Unit 1 Basic Physical Science

1 Unit 1 Basic physical science 1.1 Measurement and units Units Scientists around the world use the same internationally agreed system of units. These are called SI (Systeme International) units. The system is built upon seven base units. . The metre (m) is the base unit of length. . The kilogram (kg) is the base unit of mass. . The second (s) is the base unit of time. . The ampere (安培, A) is the base unit of electrical current. . The kelvin (克耳文, K) is the base unit of temperature. . The mole (摩爾, mol) is the base unit of the amount of a substance. . The candela (堪德拉, cd) is the base unit of light intensity (光強度). Quantities such as speed (ms-1) and density (kgm-3) which are not expressed in a single base unit are expressed in derived units. Table 1.1 shows some of the common derived units of the SI system. Quantity speed or velocity acceleration force energy power pressure frequency charge Potential difference 電位差

Symbol v a F E P p f Q V

resistance電阻

R

Name of unit Symbol for unit m s-1 m s-2 newton N joule J watt W pascal 帕斯卡 Pa hertz赫茲 Hz coulomb 庫侖 C volt伏特 V ohm 歐姆 Q

capacitance電容 magnetic flux density 磁通密度

C B

farad法拉 tesla 特斯拉

F T

Base units m s-1 m s-2 kg m s-2 kg m2 s-2 kg m2 s-3 kg m-l s-2 s-1 As A-1 kg m2 s-3

A2 kg-1 m-2 s4 A-1kg s-2

A-2 kg m2 s-3

Quantities which have no units are described as being dimensionless 無 單位 - for example the refractive index (折射率) of a material is a ratio of like quantities and therefore has no unit.

2 The base units of any quantity can be found by considering an equation that relates it to quantities whose units are known. Example 1 Show that the base units of density are kgm-3. density =

mass volume

so the units are

kg or kg/m3 3 m

This is more usually written as kgm-3 - division is indicated by a negative index. e.g distance = speed × time = (km/s) × (s) = (km) Sometimes it is necessary to convert between identical physical quantities (e.g. distance) between different systems of units (e.g. km and miles). e.g. 1 mile = 1.6 km; 240 km = 240 × (1 mile/ 1.6 km) = 149 miles.

Powers of ten shorthand: e.g.

4000 400 40 4 0.4 0.04 0.004

= 4× 10× 10× 10 = 4× 10× 10 = 4× 10 = 4× 1 = 4/10 = 4/101 = 4/10 = 4/102 = 4/10 = 4/103

= 4× 103 = 4× 102 = 4× 101 = 4× 100 = 4× 10-1 = 4× 10-2 = 4× 10-3

Prefixes Prefixes are used with units to change numerical values into a more convenient form. For example, the energy contained in a flash of lightning is approximately one thousand million joules or 1× 109J. Using a prefix this becomes 1 GJ (one gigajoule). Table 1.2 shows the most commonly used prefixes. Multiple 10-12 10-9 10-6 10-3 103 106 109

Prefix pico皮 nano納 micro微 milli kilo mega giga

Symbol p n µ m k M G

Example pF picofarad nm nanometre µ A microamp ms millisecond kg kilogram MJ megajoule GW gigawatt

Standard form It is accepted practice to express numerical quantities as a number between 1 and 10 multiplied by the appropriate power of 10. This is known as standard form. Number 1 000 140 000 000 128 600 0.015 0.003 86

Significant figures 有效數字:

Number in standard form 1.0 × 103 1.4 × 108 1.286 × 105 1.5 × 10-2 3.86 × 10-3

3 At the first glance the values 2 cm, 2.0 cm and 2.00 cm may appear identical. There is, however, a very important difference between them. The first value is given to just one significant figure. This indicates that the true value of this length lies between 1.5 cm and 2.4 cm. The second value is given to two significant figures; the true value of this length lies between 1.95 cm and 2.04 cm. The third value is the most precise of the figures as it is given to three significant figures, indicating that its true value lies between 1.995 cm and 2.004 cm. The greater the number of significant figures given, the greater the implied precision of the measurement. Note that the number of significant figures given and the number of decimal places are not necessarily the same. Writing the above values in m or km would alter the number of decimal places but not the number of significant figures or the implied precision of the values. When calculating, the final answer should not be stated to more significant figures than the least precise of the given figures.

0.0385 (___sig. fig.); 2.73× 103 (___sig. fig.); 5000 (___sig. fig.); 5.0× 103 (___sig. fig.); 5× 103 (___sig. fig.); 5.00× 103 (___sig. fig.); Examples 1.1 1. How many millimeters are there in a 1 cm, b 4 cm, c 0.5 cm,

d 6.7 cm,

e 1 m?

2. What are these lengths in meters: a 300cm, b 550 cm, c 870 cm,

d 43 cm,

e 100 mm?

3. a Write the following as powers of ten with one figure before the decimal point: 100 000 3500 428 000 000 504 27 056 b Write out the following in full: 103 2× 106 6.9× 104

1.34× 102

4. a Write these fractions as powers of tens: 1/1000 7/1000 0000 1/10 000 000

109 3/60 000

b Express the following decimals as powers of ten with one figure before the decimal point: 0.5 0.084 0.000 36 0.001 04 5. How many significant figures are there in a length measurement of 2.5 cm 5.32 cm 7.1080 cm 0.042 cm 6. A rectangular block measures 4.1 cm by 2.8 cm by 2.1 cm. Calculate its volume giving your answer to an appropriate number of significant figures.

4 1.2 Nature of matter Matter is made up of tiny particles or molecules (分子) which are too small for us to see directly. Molecules consist of even smaller particles called atoms. Brownian motion Qualitative evidence of the microscopic nature of gases is shown by an effect called Brownian motion (布朗運動). States of matter Matter can exist in any one of three states depending on temperature and pressure. The three states of matter are:

Particles have a regular pattern, are close together, they move slightly and have high density

Particles are more widely spaced, move more freely and have a medium density

Particles are widely spaced, move randomly at high speed and have a low density

The electric forces between molecules in a solid can be represented by springs

Diffusion Smells, pleasant of otherwise, travel quickly and are caused by rapidly moving molecules. The spreading of a substance of its own accord is called diffusion (擴散) and is due to molecular motion.

Example 1.2

1. Which one of the following statements is not true? A The molecules in a solid vibrate about a fixed position. B The molecules in a liquid are arranged in a regular pattern. C The molecules in a gas exert negligibly small forces on each other, except during collisions. D The densities of most liquids are about 1000 times greater than those of gases, because liquid molecules are much closer together than gas molecules. E The molecules of a gas occupy all the space available.

5 1.3 Mass 質量, weight 重量 and density In everyday language lead is said to be ‘heavier’ than wood. By this it is meant that a certain volume of lead is heavier than the same volume of wood. In science such comparisons are made by using the term density. This is the mass per unit volume of a substance and is calculated from density =

mass volume

d=

m V

SI unit of density is the kilogram per cubic meter. To convert a density from g/cm3 to kg/m3, we multiply by 103. For example the density of water is 1.0g/cm3 or 1.0× 103kg/m3. Worked example Taking the density of copper as 9g/cm3, find (a) the mass of a 5cm3 copper block, and (b) the volume of a copper block with mass 63g. (a). m =V ×d = 5cm 3 ×9 g / cm 3 = 45 g (b). V =

m 63 g = = 7cm 3 3 d 9 g / cm

Simple density measurements a. Regularly shaped solid The mass is found on a balance and the volume by measuring its dimensions with a ruler. b. Irregularly shaped solid, e.g. pebble or glass stopper The solid is weighed and its volume measured by one of the methods shown in the following figures. c. Liquid A known volume is transferred from a measuring cylinder into a weighed beaker which is reweighed to give the mass of liquid. d. Air A 500cm3 round-bottomed flask is weighed full of air and then after removing the air with a vacuum pump; the difference gives the mass of air in the flask. The volume of air is found by filling the flask with water and pouring it into a measuring cylinder. Floating and sinking An object sinks in a liquid with density smaller than its own; otherwise it floats, partly or wholly submerged. For example, a piece of glass of density 2.5g/cm3 sinks in water (density 1.0 g/cm3) but floats in mercury (density 13.6 g/cm3). An iron nail sinks in water but an iron ship floats because its average density is less than that of water.

6 Example 1.3

1. a. If the density of wood is 0.5 g/cm3 what is the corresponding mass of wood blocks with volume (i) 1 cm3, (ii) 2 cm3 (iii) 10cm3 b. What is the density of a substance of (i) mass 100 g and volume 10cm3, (ii) volume 3 m3 and mass 9 kg? c. The density of gold is 19 g/cm3. Find the volume of gold with mass (i) 38 g (ii) 95 g.

2. A piece of steel has a volume of 12 cm3 and a mass of 96 g. What is its density in a. g/cm3

b. kg/m3

3. What is the mass of 5 m3 of cement of density 3000 kg/m3? 4. What is the mass of air in a room measuring 10 m × 5.0 m × 2.0 m if the density of air is 1.3 kg/m3 ?

5. When a golf ball is lowered into a measuring cylinder of water, the water level rises by 30 cm3 when the ball is completely submerged. If the ball weighs 33 g in air, find its density.

7 1.4 Force and energy Force A force is a push or a pull. It can cause a body to start moving, or if the body is already moving it can change its speed or direction of motion. It can also change its shape or size. Weight The weight of a body is the force of gravity on it. gravity is a force between masses magnetic force is a force between magnets electric force is a force between electric charges The Newton The unit of force is Newton (N). The weight of a body can be measured by hanging it on a spring balance marked in newton. The greater the pull the more the spring stretches. On most of the Earth’s surface: The weight of a body of mass 1kg is 9.8N. (Often this taken as 10N) Hooke’s Law 虎克定律 extension ∝ stretching force (It is true only if the elastic limit of the spring is not exceeded.)

The force constant 力常數 k of a spring is the force needed to cause an extension for one unit of length, i.e. 1 m. k=

F e

( N / m)

Worked example A spring is stretched 10mm (0.01m) by a weight of 2.0N. Calculate (a) the force constant k of the spring, and (b) the weight W of an object which causes an extension of 80mm (0.08m). a. k =

F 2.0 N = 200 N / m ; e 0.01m

b. W = stretching force F = k ×e = 200 N / m ×0.08 m =16 N Buoyancy force 浮力

8 Any body completely or partially submerged in a fluid is lifted up by a buoyancy force. According to the Archimedes’ principle 阿基米德原理, the magnitude of the lifting force is always equal to the weight of the fluid displaced by the body. Energy When a rock of mass m falls freely, its altitude z and speed v change together in such a way that the 1 2

quantity E = mgz + mv 2 stays constant, where g is the acceleration of gravity at Earth’s surface. We call the first term of the above expression, mgz, the potential energy 位能 of the rock, and the second term,

1 mv 2 , the kinetic energy 動能. We will call their sum E the mechanical energy 機 2

械能. In an ideal system, E stays constant, we say that the mechanical energy is conserved.

In physics, kinetic energy is the energy possessed by an object due to its motion. A fast moving object will have more kinetic energy than an identical slow moving object. Potential energy is the energy stored by an object due to its position relative to some others objects. For example, an object will store up potential energy when it is lifted up, or when an elastic object (such as a spring) is stretched or compressed. Mechanical energy, including kinetic energy and potential energy, underlines other different forms of energy such as heat, sound, and light. For example, average kinetic energy of random molecular motion is related to temperature, and kinetic and potential energies of vibrating air define sound intensity. Electrons in motion make electric currents. Light energy originates from the motion of electrons within atoms. Atomic energy is due to the re-arrangement of the particles within the nuclei of the atom. We will find there is much in common among the various forms of energy that we will investigate. Energy has the unit of Joule (J): 1 J = 1 N x 1 m= kg m2 s-2 Worked example A rock is thrown vertically upwards, and reaches a maximum height of 30 m in air. Calculate the speed with which the stone is thrown into the air. (Take the gravitational acceleration g=10 m s-2). By conservation of mechanical energy: kinetic

energy at the moment of throw = potential energy at the top of the throw

1 mv 2 = mgz 2 ∴v = 24 .5m / s

1 ∴ v 2 = gz 2

∴v 2 = 2 gz = 2 ×10 ×30

Conservation of Energy 能量守恆 If our rock falls on an inclined plane, the mechanical energy will be conserved if the surface is very smooth. But if the surface is rough, then the friction between the surface and the rock will consume energy and the mechanical energy is not conserved. But the friction actually converts the mechanical energy into heat. The study of various forms of energy and their transformations from one form into another form has led to one of the greatest generalizations in physics - the law of conservation of energy:

9 Energy can not be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Example 1.4 1. A body of mass of 1 kg has weight 10N at a certain place. What is the weight of masses a. 100g b. 5 kg, c. 50 g

2. The force of gravity on the Moon is said to be one-sixth that on the Earth. What would a mass of 12 kg weigh a. on the Earth, and

b. on the Moon?

3. What is the force constant of a spring which is stretched a. 2 mm by a force of 4 N, b. 4 cm by a mass of 200 g?

4. A spring stretches from 10 cm to 22 cm when a force of 4 N is applied. If it obeys Hooke’s law, its total length in cm when a force of 6 N is applied is A. 28 B. 42 C. 50 D. 56

E. 100

5

If an immersed object displaces liquid weighing 10 N, according to Archimedes’ principle, what is the buoyant force on the object?

6

What energy is described as being the energy due to its position? a. heat energy; b. potential energy, c. kinetic energy

7

What energy is described as being the energy due to its speed? a. nuclear energy, b. potential energy, c. kinetic energy

10 Checklist After studying this chapter you should be able to 1.1 Measurement and units • recall three basic quantities in physics • write a number in the power of ten (standard) form • recall the unit of length and the meaning of the prefixes kilo, centi, milli, micro, nano • give a result with an appropriate number of significant figures 1.2 Nature of matter • recall the Brownian motion • recall the three states of matter • recall the definition of diffusion • define density and perform calculations using d=m/V • describe experiments to measure the density of solids, liquids and air • relate floating and sinking to density 1.3 Mass, weight and density • recall the definition of density • recall the measurement of density recall that a force can cause a change in the motion, size or shape of a body 1.4 Force and energy • recall that the weight of a body is the force of gravity on it • recall that the unit of force and how force is measured • describe an experiment to study the relation between force and extension for springs • draw conclusions from force-extension graphs • recall Hooke’s law and solve problems using it • explain the term force constant • recall the buoyant force • describe the Archimedes’s principle • recall mechanical energy, potential energy and kinetic energy • apply the principle of conservation of energy