Physics is inherently a science of measurement. Physical Quantities is any number or set of number used for a quantitative description of a physical phenomenon. All physical quantities consist of a numerical magnitude and a unit. For example, the measurement result of the length of a copper stick is 100 cm. 100 represents the numerical magnitude and cm represents the unit.
Physical Quantities and Units
A. Base Quantities, Base Units and Derived Units
In all of physics there are only seven base quantities, each quantity has a unit, corresponding to the quantities. These seven base quantities are presented in Table I-1 below.
Table I-1. Seven Base Quantities
Quantity Unit Symbol Dimension
Length meter m L
Mass kilogram kg M
Time second s T
Electric Current ampere A I
Thermodynamic kemperature kelvin K
Amount of substance mole mol N
Luminous intensity candela cd J
In measuring a quantity, we always compare it with some established reference standard:
The standard of Mass is the mass of cylinder of platinum-iridium alloy, designated as one kilogram.
2. The standard of length is a meter bar of platinum-iridium alloy
3. The standard of time is the time required for 9,192,631,770 cycles of this radiation (1 Second)
4. Amount of substance in mole represents the amount containing a number of particles equal to the Avogadro constant (NA = 6,02 x 1023 molecules/mol). Historically, the reverse process was one used to obtain NA: that is, from the measured mass of the hydrogen atom.
Example I-1
Use the Avogadro constant to determine the mass of a hydrogen atom
Solution:
One mole of hydrogen (atomic mass = 1.008 u) has a mass of 1.008 x 10-3 kg and contains 6.02 x 1023 atoms. Thus one atom has a mass
Most of physics quantities have the units as a combination of base units. Such units are called Derived units. Table 2 shows some derived units in mechanics.
Table I-2. Basic Mechanical Units
Quantities SI Units (MKS) CGS US Common Dimension
Length meter (m) Centimeter (cm) Foot (ft) L
Time second (s) second (s) Second (s) T
Mass kilogram (kg) gram (gr) slug M
Velocity m/s cm/s ft/s L/T
Acceleration m/s2 cm/s2 ft/s2 L/T2
Force kg m/s2 = Newton (N) gr m/s2 = dyne slug ft/s2 = pound (lb) M L/T2
Work N m = joule (j) dyne cm = erg lbft = ftlb M L2/T2
Energy joule erg ftlb M L2/T2
Power j/s = watt erg/s ftlb/s M L2/T3
A.1. Unit Consistency and Conversion
An equation must always be dimensionally consistent; this means that two terms may be added or equated only if they have the same units.
Example I-2
1. 2 m + 20 cm = 2 m + 0,2 m = 2,2 m
2. Distance = velocity x time = (m/s) x s = m
The algebraic properties of units provide a convenient procedure for converting a quantity from one unit to another. Equality is sometimes used to represent the same physical quantity expressed in two different units.
Example I-3
1. 1 min = 60 s does not mean that the number 1 is equal to the number 60, but rather that 1 min represents the same physical time interval as 60 s. and then divide by 60 s, or multiply by quantity (1 min/60s), without changing the physical meaning. To find the number of seconds in 3 min, we write: 3 min = (3 min)(60s/1 min) = 180 s.
2. Similarly, converting 50 km/h (kilometer per hour) in to meter per second
50 km/h = (50 km / h)(1000m/km)(I h/3600 s) = 13.89 m/s
A.2. Scientific Notation
In calculation with very large or very small numbers, we encounter the difficulty because we have to write a series of number. To overcome this difficulty one use the scientific notation, i.e.the scientifically methode to write the number.
Table of the scientific notation is given in Table I-3 below.
Table I-3. The Scientific Notation
Number Powers of ten Prefix Symbol
0.000 000 000 000 000 001 10-18 exa E
0.000 000 000 000 001 10-15 femto f
0.000 000 000 001 10-12 pico p
0.000 000 001 10-9 nano n
0.000 001 10-6 mikro
0.001 10-3 mili m
0.01 10-2 centi c
0.1 10-1 deci d
10 101 deka da
100 102 hecto h
1000 103 kilo k
1,000,000 106 mega M
1,000,000,000 109 giga G
1,000,000,000,000 1012 tera T
1,000,000,000,000,000 1015 peta P
1,000,000,000,000,000 000 1018 atto a
Example I-4
384 000 000 m can be written as 3.84 x 108 m.
0. 000 000 000 053 m can be written as 5,3 x 10-11m
It seem that the scientific notation facilitate us to write a very large or very small numbers
Example I-5
The mass of Earth is about 5,980,000,000,000,000,000,000,000 kilograms (kg), and the diameter of a proton is about 0.000000000000001 meter (m). This many zeros are inconvenient, and we employ a shorthand method of writing very large and very small numbers.By using powers of 10, Earth’s mass is more easily written as 5.98 x 1024 kg, and the diameter of a proton is written as 10-15 m
A considerable advantage of scientific notation is that multiplication and division are easily performed by adding and subtracting exponents of 10. Thus the product 100 x 100 = 10,000 can be written as 102 x 102 = 102+2 = 104. The awkward multiplication 0.00000055 x 24,000 can be done more easily as (5.5 x 10-3) x 10-7+4 = 13 x 10-3 = 1.3 x 101 x 10-3 = 1.3 x 10-2. Where division is involved, we simply change the sign of an exponent and use the multiplication rules. For example,
/
II. Measurement
A. Measurement of Length
Metre Rule
Figure II-1. The correct position to read the scale is at B. The actual reading is 8.3 cm. If the eye is placed at A or C, the reading obtained is inaccurate. The type of error due to the incorrect positioning of the eye with respect to the marking of the scale is known as parallax error.
To measure lengths, we can use rulers or measuring tapes. The correct way to read the scale on a ruler is shown in Figure II.1. Place your eye perpendicularly at the required mark on the scale to minimize parallax error. We can only measure with an accuracy up to 0.1 cm using a ruler. This means that the reading may be 0.1 cm more (+0.1 cm) than the actual reading or 0.1 cm less (- 0.1 cm) than actual reading. For smaller lengths or for greater accuracy we need special instruments like the vernier calipers or the micrometer screw gauge.
Vernier Calipers
We can use a pair of vernier calipers to measure small lengths to an accuracy of 0.1 mm or 0.01 cm. It consists of a main scale and a vernier scale (Figure II-2).
When the jaws are closed, the zero marks on the main scale and vernier scale should coincide (Figure II-3a). If this does not happen, there is a zero error in the vernier calipers
The following steps show the vernier calipers can be used to measure the diameter of a sphere.
Step 1: Check for zero errors (Figure II-3a, b, and c). Zero error is the difference in value between the zero marks on the main and vernier scales when the jaws of the calipers are completely closed together.
(a) If AB coincides with CD, there is no zero error.
(b) If AB lies to the right of CD, the zero error is taken as a positive error.
(c) If AB lies to the left of CD, the zero error is taken as a negative error.
Figure II-2.A picture of avernier calipers. The outside jaws are used to measure the length of a solid or the diameter of sphere. The inside jaws are used to measure the inner diamater of a tube.
(a) (b) (c)
Figure II-3.(a) AB coincides with CD. There is no zero error. (b) Identify the marking from AB that coincides with marking on the main scale. The zero error is + 0.01 cm. (c) Identify the marking from EF that coincides with the marking on the main scale. The zero error is –0.02 cm.
Figure II-4. Reading the main and the vernier scale
Reading = main scale reading + vernier scale reading
= 2.4 cm + 0.08 cm = 2.48 cm
Step 2: Grip the sphere gently with the outside jaws. The vernier scale can be tightened with a knob located on top of it. This prevents the scale from sliding before a reading is taken.
Step 3: Read the value on the main scale and the vernier scale. (Figure II-4)
Micrometer
Gambar II-5.A picture of a micrometer screw gauge. It has two scales: the main scale on the sleeve and the circular scale on the thimble. Turning the thimble and moving the circular scale up or down one division, will cause thespindle to move 0.01 mm or 0.001 cm horizontally.
To measure the diameter of fine wire, the thickness of paper and pther very short lengths, a micrometer screw gauge is used (Figure II-5). It has an accuracy of 0.01 mm or 0.001 cm.
The following steps show how the micrometer screw gauge can be used to measure the diameter of a wire:
Step 1: Check for zero error (Figure II-6 a, b, and c)
(a). If the 0 mark on the thimble scale coincides with CD, there is no zero error.
(b). If the 0 mark on the thimble scale lies to the right of CD the zero error is taken as a positive error.
(c). If the 0 mark on the thimble scale lies to the left of CD the zero error is taken as a negative error.
(a) (b) (c)
Figure II-6. (a). 0 mark on the thimble scale coincides with CD. There is no zero error. (b). Identify the marking on the thimble which coincides with CD on the sleeve. The zero error is +0.02 mm. (c) Identify the marking on the thimble which coincides with CD on the sleeve. The zero error is -0.03 mm.
Step 2: Turn the thimble to grip the wire gently. Then turn the ratchet a few times until a ‘click’ is heard. This will maintain firm contact between the wire and the spindle and anvil.
Step 3: Read the value on the sleeve and thimble (Figure II-7)
(a) (b)
Figure II-7. Reading the sleeve and thimble
Reading in Figure II-7.a = sleeve reading + thimble reading
= 4.00 mm + 0.12 mm = 4.12 mm
Reading in Figure II-7.b = sleeve reading + thimble reading
= 4.50 mm + 0.12 mm = 4.62 mm
Step 4: Correct your reading in step 3 by adjusting for the zero error (if any) found in step 1.
B. Measurement of Volume
1. Regular Volume
The volume of an object with a regular shape can be calculated after measuring the lengths of its sides, its diameter, or other lengths. Then the appropriate formulae (as described below) for the volumes are used. The SI units for volume is cubic metres (m3).
Volume of a cube = length3
Volume of a rectangular block = length × width × height
Volume of a sphere = (where r is the radius)
Volume of a cylinder = r2h (where r is the radius and h is the height)
Volume can be expressed as mm3, cm3 or m3. Sometimes you will see litres being used.
1 litre (l) is equivalent to 1000 cm3.
2. Irregular Volume
The volume of an object with an irregular shape can be measured by using a measuring cylinder or displacement can. Two figures below are shown methods to measure the volume of an irregular shape object.
C. Measurement of Mass
How heavy are you? Your answer might be, “Well…actually I am a little overweight. Don’t tell anybody but my weight is close to 70 kg!” In ordinary conversation, we do not always distinguish between mass and weight. In physics, we have to be very careful between these two terms have quite different meanings. Weight is measured in newtons whereas mass is measured in kilograms.
The mass of an object is a measure of the a mount of matter in it. The SI unit for mass is the kilogram (kg). The mass of a given object is always the same no matter where the object happens to be, i.e., mass is constant. Small masses may be measured in grams (g) amd large masses in tones (1 tonne = 1000 kg). Mass is measured using a balance. There are several types of balance and two are shown below.
(a) (b)
Figure II-7. (a). A sliding mass balance- the unknown mass is placed on the pan of the balance and its mass is obtained by sliding the given the given fixed masses on the beams until the beams are balanced. (b). An electronic balance- the object is placed on a pan and its mass is read from a screen.
D. Measurement of Time Interval
Time is measured in years, months, days, hours, minutes and seconds. The SI unit for time is the second (s). Clocks and watches are normally used to measure time.
All clocks make use of some regular repeating motion called oscillations. An example moves through positions O A O B O for example, we say it has made one oscillation. The time taken to make one oscillation is referred to as the periode of the oscillation.
Stopwatch
A modern electronics stopwatch has a digital display and can be read to the nearest 0.01 s. To measure a time interval, the stopwatch must be started and stopped by hand. When we want to start the stopwatch, our hand will take a split second to react. An error therefore introduced because it takes a certain amount of time to start or stop a watch. This error is called the reaction time and it varies from person to person. For most people, their reaction time is about 0.3 s. Hence generally it will be sufficient to measure time to the nearest 0.1 s.
Figure II-8. A digital stopwatch which gives an accuracy of 0.01 s
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