1 Skills, Methods, and the Nature of Physics - BC Science Physics 11

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Dimensional Analysis �� Figure 1.4.2 A ruler with both imperial and metric scales shows that 1 inch = 2.54 cm. The International Bureau of Weights and Measures (BIPM) was established in Sévres, France, in 1825. The BIPM has governed the metric system ever since. Since 1960, the metric system has become the International System of Units, known as the SI system. SI is from the French Système International. The SI system’s use and acceptance has grown to the point that only three countries in the entire world have not adopted it: Burma, Liberia, and the United States (Figure 1.4.1). �� Figure 1.4.1 Map of the world showing countries that have adopted the SI/metric system Dimensional analysis is a method that allows you to easily solve problems by converting from one unit to another through the use of conversion factors. The dimensional analysis method is sometimes called the factor label method. It may occasionally be referred to as the use of unitary rates. A conversion factor is a fraction or factor written so that the denominator and numerator are equivalent values with different units. One of the most useful conversion factors allows the user to convert from the metric to the imperial system and vice versa. Since 1 inch is exactly the same length as 2.54 cm, the factor may be expressed as: 1 inch 2.54 cm 20 Chapter 1 Skills, Methods, and the Nature of Physics © Edvantage Interactive 2012 ISBN 978-0-9864778-3-6 or �� 2.54 cm 1 inch These two lengths are identical so multiplication of a given length by the conversion factor will not change the length. It will simply express it in a different unit (Figure 1.4.2). Now if you wish to determine how many centimetres are in a yard, you have two things to consider. First, which of the two forms of the conversion factor will allow you to cancel the imperial unit, converting it to a metric unit? Second, what other conversion factors will you need to complete the task?
Converting Within the Metric System Table 1.4.1 SI Prefixes Prefix Symbol 10 n yotta Y 1024 zetta Z 1021 exa E 1018 peta P 1015 tera T 1012 giga G 109 mega M 106 kilo k 103 hecto h 102 deca da 101 deci d 10-1 centi c 10 –2 milli m 10 –3 micro µ 10 –6 nano n 10 –9 pico p 10 –12 femto f 10 –15 atto a 10 –18 zepto z 10 –21 yocto y 10 –24 Assuming you know, or can access, these equivalencies: 1 yard = 3 feet and 1 foot = 12 inches, your approach would be as follows: 1.00 yards × 3 feet 1 yard × 12 inches 1 foot © Edvantage Interactive 2012 ISBN 978-0-9864778-3-6 Chapter 1 Skills, Methods, and the Nature of Physics 21 × 2.54 cm 1 inch = 91.4 cm Notice that as with the multiplication of any fractions, it is possible to cancel anything that appears in both the numerator and the denominator. We’ve simply followed a numerator-to-denominator pattern to convert yards to feet to inches to cm. The number of feet in a yard and inches in a foot are defined values. They are not things we measured. Thus they do not affect the number of significant digits in our answer. This will be the case for any conversion factor in which the numerator and denominator are in the same system (both metric or both imperial). Interestingly enough, the BIPM has indicated that 2.54 cm will be exactly 1 inch. So it is the only multiplesystem conversion factor that will not influence the number of significant digits in the answer to a calculation. As all three of the conversion factors we used are defined, only the original value of 1.00 yards influences the significant digits in our answer. Hence we round the answer to three sig digs. The metric system is based on powers of 10. The power of 10 is indicated by a simple prefix. Table 1.4.1 is a list of SI prefixes. Your teacher will indicate those that you need to commit to memory. You may wish to highlight them. Metric conversions require either one or two steps. You will recognize a onestep metric conversion by the presence of a base unit in the question. The common base units in the metric system are shown in Table 1.4.2. Table 1.4.2 Common Metric Base Units Measures Unit Name Symbol length metre m mass gram g volume litre L time second s One-step metric conversions involve a base unit (metres, litres, grams, or seconds) being converted to a prefixed unit or a prefixed unit being converted to a base unit. Two-step metric conversions require the use of two conversion factors. Two factors will be required any time there are two prefixed units in the question. In a two-step metric conversion, you must always convert to the base unit first.
Page 1 and 2: 1 Skills, Methods, and the Nature o
Page 3 and 4: Figure 1.1.1 Galileo (top) and Newt
Page 5 and 6: The Many Faces of Physics ��
Page 7 and 8: Figure 1.2.1 A recording timer that
Page 9 and 10: 1.3 Physics Essentials Warm Up What
Page 11 and 12: Figure 1.3.2 This kilogram mass was
Page 13 and 14: Combining Measurements Imagine that
Page 15 and 16: Multiplying or Dividing Measurement
Page 17 and 18: Quick Check 1. Write the following
Page 19: 1.4 Analysis of Units and Conversio
Page 23 and 24: Practice Problems 1.4.1 — One- an
Page 25 and 26: Sample Problem 1.4.3 — Use of Den
Page 27 and 28: Graphing ��
Page 29 and 30: Practice Problems 1.4.5 — Determi
Page 31 and 32: Investigation 1-4 Making a Pendulum
Page 33 and 34: 1.5 Vectors Warm Up Your teacher wi
Page 35 and 36: Adding Vectors Scalars and Vectors

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