and device interaction cause errors or deviation from the “true” values of the items that are measured; these are known errors in measurement. Some errors in reading equipment are avoidable, such as parallax; which can be caused by taking a measurement from either side of an instrument instead of facing directly in front of the device. ￼

Figure 1 – Parallax error in visual measurements.

There were also a couple of variations of the formula to find volume; which is how much three-dimensional space the object occupies, such as: solid, liquid, plasma, vacuum or theoretical object, often quantified numerically. The formulas...

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