After learning this chapter, we are expected to be able to group physical quantities and their units into basic quantities and derived quantities, as well as measure physical quantities by using standard units and nonstandard units.
Before we learn, it will be better if you first we know what physics is. Certainly in elementary school we have learned the things which relate to physics in science. Physics is included into science, because science covers physics, chemistry, biology, astronomy, and geology. Etymologically, Indonesian word “Fisika” comes from the English word “physics”, while physics is derived from the word physikos meaning natural philosophy. As the result, physics is a science dealing with nature phenomena and the interaction of those natural phenomena which are expressed in mater and energy.
In everyday life many activities corresponding to physics, for example measuring the length of wood, measuring body height, weighing mass or weight, measuring the length and width of land that will be built house and so on. Those activities are closely related to physical concept concerning with the measurement, quantities, and units.
In this chapter we will study quantities, units, and measurement covering the following topics :
1. Definition of quantities, units, and measurement
2. Basic quantities
3. Derived quantities
A. Definition of quantities, units, and measurement
In everyday life, certainly we often hear the terminologies such as length, width, time, temperature, and so on. Those terminologies are included into quantities. In physics, quantities are very closely related to measurement. Meanwhile, the measurement has very important role in physics, moreover physics is not complete without the measurement of physical quantities.To more understand the definition of measurement, quantities, and units, let’s consider the following examples :
1. When we go to a shop to buy flour of 3 kg as stuff to make cakes, we will see the shopkeeper do a measurement by using a balance, so it is obtained flour of 3 kg according to what we need.
2. When we measure the length of the desk by using our span, after the measurement is done, obviously span.
The two examples above show the activities of measurement, that is the measurement of the amount of flour by using the balance and the measurement of the length of the desk by using the span. By the result of measurement in those two examples above, there are obtained the mass of flour is 3 kg and the length of desk is 8 spans. The number 3 shows the value of mass quantity and kg shows the value of length quantity and span shows the unit of the length quantity. By the information above, we can define quantities, units, and measurement. Meanwhile, the definition of quantities, units, and measurement in physics can be expressed as follows.
Quantities are everything that can be measured, has value that can be expressed by numbers, and has the certain units.
Units are a statement that explains the meaning of a quantity. Measurement is a process of comparing something measured with another as measures made as a standard. In other words, measurement is the process of comparing a quantity with another quantity which is used as unit.In the table below there are shown several examples of quantities which have their own value and units.
B. Basic Quantities
Quantities which are usually used in physics are differentiated into two, those are basic quantities and derived quantities. Basic quantities are quantities the units of which are predetermined and they are not derived from another quantities. Basic quantities consist of seven quantities, those are as shown in the table below.
Actually, in many regions on the earth there are still used various kinds of units for a quantity. For example, in measuring length, some using the units of hasta, span, feet, step and so on. It causes the difference in measurement result. That’s why those units cannot be valid internationally. Units which are not acknowledged internationally are called nonstandard units. Hence, it is necessary to be determined a unit system that is valid internationally functioning as standard units (or also called fundamental units).
In 1960, some scientists organized international conference which agreed standard units called International System Units (SI). This system replaces all of another systems found in the countries which use own numeric system. Metric system agreed using meter for length unit, kilogram for mass, and second for time. International system units by using basic units of meter, kilogram, and second (mks). Meanwhile another units the value of which are smaller and often used are cgs system units are : centimeter as the unit of length, gram as the unit of mass, and second as the unit of time.
Besides that, there are another unit systems that still widely used in several countries, those are British system units or fps system, among others, are as follows : the unit of length is expressed in feet, the unit of mass is expressed in pound, the unit of time is expressed in second.
Equivalence among mks, cgs, and British units are as follows :
1 kg = 1000 g1 m = 100 cm1 feet = 0,3048 m
1. Length
Length is the distance between two points in a space. According to SI units, the length quantity is expressed in meter. It is necessary to be known, that width, height, distance, depth, circumference, and diameter are also length quantities.
Before the agreement in using SI, the first international standard of length unit was a bar made of platinum-iridium alloy called standard meter. Nowadays, the device is stored in The International
Bureau of Weights and Measures Paris, France. Below is a picture of a standard meter :
The use of this has several difficulties are as follows :
a. It is easily to be broken and it is difficult to be remade
To solve that problem, in 1990 physicists organized general conference about Weight and Measure. In the conference there was agreed that the length of 1 meter is equal to 1,650,763.73 times of the wavelengths of reddish-orange light emission from Krypton-86 (symbolized by Kr-86) in a vacuum, the accuracy level of which is higher than the bar of platinum-iridium alloy.
In 1983, meter standard was reconverted to be one meter is equal to the distance traveled by light in a vacuum for 1/299,792,458 seconds. Another length units can use the multiplication of meter unit. For example are as follows :1 km = 1000 m = 10^3 m1 hm = 100 m = 10^2 m1 dam = 10 m = 10^11 dm = (1/10) m = 10^-1 m1 cm = (1/100) m = 10^-2 m1 mm = (1/1000) m = 10^-3 m
There are several kinds of measuring devices used to measure the quantity of length, among others, are as follows :
- Ruler
We certainly often see or moreover use a ruler to measure something, such as for measuring the length of the desk. Commonly, the ruler uses cm or mm scale with accuracy of 0.1 cm or 1 mm. Below is picture of ruler :
A vernier caliper has two main parts, namely outer jaw to measure thickness, such as the thickness of metal plate, and inner jaw part to measure the diameter of inner part of an object, for example the inner diameter of a tube and the inner diameter of the ring. The accuracy of the vernier caliper reaches 0.1 mm.
By the figure below, it looks that in a vernier caliper there are found two jaws, namely fixed jaw and sliding jaw. The fixed jaw has length scale which is called main scale, while the sliding jaw has short scale, which is called vernier scale.
- Screw micrometers
A screw micrometer has accuracy until 0.01 mm. The screw micrometer is usually used to measure tiny or small objects, such as the diameter of a wire and the thickness of paper. The screw micrometer has two scales, those are main scale and vernier scale, such as scales found in Vernier Calipers.
2. Mass
The mass of the body is the amount of matter contained by the body. According to SI units, the unit of mass is kilogram (kg). In everyday life, we often use the terminology weight. For example, the weight of Usman’s body is 55 kg. According to physics, weight is the force experienced by a body which has mass because of gravity. According to the definition, the weight of the body in different places may be different depending on the magnitude of the gravity in that place.
Mass standard of one kilogram in SI is fixed to be equal to the mass of platinum-iridium cylinder stored in International Bureau of Weight and Measures in Paris, France. This is the picture of platinum-iridium cylinder,
Another mass units can be derived from kilogram unit as follows,
1 kilogram (kg) = 10 hectogram (hg) = 1000 g
1 g = 100 cg = 1000 mg
1 quintal = 100 kg
1 ton = 10 quintal = 1000 kg
Measuring device used to measure mass quantity is balances. Several kinds of balances are as follows :
- Market balance
- Electronic balance
- Arm balance
3. Time
Another time units are the multiplication of second unit.
1 ms = (1/1000) s = 0,001 s
1 mikro s = (1/1000000) s = 0,000001 s
Meanwhile time units usually used everyday are as follows :
1 minute = 60 s
1 hour = 60 x 60 s = 3600 s
1 day = 24 x 3600 s = 86400 s
Before we learn, it will be better if you first we know what physics is. Certainly in elementary school we have learned the things which relate to physics in science. Physics is included into science, because science covers physics, chemistry, biology, astronomy, and geology. Etymologically, Indonesian word “Fisika” comes from the English word “physics”, while physics is derived from the word physikos meaning natural philosophy. As the result, physics is a science dealing with nature phenomena and the interaction of those natural phenomena which are expressed in mater and energy.
In everyday life many activities corresponding to physics, for example measuring the length of wood, measuring body height, weighing mass or weight, measuring the length and width of land that will be built house and so on. Those activities are closely related to physical concept concerning with the measurement, quantities, and units.
In this chapter we will study quantities, units, and measurement covering the following topics :
1. Definition of quantities, units, and measurement
2. Basic quantities
3. Derived quantities
A. Definition of quantities, units, and measurement
In everyday life, certainly we often hear the terminologies such as length, width, time, temperature, and so on. Those terminologies are included into quantities. In physics, quantities are very closely related to measurement. Meanwhile, the measurement has very important role in physics, moreover physics is not complete without the measurement of physical quantities.To more understand the definition of measurement, quantities, and units, let’s consider the following examples :
1. When we go to a shop to buy flour of 3 kg as stuff to make cakes, we will see the shopkeeper do a measurement by using a balance, so it is obtained flour of 3 kg according to what we need.
2. When we measure the length of the desk by using our span, after the measurement is done, obviously span.
The two examples above show the activities of measurement, that is the measurement of the amount of flour by using the balance and the measurement of the length of the desk by using the span. By the result of measurement in those two examples above, there are obtained the mass of flour is 3 kg and the length of desk is 8 spans. The number 3 shows the value of mass quantity and kg shows the value of length quantity and span shows the unit of the length quantity. By the information above, we can define quantities, units, and measurement. Meanwhile, the definition of quantities, units, and measurement in physics can be expressed as follows.
Quantities are everything that can be measured, has value that can be expressed by numbers, and has the certain units.
Units are a statement that explains the meaning of a quantity. Measurement is a process of comparing something measured with another as measures made as a standard. In other words, measurement is the process of comparing a quantity with another quantity which is used as unit.In the table below there are shown several examples of quantities which have their own value and units.
Quantities
|
value
|
Units
|
length
|
25
|
Meter
|
mass
|
3
|
Kilogram
|
time
|
45
|
Second
|
B. Basic Quantities
Quantities which are usually used in physics are differentiated into two, those are basic quantities and derived quantities. Basic quantities are quantities the units of which are predetermined and they are not derived from another quantities. Basic quantities consist of seven quantities, those are as shown in the table below.
No
|
Basic
quantities
|
Units
name
|
Units
symbol
|
1
|
Length
|
Meter
|
m
|
2
|
Mass
|
Kilogram
|
kg
|
3
|
Time
|
Second
|
s
|
4
|
Electric
current
|
Ampere
|
A
|
5
|
Temperature
|
Kelvin
|
K
|
6
|
Luminous
intensity
|
Candela
|
Cd
|
7
|
The
amount of substance
|
mole
|
Mol
|
Actually, in many regions on the earth there are still used various kinds of units for a quantity. For example, in measuring length, some using the units of hasta, span, feet, step and so on. It causes the difference in measurement result. That’s why those units cannot be valid internationally. Units which are not acknowledged internationally are called nonstandard units. Hence, it is necessary to be determined a unit system that is valid internationally functioning as standard units (or also called fundamental units).
In 1960, some scientists organized international conference which agreed standard units called International System Units (SI). This system replaces all of another systems found in the countries which use own numeric system. Metric system agreed using meter for length unit, kilogram for mass, and second for time. International system units by using basic units of meter, kilogram, and second (mks). Meanwhile another units the value of which are smaller and often used are cgs system units are : centimeter as the unit of length, gram as the unit of mass, and second as the unit of time.
Besides that, there are another unit systems that still widely used in several countries, those are British system units or fps system, among others, are as follows : the unit of length is expressed in feet, the unit of mass is expressed in pound, the unit of time is expressed in second.
No
|
quantities
|
mks units
|
cgs units
|
British units
|
1
|
Length
|
m
|
cm
|
feet (ft)
|
2
|
Mass
|
kg
|
g
|
Pound (lb)
|
3
|
Time
|
s
|
s
|
Second (s)
|
Equivalence among mks, cgs, and British units are as follows :
1 kg = 1000 g1 m = 100 cm1 feet = 0,3048 m
1. Length
Length is the distance between two points in a space. According to SI units, the length quantity is expressed in meter. It is necessary to be known, that width, height, distance, depth, circumference, and diameter are also length quantities.
Before the agreement in using SI, the first international standard of length unit was a bar made of platinum-iridium alloy called standard meter. Nowadays, the device is stored in The International
Bureau of Weights and Measures Paris, France. Below is a picture of a standard meter :
The use of this has several difficulties are as follows :
a. It is easily to be broken and it is difficult to be remade
To solve that problem, in 1990 physicists organized general conference about Weight and Measure. In the conference there was agreed that the length of 1 meter is equal to 1,650,763.73 times of the wavelengths of reddish-orange light emission from Krypton-86 (symbolized by Kr-86) in a vacuum, the accuracy level of which is higher than the bar of platinum-iridium alloy.
In 1983, meter standard was reconverted to be one meter is equal to the distance traveled by light in a vacuum for 1/299,792,458 seconds. Another length units can use the multiplication of meter unit. For example are as follows :1 km = 1000 m = 10^3 m1 hm = 100 m = 10^2 m1 dam = 10 m = 10^11 dm = (1/10) m = 10^-1 m1 cm = (1/100) m = 10^-2 m1 mm = (1/1000) m = 10^-3 m
There are several kinds of measuring devices used to measure the quantity of length, among others, are as follows :
- Ruler
We certainly often see or moreover use a ruler to measure something, such as for measuring the length of the desk. Commonly, the ruler uses cm or mm scale with accuracy of 0.1 cm or 1 mm. Below is picture of ruler :
A vernier caliper has two main parts, namely outer jaw to measure thickness, such as the thickness of metal plate, and inner jaw part to measure the diameter of inner part of an object, for example the inner diameter of a tube and the inner diameter of the ring. The accuracy of the vernier caliper reaches 0.1 mm.
By the figure below, it looks that in a vernier caliper there are found two jaws, namely fixed jaw and sliding jaw. The fixed jaw has length scale which is called main scale, while the sliding jaw has short scale, which is called vernier scale.
- Screw micrometers
A screw micrometer has accuracy until 0.01 mm. The screw micrometer is usually used to measure tiny or small objects, such as the diameter of a wire and the thickness of paper. The screw micrometer has two scales, those are main scale and vernier scale, such as scales found in Vernier Calipers.
2. Mass
The mass of the body is the amount of matter contained by the body. According to SI units, the unit of mass is kilogram (kg). In everyday life, we often use the terminology weight. For example, the weight of Usman’s body is 55 kg. According to physics, weight is the force experienced by a body which has mass because of gravity. According to the definition, the weight of the body in different places may be different depending on the magnitude of the gravity in that place.
Mass standard of one kilogram in SI is fixed to be equal to the mass of platinum-iridium cylinder stored in International Bureau of Weight and Measures in Paris, France. This is the picture of platinum-iridium cylinder,
Another mass units can be derived from kilogram unit as follows,
1 kilogram (kg) = 10 hectogram (hg) = 1000 g
1 g = 100 cg = 1000 mg
1 quintal = 100 kg
1 ton = 10 quintal = 1000 kg
Measuring device used to measure mass quantity is balances. Several kinds of balances are as follows :
- Market balance
- Electronic balance
- Arm balance
3. Time
Another time units are the multiplication of second unit.
1 ms = (1/1000) s = 0,001 s
1 mikro s = (1/1000000) s = 0,000001 s
Meanwhile time units usually used everyday are as follows :
1 minute = 60 s
1 hour = 60 x 60 s = 3600 s
1 day = 24 x 3600 s = 86400 s
The time measuring device usually used in ancient were hourglass and sundial. Nowadays, the devices usually used as time measurer are watch and stopwatch. Below is the picture of several instrument of time measurement :
a. Watch
Commonly, watches have three hands, those are hour hand, minute hand, and second hand.
b. Stopwatch
Stopwatch is usually used in a laboratory or in sport activities that is to measure time interval of an event that activities. There is a stopwatch using hands to show its time, but there is also a digital stopwatch.
C. Derived Quantities
Derived quantities are quantities derived from basic quantities. In the table there are shown the examples of derived quantities with their units.
1. Area
Area is derived quantity which is obtained by multiplying two length quantities. For example we will calculate the area of rectangle.
Area = length x width
= length quality x length quantity
= m x m
= m^2
2. Volume
Volume is the number of spaces used by a body. Similar to area, volume is also derived of basic quantities, that is the product of three length quantities. Solids which have uniform shape such as cube, cuboid, sphere, and tube their volume can be calculated by using certain formula. (remember mathematics). Meanwhile solids which have nonuniform shape such as stone, its volume can be calculated directly. The measurement of its volume is done by using a measuring glass. What is the method?
The method to measure the volume of nonuniform solids can be done as in the following example :
a. fill the measuring glass with water about 200 mL. It means the initial is 200 mL.
b. then, put a stone that will be measured into the measuring glass. For example the volume of water and the
stone becomes 300 mL. This volume is called the final volume.
c. subtract the final volume by the initial volume, so the difference is the volume of the stone
mengukur volume batu dengan gelas ukur
So, the volume of stone = final volume - initial volume
= 300 mL - 200 mL
= 100 mL = 100 cm^3 = (100) / (1000000) = 0,0001 m^3
D. Working in the laboratory
In learning physics, besides learn theory in a class you need also to do several experiment or practicums in a laboratory to apply or prove the theories obtained in the class. Besides that, by doing practicum, you will get valuable experience and joyful impression in learning physics.
1. Laboratory equipment
In a laboratory there are found devices and materials to do a practicum. Devices usually found in a physics laboratory are balances, thermometer, stopwacth, ruler, vernier caliper, glasess, glass jars, bunsen burner, reaction tubes, and so on. Meanwhile the materials usually found in the laboratory are chemicals.
beaker glass
2. Working safety
Practicum in a laboratory closely relates to devices and materials which sometime can cause any accident if it is done by inappropiate method. For example, when you use spirit burner or bunsen burner you must be careful because spirit is flammable, so don't make it spill on a desk and the connecting tube of the gas flow in bunsen must be attached strongly, do not to be released. Hence, it is necessary to be considered the use of those devices and materials, so not happen any accident when doing practicum, because working safety in the laboratory is an important factor for everyone. Besides that, it is necessary also to understand the meaning of symbols or sign which are usually written in the package of chemicals or the certain devices, among others, are as follows :
The things that must be considered in doing practicum in a laboratory are as in the below :
- plan the experiment which will be done before starting the practicum
- prepare the things required and what must be considered before entering the laboratory such as a note book, the kind of experiment, the kind of materials, the kind if devices, and the methods to remove the waste of the experiment remain
- master the working procedure and ask your theacer if you have any doubt or do not know about something
- wear a coat and goggle while you are doing an activity. They are useful for protecting our skin, eyes, and other body parts from a harmful chemical substance
- do not wear a sandal or opened shoes or highly sole shoes
- fit your hair if your hair is long
- do not eat or drink while you are in the laboratory
- keep the cleaness of a practicum desk. If the practicum desk is wet, immediately dry it by using a napkin
- avoid direct contact with chemical stuffs
- do not smell a chemical substance directly from a bottle nozzle
- make sure the gas tap is not leak when using bunsen
- make sure the water and gas taps are always in closed position before and after practicum is finished
- do not work alone in the laboratory, minimally there is a theacher observing
- do not play with a laboratory equipment and chemical stuff
- do not make mistake among friends
- if your body is splashed by a certain chemical substance, wash it with water as much as possible
- if accident happens, immediately contact paramedics
- devices used in practicum must be kept as well as possible, do not until be broken
The time measuring device usually used in ancient were hourglass and sundial. Nowadays, the devices usually used as time measurer are watch and stopwatch. Below is the picture of several instrument of time measurement :
a. Watch
Commonly, watches have three hands, those are hour hand, minute hand, and second hand.
b. Stopwatch
Stopwatch is usually used in a laboratory or in sport activities that is to measure time interval of an event that activities. There is a stopwatch using hands to show its time, but there is also a digital stopwatch.
C. Derived Quantities
Derived quantities are quantities derived from basic quantities. In the table there are shown the examples of derived quantities with their units.
Area is derived quantity which is obtained by multiplying two length quantities. For example we will calculate the area of rectangle.
Area = length x width
= length quality x length quantity
= m x m
= m^2
= length quality x length quantity
= m x m
= m^2
2. Volume
Volume is the number of spaces used by a body. Similar to area, volume is also derived of basic quantities, that is the product of three length quantities. Solids which have uniform shape such as cube, cuboid, sphere, and tube their volume can be calculated by using certain formula. (remember mathematics). Meanwhile solids which have nonuniform shape such as stone, its volume can be calculated directly. The measurement of its volume is done by using a measuring glass. What is the method?
The method to measure the volume of nonuniform solids can be done as in the following example :
a. fill the measuring glass with water about 200 mL. It means the initial is 200 mL.
b. then, put a stone that will be measured into the measuring glass. For example the volume of water and the
stone becomes 300 mL. This volume is called the final volume.
c. subtract the final volume by the initial volume, so the difference is the volume of the stone
So, the volume of stone = final volume - initial volume
= 300 mL - 200 mL
= 100 mL = 100 cm^3 = (100) / (1000000) = 0,0001 m^3
The method to measure the volume of nonuniform solids can be done as in the following example :
a. fill the measuring glass with water about 200 mL. It means the initial is 200 mL.
b. then, put a stone that will be measured into the measuring glass. For example the volume of water and the
stone becomes 300 mL. This volume is called the final volume.
c. subtract the final volume by the initial volume, so the difference is the volume of the stone
mengukur volume batu dengan gelas ukur
= 300 mL - 200 mL
= 100 mL = 100 cm^3 = (100) / (1000000) = 0,0001 m^3
D. Working in the laboratory
In learning physics, besides learn theory in a class you need also to do several experiment or practicums in a laboratory to apply or prove the theories obtained in the class. Besides that, by doing practicum, you will get valuable experience and joyful impression in learning physics.
1. Laboratory equipment
In a laboratory there are found devices and materials to do a practicum. Devices usually found in a physics laboratory are balances, thermometer, stopwacth, ruler, vernier caliper, glasess, glass jars, bunsen burner, reaction tubes, and so on. Meanwhile the materials usually found in the laboratory are chemicals.
1. Laboratory equipment
In a laboratory there are found devices and materials to do a practicum. Devices usually found in a physics laboratory are balances, thermometer, stopwacth, ruler, vernier caliper, glasess, glass jars, bunsen burner, reaction tubes, and so on. Meanwhile the materials usually found in the laboratory are chemicals.
beaker glass
2. Working safety
Practicum in a laboratory closely relates to devices and materials which sometime can cause any accident if it is done by inappropiate method. For example, when you use spirit burner or bunsen burner you must be careful because spirit is flammable, so don't make it spill on a desk and the connecting tube of the gas flow in bunsen must be attached strongly, do not to be released. Hence, it is necessary to be considered the use of those devices and materials, so not happen any accident when doing practicum, because working safety in the laboratory is an important factor for everyone. Besides that, it is necessary also to understand the meaning of symbols or sign which are usually written in the package of chemicals or the certain devices, among others, are as follows :
The things that must be considered in doing practicum in a laboratory are as in the below :
- plan the experiment which will be done before starting the practicum
- prepare the things required and what must be considered before entering the laboratory such as a note book, the kind of experiment, the kind of materials, the kind if devices, and the methods to remove the waste of the experiment remain
- master the working procedure and ask your theacer if you have any doubt or do not know about something
- wear a coat and goggle while you are doing an activity. They are useful for protecting our skin, eyes, and other body parts from a harmful chemical substance
- do not wear a sandal or opened shoes or highly sole shoes
- fit your hair if your hair is long
- do not eat or drink while you are in the laboratory
- keep the cleaness of a practicum desk. If the practicum desk is wet, immediately dry it by using a napkin
- avoid direct contact with chemical stuffs
- do not smell a chemical substance directly from a bottle nozzle
- make sure the gas tap is not leak when using bunsen
- make sure the water and gas taps are always in closed position before and after practicum is finished
- do not work alone in the laboratory, minimally there is a theacher observing
- do not play with a laboratory equipment and chemical stuff
- do not make mistake among friends
- if your body is splashed by a certain chemical substance, wash it with water as much as possible
- if accident happens, immediately contact paramedics
- devices used in practicum must be kept as well as possible, do not until be broken
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