Pearson Baccalaureate Physics SL Chapter1

7/24/2019 Pearson Baccalaureate Physics SL Chapter1

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1 Physics and physicalmeasurement

Range of magnitudes of quantities in ouruniversePhysics seeks to explain the universe itself, from the very large to the very

small. At the large end, the size of the visible universe is thought to be around

1025m, and the age of the universe some 1018s. The total mass of the universe is

estimated to be 1050kg.

The realm of physics1.1

Assessment statements

1.1.1 State and compare quantities to the nearest order of magnitude.

1.1.2 State the ranges of magnitude of distances, masses and times that

occur in the universe, from the smallest to the largest.

1.1.3 State ratios of quantities as different orders of magnitude.

1.1.4 Estimate approximate values of everyday quantities to one or two

significant figures and/or to the nearest order of magnitude.

How do we know all this is true?

What if there is more than one

universe?

A planet was recently discovered in

the constellation Libra (about 20 light

years from Earth) that has all the right

conditions to support alien life. This

artists impression shows us how it

might look.

downloaded from www.pearsonbaccalaureate.com/diploma

UNCORRECTED PROOF COPY


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Physics and physical measurement

Rest mass is the mass of a particle

when at rest; the mass increases ifthe particle moves fast enough.

If we can split an atom why cant

we split an electron?

The diameter of an atom is about 1010m, and of a nucleus 1015m. The smallest

particles may be the quarks, probably less than 1018m in size, but there is a much

smaller fundamental unit of length, called the Planck length, which is around 1035m.

There are good reasons for believing that this is a lower limit for length, and we

accept the speed of light in a vacuum to be an upper limit for speed (3 108ms1).

This enables us to calculate an approximate theoretical lower limit for time:

timedistance

_______

speed

1035m

________

108ms11043s.

If the quarks are truly fundamental, then their mass would give us a lower limit.

Quarks hide themselves inside protons and neutrons so it is not easy to measure

them. Our best guess is that the mass of the lightest quark, called the up quark, is

around 1030kg, and this is also the approximate rest mass of the electron.

You need to be able to state ratios of quantities as differences of orders of magnitude.

For example, the approximate ratio of the diameter of an atom to its nucleus is:

1010m

_______

1015m105

105is known as a difference of five orders of magnitude.

Some physicists think that there are

still undiscovered particles whose

size is around the Planck length.

What are the reasons for there

being a lower limit for length?Why should there be a lower limit

for time?

Production and decay of bottom quarks.

There are six types of quarks calledup,

down, charm, strange, topand bottom.

Figure 1.1 The exact position of

electrons in an atom is uncertain; we

can only say where there is a high

probability of finding them.




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This is not a small ratio; it means that if the atom were as big as a football pitch,

then the nucleus would be about the size of a pea on the centre circle. This implies

that most of the atoms of all matter consist of entirely empty space.

Another example is that the ratio of the rest mass of the proton to the rest mass of

the electron is of the order:

1.67 1027kg

_____________

9.11 1031kg2 103

You should be able to do these estimations without using a calculator.

You also need to be able to estimate approximate values of everyday quantities to

one or two significant figures.

For example, estimate the answers to the following:

How high is a two-storey house in metres?

What is the diameter of the pupil of your eye?

How many times does your heart beat in an hour when you are relaxed?

What is the weight of an apple in newtons?

What is the mass of the air in your bedroom?

What pressure do you exert on the ground when standing on one foot?

There is help with these estimates at the end of the chapter.

Measurement and uncertainties1.2


1.2.1 State the fundamental units in the SI system.

1.2.2 Distinguish between fundamental and derived units and give

examples of derived units.

1.2.3 Convert between different units of quantities.

1.2.4 State units in the accepted SI format.

1.2.5 State values in scientific notation and in multiples of units with

appropriate prefixes.

1.2.6 Describe and give examples of random and systematic errors.

1.2.7 Distinguish between precision and accuracy.

1.2.8 Explain how the effects of random errors may be reduced.

1.2.9 Calculate quantities and results of calculations to the appropriate

number of significant figures.

1.2.10 State uncertainties as absolute, fractional and percentage uncertainties.

1.2.11 Determine the uncertainties in results.

1.2.12 Identify uncertainties as error bars in graphs.

1.2.13 State random uncertainty as an uncertainty range () and represent it

graphically as an error bar.

1.2.14 Determine the uncertainties in the slope and intercepts of a straightline graph.

1 The diameter of a proton is of the order of magnitude of

A 1012m. B 1015m. C 1018m D 1021m.

Exercise

If most of the atom is empty space

why does stuff feel so solid?




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The SI system of fundamental and derived unitsIf you want to measure something, you have to use a unit. For example, it is useless

to say that a persons mass is 10, 60, 140 or 600 if we do not know whether it is

measured in kilograms or some other unit such as stones or pounds. In the old

days, units were rather random; your mass might be measured in stones, but your

height would not be measured in sticks, but in feet.

Soon after the French Revolution, the International System of units was developed.

They are called the SI units because SI stands for Systme International.

There are seven base, or fundamental, SI units and they are listed in the table

below.

Name Symbol Concept

metre or meter m length

kilogram kg mass

second s second

ampere A electric current

kelvin K temperature

mole mol amount of matter

candela cd intensity of light

Mechanics is the study of matter, motion, forces and energy. With combinations

of the first three base units (metre, kilogram and second), we can develop all the

other units of mechanics.

density mass

_______

volumekg m3

speed distance

_______

time m s1

As the concepts become more complex, we give them new units. The derived SI

units you will need to know are as follows:

Name Symbol ConceptBroken down intobase SI units

newton N force or weight kg m s2

joule J energy or work kg m2s2

watt W power kg m2s3

pascal Pa pressure kg m1s2

hertz Hz frequency s1

coulomb C electric charge As

volt V potential difference kg m2s3A1

ohm resistance kg m2s3A2

tesla T magnetic field strength kg s2A1

weber Wb magnetic flux kg m2

s2

A1

becquerel Bq radioactivity s1

Some people think the foot was

based on, or defined by, the length

of the foot of an English king, but it

can be traced back to the ancient

Egyptians.

The system of units we now call SI

was originally developed on the

orders of King Louis XVI of France.

The unit for length was defined

in terms of the distance from the

equator to the pole; this distance

was divided into 10 000 equal parts

and these were called kilometres.

The unit for mass was defined in

terms of pure water at a certain

temperature; one litre (or 1000 cm3)

has a mass of exactly one kilogram.

Put another way, 1 cm3of water

has a mass of exactly 1 gram.

The units of time go back to the

ancients, and the second was

simply accepted as a fraction

of a solar day. The base unit for

electricity, the ampere, is defined

in terms of the force between two

current-carrying wires and the unit

for temperature, the kelvin, comes

from an earlier scale developed by

a Swedish man called Celsius.




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Worked examples

1 Give units for the following expressed as (i)the derived unit (ii)base SI units:

(a) force

(b) kinetic energy.

2 Check if these equations work by substituting units into them.

(a) powerwork/time or energy/time

(b) powerforcevelocity

Solutions

1 (a) (i) N (ii) kg(m s2) or kg m s2

(b) (i) J (ii) kg (m s1)2or kg m2s2

2 (a) W : J/s or W : (kg m2s2)/s or W : kg m2s3

(b) W : N(m s1) or W : (kg m s2)(m s1) or W : kg m2s3

In addition to the above, there are also a few important units that are not

technically SI, including:

Name Symbol Concept

litre l volume

minute, hour, year, etc. min, h, y, etc. time

kilowatt-hour kWh energy

electronvolt eV energy

degrees celsius C temperature

decibel dB loudness

unified atomic mass unit u mass of nucleon

Examiners hint:

forcemass acceleration.

Examiners hint:

kinetic energy1

_

2

mv2

2 Which one of the following units is a unit of energy?

A eV B W s1 C W m1 D N m s1

3 Which one of the following lists a derived unit and a fundamental unit?

A ampere second

B coulomb kilogram

C coulomb newton

D metre kilogram

Exercises




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Worked example

Convert these units to SI:.

(a) year (b)C (c) kWh (d)eV

Solution

(a) 1 year1 365 days 24 hours 60 minutes 60 seconds

3.15107s

(b) Here are some common conversions:

0 K273 C

273 K0 C

300 K27 C

373 K100 C

(c) 1 kWh (energy)1000 W (power) 3600 s (time)

3 600 000 J

3.6106J

(d) electrical energyelectric charge potential difference

1 eV 1.6 1019C 1 V

1.61019 J

The SI units can be modified by the use of prefixes such as millias in millimetre

(mm) and kiloas in kilometre (km). The number conversions on the prefixes are

always the same; millialways means one thousandth or 103and kiloalways means

one thousand or 10

3

.These are the most common SI prefixes:

Prefix Abbreviation Value

tera T 1012

giga G 109

mega M 106

kilo k 103

centi c 102

milli m 103

micro 106

nano n 109

pico p 1012

femto f 1015

Examiners hint: To change kilowatt-

hours to joules involves using the

equation:

energypower time.

1 kW1000 Wand 1 hour60 60 seconds.

Examiners hint: The electronvolt

is defined as the energy gained by an

electron accelerated through a potential

difference of one volt. So the electronvolt

is equal to the charge on an electron

multiplied by one volt.

4 Change 2 360 000 J to scientific notation and to M J.

5 A popular radio station has a frequency of 1 090 000 Hz. Change this to scientific notation and to MHz.

6 The average wavelength of white light is 5.0 107m. What would this be in nanometres?

7 The time taken for light to cross a room is about 1 108seconds. Change this intomicroseconds.

Exercises

Examiners hint: The size of one

degree Celsius is the same as one Kelvin

the difference is where they start, or the

zero point. The conversion involves adding

or subtracting 273. Since absolute zero or

0 K is equal to273 C, temperature in

Ctemperature in K 273.




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Uncertainty and error in measurementEven when we try to measure things very accurately, it is never possible to be

absolutely certain that the measurement is perfect.

The errors that occur in measurement can be divided into two types, randomand

systematic. If readings of a measurement are above and below the true value with

equal probability, then the errors are random. Usually random errors are causedby the person making the measurement; for example, the error due to a persons

reaction time is a random error.

Systematic errors are due to the system or apparatus being used. Systematic errors

can often be detected by repeating the measurement using a different method

or different apparatus and comparing the results. A zero offset, an instrument

not reading exactly zero at the beginning of the experiment, is an example of a

systematic error. You will learn more about errors as you do your practical work in

the laboratory.

Random errors can be reduced by repeating the measurement many times and

taking the average, but this process will not affect systematic errors. When you

write up your practical work you need to discuss the errors that have occurred in

the experiment. For example: What difference did friction and air resistance make?

How accurate were the measurements of length, mass and time? Were the errors

random or systematic?

Another distinction in measuring things is betweenprecisionand accuracy.

Imagine a game of darts where a person has three attempts to hit the bulls-eye.

If all three darts hit the double twenty, then it was a precise attempt, but not

accurate. If the three darts are evenly spaced just outside and around the bulls-eye,

then the throw was accurate, but not precise enough. If the darts all miss the board

entirely then the throw was neither precise nor accurate. Only if all three darts hitthe bulls-eye can the throws be described as both precise and accurate!

What conditions would be

necessary to enable something to

be measured with total accuracy?

Figure 1.2 All the players try to hit

the bulls eye with their three darts, but

only the last result is both precise and

accurate.

205

12

9

14

1

1

8

16

719 3 17

2

15

10

6

13

4

181 205

12

9

14

1

1

8

16

719 3 17

2

15

10

6

13

4

181

205

12

9

14

1

1

8

16

7

19 3 17

2

15

10

6

13

4

181 205

12

9

14

1

1

8

16

7

19 3 17

2

15

10

6

13

4

181

precise,

not accurate

neither precise

nor accurate

accurate,

not precise

both accurate

and precise




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It is the same with measurements; they can be precise, accurate, neither or both. If

there have been a large number of measurements made of a particular quantity, we

can show these four possibilities on graphs like this:

Significant figures

When measuring something, in addition to a unit, it is important to think aboutthe number of significant figures or digits we are going to use.

For example, when measuring the width and length of a piece of A4 paper with a

30 cm ruler, what sort of results would be sensible?

Measurements (cm)Number of

significant figuresSensible?

21 30 1 2 yes

21.0 29.7 0.1 3 maybe

21.03 29.68 0.01 4 no

With a 30 cm ruler it is not possible to guarantee a measurement of 0.01 cm or

0.1 mm so these numbers are not significant.

This is what the above measurements of width would tell us:

Measurements (cm) Number ofsignificant figures

Value probablybetween (cm)

21 1 2 2022

21.0 0.1 3 20.921.1

21.03 0.01 4 21.0221.04

The number of significant figures in any answer or result should not be more than

that of the least precise value that has been used in the calculation.

precise but

not accurate

true value ofmeasured quantity

number ofreadings

number ofreadings

number ofreadings

number ofreadings

accurate but

not precise

true value

neither accurate

nor precise

true value

accurate and precise

true value

Figure 1.3 Here is another way of

looking at the difference between

precision and accuracy, showing the

distribution of a large number of

measurements of the same quantity

around the correct value of the

quantity.

If you are describing a person

you have just met to your best

friend, which is more important

accuracy, precision or some other

quality?




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Worked example

Calculate the area of a piece of A4 paper, dimensions 21 cm 29.7 cm. Give your

answer to the appropriate number of significant figures.

Solution

21 29.7623.7

Area620 cm2

6.2102cm2

Uncertainties in calculated results

If we use a stopwatch to measure the time taken for a ball to fall a short distance,

there will inevitably be errors or uncertainties due to reaction time. For example, if

the measured time is 1.0 s, then the uncertainty could reasonably be0.1 s. Here

the uncertainty, or plus or minus value, is called an absolute uncertainty. Absolute

uncertainties have a magnitude, or size, and a unit as appropriate.

There are two other ways we could show this uncertainty, either as a fraction or asa percentage. As a fraction, an uncertainty of 0.1 s in 1.0 s would be 1__10and as a

percentage it would be 10%.

These uncertainties increase if the measurements are combined in calculations or

through equations. In an experiment to find the acceleration due to gravity, the

errors measuring both time and distance would influence the final result.

If the measurements are to be combined by addition or subtraction, then the

easiest way is to add absolute uncertainties. If the measurements are to be

combined using multiplication, division or by using powers like x2, then the best

method is to add percentage uncertainties. If there is a square root relationship,

then the percentage uncertainty is halved.

Uncertainties in graphs

When you hand in your lab reports, you must always show uncertainty values

at the top of your data tables asa sensible value. On your graphs, these are

represented as error bars. The error bars must be drawn so that their length on

the scale of the graph is the same as the uncertainty in the data table. Error bars

can be on either or both axes, depending on how accurate the measurements are.

The best-fit line must pass through all the error bars. If it does not pass through

a point, then that point is called an outlier and this should be discussed in the

evaluation of the experiment.

Examiners hint: The least precise

input value, 21 cm, only has 2 significant

figures.

Examiners hint: Because we are

using scientific notation, there is no

doubt that we are giving the area to 2

significant figures.

8 When a voltage Vof 12.2 V is applied to a DC motor, the current Iin the motor is 0.20 A. Which

one of the following is the output power VIof the motor given to the correct appropriate

number of significant digits?

A. 2 W B. 2.4 W C. 2.40 W D. 2.44 W

Exercise




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Scalarsare measurements that have size, or magnitude. A scalar almost always

needs a unit. Vectorshave magnitude and also have a direction. For example, a

Boeing 747 can fly at a speed of 885 kmh1or 246 ms1. This is the speed and is a

scalar quantity. If the plane flies from London to New York at 246 ms1then this

is called its velocity and is a vector, because it tells us the direction. Clearly, flying

from London to New York is not the same as flying from New York to London;

the speed can be the same but the velocity is different. Direction can be crucially

important.

1.0O

2.0

time (s)0.2

outlier

distance

(m)0.1

3.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

y

x

Motion showing a body travelling at a steady speedFigure 1.4 Error bars can

be on thex-axis only,

y-axis only or on both

axes, as shown here.

Vectors and scalars1.3


1.3.1 Distinguish between vector and scalar quantities, and give examples ofeach.

1.3.2 Determine the sum or difference of two vectors by a graphical method.

1.3.3 Resolve vectors into perpendicular components along chosen axes.




11/1411

Here is another example of the difference between a vector and a scalar. Suppose

you walk three metres to the east and then four metres towards the north.

The distance you have travelled is seven metres but your displacement, the distance

between where you started and where you ended up, is only five metres. Because

displacement is a vector, we also need to say that the five metres had been moved

in a certain direction north of east.

Here are some common examples:

Scalar Vector

Distance Displacement

Speed Velocity

Temperature Acceleration

Mass Weight

All types of energy All forces

Work Momentum

Pressure All field strengths

A vector is usually represented by a bold italicized symbol, for example F for force.

Free body diagrams

4

m north

distance walked7

m

displacement5m (north of east)

3

m east

5

m

Figure 1.5 Distance is a scalar, and

in this case, the distance travelled is

3 m4 m7 m. Displacement is a

vector, and here it is the hypotenuse of

the triangle (5 m).

9 Which oneof the following is a scalar quantity?

A Pressure B Impulse

C Magnetic field strength D Weight

10 Which oneof the following is a vector quantity?

A Electric power B Electrical resistance

C Electric field D Electric potential difference

Exercises

weightliftthrustdrag

lift

thrust of jets

weight

drag of air

weightnormal force

weight

normal orsupporting force

Figure 1.6 Free-body diagrams show

all the forces acting on the body. The

arrows should be drawn to represent

both the size and direction of the forces

and should always be labelled.(c) Aeroplane in level flight acceleratingto the right:

(a) Book resting on a table: (b) Car travelling at constant velocityto the left:

weightnormal forcesdriving forceresistive forces

weight

normal forces

resistive forcesdriving force

of engine




12/1412


If two or more forces are acting at the same point in space, you need to be able to

calculate the resultant, or total effective force, of the combination. The resultant is

the single force that has the same effect as the combination.

If they are not parallel, the easiest way to determine the resultant is by the

parallelogram law. This says that the resultant of two vectors acting at a point is

given by the diagonal of the parallelogram they form.

You also need to be able to resolve, or split, vectors into components or parts. A

component of a vector shows the effect in a particular direction. Usually we resolve

vectors into an x-component and ay-component.

Worked example

A force of 20 N pulls a box on a bench at an angle of 60 to the horizontal. What is

the magnitude of the force Fparallel to the bench?

Figure 1.7 When the vectors are

parallel, the resultant is found by simple

addition or subtraction.

(a) (b)

(c)

2

N 3

N

resultant5N to right

2

N 3

N

resultant1N to left

3N

3N

6N

resultantzero

10

N

6

N resultant

magnitude of resultant14

N

60

Figure 1.8 We can use a graphical

method to find the resultant accurately.

Examiners hint: You can do this is

by scale drawing using graph paper.

11 The diagram below shows a boat that is about to cross a river in a direction perpendicular to the

bank at a speed of 0.8 ms1. The current flows at 0.6 ms1in the direction shown.

The magnitude of the displacement of the boat 5 seconds after leaving the bank is

A 3 m. B 4 m. C 5 m. D 7 m.

Exercise

bank

bank

0.6

ms1

0.8

ms1

boat

y-component

x-component (F)A

B20

N

C60

Figure 1.9 Resolving into

components is the opposite process

to adding vectors and finding the

resultant.




13/1413

Solution

The string will tend to pull the box along the bench but it will also tend to pull it

upwards.

cosine 60adjacent

__________

hypotenuse

F___

20

F20 N cos 6010 N

Examiners hint: In the right-angled

triangle ABC, thex-component (F) is

adjacent to the 60 angle while the 20 N

force is the hypotenuse.

12 A force of 35 N pulls a brick on a level surface at an angle of 40 to the horizontal. The frictional

force opposing the motion is 6.8N. What is the resultant force Fparallel to the bench?

Exercise Examiners hint: Here is an example

of how notto answer a basic question:

Findx.

x

3cm

4cmHereitis

1 Which one of the following contains three fundamental units?

A Metre Kilogram Coulomb

B Second Ampere Newton

C Kilogram Ampere Kelvin

D Kelvin Coulomb Second

2 The resistive force Facting on a sphere of radius rmoving at speed vthrough a liquid is

given by

Fcvr

where cis a constant. Which of the following is a correct unit for c?

A N

B N s1

C N m2s1

D N m2s

3 Which of the following is nota unit of energy?

A W s

B W s1

C k Wh

D k g m2s2

4 The power Pdissipated in a resistor Rin which there is a current Iis given by

PI 2R

The uncertainty in the value of the resistance is10% and the uncertainty in the value

of the current is 3%. The best estimate for the uncertainty of the power dissipated is

A 6%

B 9%

C 6%

D 19%

actice questions




14/14


Here are some ideas to help you with the estimates on page 3:

1 How high is a two floor house in metres?

First we could think about how high a normal room is. When you stand up

how far is your head from the ceiling? Most adults are between 1.5 m and 2.0 m

tall, so the height of a room must be above 2.0 m and probably below 2.5 m.

If we multiply by two and add in some more for the floors and the roof then asensible value could be 7 or 8 m.

2 What is the diameter of the pupil of your eye?

This would change with the brightness of the light, but even if it were really

dark it is unlikely to be above half a centimetre or 5.0 mm. In bright sunshine

maybe it could go down to 1.0 mm so a good estimate would be between these

two diameters.

3 How many times does your heart beat in an hour when you are relaxed?

You can easily measure your pulse in a minute. When you are relaxed it willmost probably be between 60 and 80 beats per minute. To get a value for an

hour we must multiply by 60, and this gives a number between 3600 and 4800.

As an order of magnitude or ball park figure this would be 103.

4 What is the weight of an apple in newtons?

Apples come in different sizes but if you buy a kilogram how many do you get?

If the number is somewhere between 5 and 15 that would give an average mass

for each apple of around 100g which translates to a weight of approximately 1

N.

5 What is the mass of the air in your bedroom?

To estimate this you need to know the approximate density of air, which is

1.3 kg m3. Then you need an estimate of the volume of your bedroom, for

example 4 m 3 m 2.5 m, which would give 30 m3.

Then massdensity volume would give around 40 kg; maybe more than

expected.

6 What pressure do you exert on the ground standing on one foot?

For this we would use the equation pressureforce

_____

area. The force would be

your weight; if your mass is 60 kg then your weight would be 600 N. If we take

average values for the length and width of your foot as 30 cm and 10 cm, change

them to 0.3 m and 0.1 m, and multiply, then the area is 0.03 m2. Dividing 600 N

by 0.03 m2gives an answer of 20 000 Pa.

You need to practise these kinds of estimations without a calculator.

If air is that heavy then why dont

we feel it?

How does the pressure exerted

by one foot compare to blood

pressure and atmospheric

pressure?

What would happen to an

astronaut in space if their space suit

suddenly ripped open?


Pearson Baccalaureate Physics SL Chapter1

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