Unit 1:Measurements

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Observational skills are of great benefit in everyday life and are extremely essential in science. Observations may be quantitative or qualitative Using one's finger,for instance to test the temperature of water represents a qualitative observation while measuring with a thermometer represents a quantitative one. Quantitative observations present more information than qualitative ones. Every measurement must specify a unit. To state that a person has a height of 2.3 is meaningless. We are left to ask,8.2 what?On the other hand to tell us that the person is 2.3m tell us the person is much above average height. Similarly, to say that a container has a volume of 2 is meaningless. Two what? On the other hand, stating thata soft drink container has a volume of 2 litres indicates tha fact that it has the size of a large sized soft drink container.

Measuring an object means comparing it to a selected unit(such as a metre)  and expressing it as a multiple or fraction of that unit(2 metres,1/2meter 1.3m etc).
Accuracy of a measurement refers to the discrepancy between the true or actual value and that obtained by measuring.
Precision refers to the agreement between repeated measures of the same quantity or object. To understand the agreement between accuracy and precison,suppoese you use a metre stick to measure the length of a table, and get these results:2.31 m,2.32 m ,2.30 m . The spread of the measures is only 0.02 m,which indicates good precision. If however the meter stick itself was not graduated correct and was actually 1.04 meters in lenght,then the marks on the stick would be further apart than they should be. Consequently although the measurements were precise they are not accurate because they do not represent the true value of the length of the table. Thus measurements can have high precision but low accuracy.

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Can meaurements have high accuracy but low precision?

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Self Assessment

We use units everyday,often without realising it In the statements that follow,you will find a awide variety of intersting facts but each is missing a crucial piece of information-the units. All the statements are meaningless untill you supply the appropriate units. On the basis of your experiences,try to find the appropriate units from the list provided. Units may be used more than once or not at all.

  1. The Nile is the longest river in Africa ,it is......long
  2. The temparature of the core of the earth is estimated to be 11,000......
  3. The dimensions of a proffesional football pitch is 100....by 50.......
  4. The world's tallest building is 1250.....high

Physical Quantities and their units

Fundamental Quantities and their Units:
There are 26 letters in the english alphabet,yet with these,it is possible to construct all the words in the english language. In a similar way,there are 7 "letters" in the "language of measurement" of which all units of scientific measurements are composed. These 7 "letters" are length,mass,time electric charge,temperature,amount and luminous intensity. They are known as the fundamental unitsbecause they cannot be expressed in a simpler fashion.
Derived units:
Derived units(quantities) on the other hand are composed of fundamental units(quantities). Velocity for instance is not a fundamental quantity because it can be expressed as a ratio of two other units (quantities),namely distance and time v=d/t. Because velocity can be derived from distance and time,it is known as a derived quantity. By contrast, distance and time cannot be expressed in any simpler terms. Acceration is considered to be a derived quantity because it can be expressed in terms of other quantities,namely, velocity and time.

Click here for the document containing the full table scientific units of measurement.
Dimensional analysis:

Applications to everyday Life

  • Astronomical distances:
    The star nearest the earth is Alpha Centauri,at a distance of 4 light years or the distance that light travels inyears time. Since light travels at299792km/s and there are 31,557,600 second in a year,Alpha Centauri is at a distance of 37.8 trillion miles from earth. Withought indirect measurement,there would be absolutely no way even short astronomical distances.
  • 'Subatomic particles:'
    Chemistry books for insatance report the mass of an electron as 9.1083 X 10(Power minus 28)grams. Since the finest balances are only sensitive in the microgram range,it is obvious that the subatomic particles must be measured by indirect means.
  • Circumfrence of the earth:

The first relatively accurate measurement of the earth 's circumfrence by was made indirectly by Eratostheneswas of Cyrene in the third Century BC. Eratosthenes noticed that the noon sun refelected off the water in a deep wel in the city of Syne in southern Egypt on the longest day of the year(Summer),indicating that the well was on a direct line between the Sun and the earth's center. During a subsquent year,he was in Alexandria in nothern Egypt in summer and noted that the sun was south of the vertical by an angle equal to approximately 1/50th of a full circle. Because of the great distance to the sun,he assumed that the sun's rays were parallel on striking the earth and that the difference in the angle between the two cities resulted from the difference in the angle between the center of the earth and the two cities. He therefor measured the distance between Alexandria and Syene and multiplied by 50 to calculate the ciucumfrence of the earth. His indirect measurement was within 15% of the currently accepted value,which is 40,075km

Indirect measurements

There are many things that are very difficult to measure or impossible to measure directly. For example,no one can measure an electron directly,yet science text books report it has a mass of 9.1083 X 10 (POWER 28 MINUS) grams. No one was present when red sea scrolls were being used but scientists tell us they are over 1000 years old. No one can see X-rays yet we know they have wavelength of the order of 10 power minus 10. Although it may be impossible or impractical to measure many quantities directly,it is possible to do so indirectly. In this section,we will use the principle of similar figures and similar ratios to learn how we can measure things such as those mentioned
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An understanding of ratios and scaling is requisite to an understanding of many phenomena in the physical and biological world,yet few textbooks give much attention to this issue. For example many textbooks will state that metabolic rate of a mammal increases as its body weight decreases but few explain that this rate is a necessary consequence because the ratio of the smaller animal's surface area to volume is much greater than a larger animal's. Thus the animal loses heat rapidily and must have a high metabolic rate to maintain its proper body temperature. Although most biological and physical structures are not cubic or spherical,the basic principles drawn from such simple geometric solids apply to irregularly shaped objects as well. The surface area of an object increases as a square,and its volume as a cube of its linear dimensions. Thus,the surface-area -to -volume ratio is aways greater than in a small scale object of the same shape.

Length of edge Surface area Volume Surface area/Volume Volume/Surface area
0.0cm .......cm2 .......cm3 ...............1/cm .............cm
0.1 .......cm2 .......cm3 ...............1/cm .............cm
1cm .......cm2 .......cm3 ...............1/cm .............cm
10cm .......cm2 .......cm3 ...............1/cm .............cm
100cm .......cm2 .......cm3 ...............1/cm .............cm

Here we are to investigate a cube to see how changes in a linear dimension affect is surface area and volume. For each cube,compute both the surface area and and the volume and write your answers in a table. Then use these results to compute the ratio of surface area to volume and the ratio of volume to surface area. Plot these on a graph.


(1) As the cube gets smaller,does the ratio of surface area to volume increase or decrease? As the cube grows larger does the ratio of surface area to volume increase or decrease?

(2) Phytoplankton are very small and often contain numerous spines. Explain how these features help keep them near the surface.

(3) In animals,heat production is proportional to mass. Heat loss is proportional to surface area. If all factors are equal,will a baby or adult be more susceptible to getting chilled?

(4) If the amount of heat lost through the skin of an animal is proportional to its surface area,what might you include about the relative heat loss of a very small animal to a very large animal? Which animal would find it easier to keep warm in cold weather,and which animal would find it easier to to keep cool in hot weather? Breathing: The alveoli (air sacs) of lungs must have appropriate radii to insure maximum diffusion of oxygen into the blood. If they were too large,their surface area to volume ratio would be too low and there would be insufficient diffusion of gases because of reduced surface contact between the tissues and the air. By contrast if they were too small,the cross-section area of alveoli and the brochioles would be too small and would restrict gas flow.

Applications to everyday life

Emphysema:Emphysema , a condition that often accompanies smoking,results in a breakdown of the walls between the alveoli and the lungs. In emphysema,a few large air sacs exist where many small air sacs previously existed,dramatically decreasing the lungs' surface area to volume ratio and thereby reducing the contact surface between blood vessels and air. As a result,people with emphysema can breath deeply,yet assimilate litlle oxygen.

Powdered milk: When you pour powdered milk into a container of water,it forms a hep on the bottom. By stirring the solution, you increase the surface area to volume ratio of the powder. Where particles were once embedded in a heap,they now come in contact with the water and dissolve. A cube of sugar will dissolve more slowly than an equal amount powdered sugar because,it has a low surface area to volume ratio.

Evaporation: The surface area to volume ration of of a liquid is critical in determining how fast it will evaporate. Water in a cup,takes much longer time to evaporate than the same amount of water spread out on on a table. The surface area to volume ratio in the glass is relatively low,while the it is high with the spilled liquid.

Animal behavior: Smaller animals have a large surface area to volume ratio and therefore lose proportionately more heat energy to the surrounding environment than larger animals do. To compensate,small homeotherms (warm-blooded animals) such as a humming bird or shrew consume relatively more food than larger animals such as a hawk or bear. The humming bird,for example, may consume an amount of food equivalent of its entire weight in one day,while a bear may do the same over a period of one or two months.

Elephant ears: The surface area to volume ratio decreases as the scale of an organism increases. Consequently larger organisms have more difficulty dissipating heat energy than smaller animals and are more prone to overheating.The larger ears of elephants dramatically increase the surface area of the elephant,allowing it to dissipate heat on warm days.