PHY 143 – Physics For Engineering I
CHAPTER 1 – PHYSICS & MEASUREMENT 1 hour (Units, Fundamental Quantities, Derived Quantities, Prefixes, Significant Figure, Conversion of Units
1.0 OBJECTIVES After studying this chapter, you should: • • • • • •
Know the differences between Base & Derived Quantities Know & be familiar with the SI Prefix Know how to apply the significant figures Able to solve any question involves conversion of unit without use the information on the top cover of calculator Able to make a conversion of any units given by using simple & common method Boost physics skills in problem solving process
1.1 UNITS - A unit is a scale with which a dimension is measured. - A standard system of units based on the metric system known as the International System or SI Unit is used where each basic quantity is assigned with a particular basic unit as shown in Table 1.1 below. Table 1.1 – Fundamental Quantities and Their Units Quantity Length Time Mass Temperature Electric current
SI Unit Meter Seconds Kilogram Kelvin Ampere
Abbreviation m s kg K A
1.2 FUNDAMENTAL QUANTITY - A fundamental quantity (physics quantity) is a quantity that can be measured, such as time, length, volume and temperature. -
There are two types of physical quantity: (1) Basic quantities - The basic of a physical measurement - Quantities that are “stand-alone”, not a combination of any other quantities
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PHY 143 – Physics For Engineering I
- each basic quantity has its own unit of measurement - time, length, mass, temperature and electricity.
(2) Derived quantities - Combination of more than two base quantities; multiply ± division - obtained & expressed in terms of basic quantities - density, area and acceleration. - SI Unit for derived quantities:
Example 1
Speed Time Length/Time Length meter m = = = = 2 = ms − 2 2 Time second x second s Time
Acceleration =
Example 2
Mass Mass = Volume Area × Length kg Mass Mass = = = 3 = kgm −3 2 3 m Length × Length Length
Density =
1.3 SI PREFIXES - In the metric system, larger or smaller units for the same physical quantity are related to the fundamental units by multiples of 10 or 1/10. The names of these units are derived by adding a prefix to the unit of the physical quantity, known as SI Prefix - SI Prefixes is an International System of prefixes - defined as name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple @ submultiples - Used:
to indicate power of ten factors to simplify pronunciation to form decimal multiples & submultiples of SI units to reduce the quantity of zeroes in numerical equivalencies.
The following Table 1.2 lists the standard SI prefixes with their meaning and abbreviation.
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PHY 143 – Physics For Engineering I
Table 1.2 – Prefixes for powers of ten Power of ten 10-18 10-15 10-12 10-9 10-6 10-3 10-2 103 106 109 1012 1015 1018
Prefix Atto Femto Pico Nano Micro Mili Centi Kilo Mega Giga Tera Peta Exa
Abbreviation a f p n µ m c k M G T P E
For example, the prefix “kilo” always means a unit larger by a factor of 1000; thus 1 kilometer = 1 km = 103 meters = 103 m , 1 kilogram = 1 kg = 103 grams = 103 g
1.4 SIGNIFICANT FIGURE - The precision of a measured value of a physical quantity is reflected in the number of the significant figure (or significant digit) used in stating the value. A significant figure is a digit in a number, except the leading zeros are not significant figures and trailing zeros are significant figures only if so specified. For example, Given the fastest timing in women’s 100 meter race is 10.49 s. Suppose you had been asked to report the time in minutes. By using a calculator, you might report the following by copying all the digits on your display as:
1 min 10.49s = (10.49s ) = 0.174833333 min 60s - No matter how precise the measuring tool is, all measured quantities have uncertainties associated with them. - We should have rounded the answer to the number of significant figure as the origin value had. The given time of 10.49 s consists of four significant figures. So, in minutes, the value should rewrite as 0.1748 min, consists four significant figures. * Final results of calculations are often rounded to match the least number of significant figures in the given data and should not be confused with decimal places.
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PHY 143 – Physics For Engineering I
- In calculations with very large or very small numbers, we can show significant numbers much more easily by using powers-of-ten notation, sometimes called scientific notation. In this form, the usual practice is to express the quantity as a number between 1 to 10 multiplied by the appropriate power of ten.
Example 3 The distance from the earth to the sun is about 149,000,000,000 m. Rewrite the value in powers-of-ten notation with 3 significant figures.
149,000,00,000 m = 1.49 × 1011 m HOMEWORK 1.1 Determine the number of significant figures in each of the following numbers: 1. 27 m 2. 0.00342987 s 3. -1.97050 x 10-11 C 4. 5280 ft / mi 5. 35.6 mm 6. 0.1748 min 7. 10.49 m 8. 20900000000 ft 9. 0.10490 mm 10. 2.50 x 10 -2 kJ
Understanding physics
1.5 CONVERSION OF UNITS - One system of unit to another @ One prefix to another - Single unit @ Multiple unit - Power of 1 @ Power of n - Same physical quantities !!! - Simple & easy method of rational no !!! - Conversion Factor !!! Conversion Factor [CF] = numerical factor used to multiply or divide a quantity, expressed in one set of units - Method: Write in the form of a ratio (rational number) - mathematical operation Apply CF The unit (CF) located at the side that opposite to the previous unit
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PHY 143 – Physics For Engineering I
‘cancelled off’ when multiplication is performed, leaving only the desired units to describe the answer
Table 1.3 – List of Conversion factors Quantity
Conversion Factor
Length
1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm 1 mi = 1609 m 1 ft = 0.3048 m 1 in = 2.54 cm 1 m = 39.37 in = 3.281 ft
Mass
1 kg = 1000 g 1 metric ton = 103 kg 1 slug = 14.59 kg
Time
1 h = 60 min 1 min = 60 s 1 h = 3600 s
Force
1 N = 0.2248 Ib = 105dyne
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PHY 143 – Physics For Engineering I
Example 4 Convert 2.438 m to feet
2.438m 1 ft = 1 0.3048m 2.438 ft = 0.3048 = 8 ft
Example 6 Convert 110 kmh-1 to ms-1
km 1000m 1h = 110 h 1km 3600 s 110 × 1000m = 3600 s = 30.6ms −1 Example7 Convert 100 MW to kW
Example 5 Convert 15 cm2 to m2 2
15cm 2 1m = 1 100cm 15cm 2 12 m 2 = 2 2 1 100 cm 15 ×1m 2 100 2 = 1.5 × 10 −3 m 2
100 MW = 1
6 10 W 1MW
1kW 3 10 W
100 ×106 kW 103 = 105 kW =
=
Example 8 European men in the age group 18 to 21 years have an average height of 5 ft 4 in. (a)What is this height in centimeters? (b)In meters? 1 in = 2.54 cm. 12in (a)5 ft = (5ft ) = 60in 1ft ⇒ 5 ft 4in = 64in
1cm (b)In meters, 163cm = (163cm) 100cm = 1.63m
2.54cm ∴ In cm, 64in = (64in) = 163cm 1in
Example 9 An undergraduate of UiTM rides a motorcycle at 50kmh-1. Express this speed in meters per second and miles per hour. 1.609km = 1 mi.
(
)
(
)
1000m 1h −1 50kmh −1 = 50kmh −1 = 13.9ms 1 km 3600 s 1mi −1 50kmh −1 = 50kmh −1 = 31.1 mih 1 . 609 km
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PHY 143 – Physics For Engineering I
HOMEWORK 1.2 1. Convert: i. 20 µm to m ii. 7.9 gcm-3 to kgm-3 iii. 15 s to ps iv. 30 mm2 to nm2 v. 10 ms-2 to cms-2 vi. 13 in to m vii. 8.5 ft to mm
2. Calculate the volume of a sphere of radius 10 cm in: i. mm3 ii. pm3 iii. m3
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