1. The realm of physics

2. What is Physics?
Physics is the study of fundamental interactions of our universe.
There are 4 types of interactions:
Gravitational
Strong Nuclear Force
Weak Nuclear Force
Electromagnetic
since 1972 scientists joined together into Electroweak interaction Weak Nuclear Force and Electromagnetic interaction
At home: compare different interactions (between what kind of bodies they interact, how strong/weak they are, how far they interact)

3. Measuring Define measuring: What do the physicists measure?
Measuring is the process of determining the ratio of a physical quantity to a unit of measurement.
What do the physicists measure?
Length,
Mass,
Time,
Electric current,
Temperature,
Etc. etc

4. How to measure?
For measuring the length of the body you must compare how many times the unit of length (1 meter) is smaller or bigger than the length of the body we measure.
For measuring the weight of the body …

5. Range of magnitude
For better understanding the magnitude of different quantities (measurements), we write them to the nearest power of ten (rounding up or down as appropriate)
Example:
Instead 0.003m we use or 10-3m
Instead s use 106s etc

6. Devise rough estimate of the number of molecules in the sun
Data we need:
mass of the sun
chemical composition of sun
Molar mass of matter of the sun
How many molecules are in 1 mol of matter

7. number of molecules in the sun
Mass of the sun 1030 kg
Chemical composition of the sun: 25% He and 75% H  100% of H2
Molar mass of matter of sun 2 g mol-1 ≈ 10-3 kg mol-1
Avogadro’s number 6x1023 mol-1 ≈ 1024 mol-1

8. How big or how small numbers we need?
Video “Powers of ten”
State the ranges of magnitude of
distances,
masses and
times
that occur in the universe, from smallest to greatest.

9. Range of magnitudes of quantities in our universe
Distance
Planck length 10-35m (theoretical value – smallest part of space in some modern theories)
diameter of sub-nuclear particles (quarks, neutrinos):  m
extent of the visible universe: 10+25 m
Mass
mass of electron neutrino: less than kg (mass is not certified)
mass of electron: 10-30 kg
mass of universe: 10+50 kg
Time
passage of light across a Planck length: 10-43s
passage of light across a nucleus: 10-23s
age of the universe : 10+18 s

10. Interactions 1 ∞ 1025 10−18 1036 1038 10−15 Type Affects to
Relative strength to gravity
Distance
Gravitational
all bodies with mass 1 ∞
Weak Nuclear Force
all known fermions (sub-nuclear particles)
1025
10−18
Electromagnetic
electric charges
1036
Strong Nuclear Force
protons and neutrons (quarks)
1038
10−15

11. Differences of orders
Using ranges of magnitude makes it easy to compare quantities
Example:
Diameter of Sun is 109m and diameter of Earth is 107m
How big is the difference between these diameters ?
109/107=102 (100) times or difference is of 2 orders of magnitude
Calculate the difference of orders between
mass of electron (10-30 kg) and mass of universe (10+50 kg)
extent of the visible universe: 10+25 m and diameter of neutrino (10 -15 m)

12. APPROXIMATE VALUES
Usually we don’t need to use very precise values of quantities in our everyday life.
Example:
distance between school and home is m or 6000m
or bus drives the distance between two stops in 5.487min or 5.5 min
We must be able to estimate approximate values of everyday quantities to one ore two significant numbers.

13. SIGNIFANT figures
The amount of significant figures includes all digits except:
leading and trailing zeros (such as (2 sig. figures) and (2 sig. figures)) which serve only as placeholders to indicate the scale of the number.
extra “artificial” digits produced when calculating to a greater accuracy than that of the original data

14. Rules for identifying significant figures
All non-zero digits are considered significant
such as 14 (2 sig. figures) and (4 sig. figures).
Zeros placed in between two non-zero digits
such as 104 (3 sig. figures) and 1004 (4 sig. figures)
Trailing zeros in a number containing a decimal point are significant
such as (5 sig. figures)
How many significant numbers? ? ? ?

15. Expressing significant figures as orders of magnitude
To represent a number using only the significant digits can easily be done by expressing it’s order of magnitude. This removes all leading and trailing zeros which are not significant.
Example:
= 2,340x10-5
= 2,3400x10-4
= 2,34x10-6

16. fundamental units in the SI system
Name
Symbol
Concept
meter (or metre) m
length
kilogram kg
mass
second s
time
ampere A
electric current
kelvin K
temperature
mole
mol
amount of matter
candela cd
intensity of light
We can develop all other units with combination of these fundamental units

17. Examples of units Density: Acceleration: Force:
𝐝𝐞𝐧𝐬𝐢𝐭𝐲= 𝐦𝐚𝐬𝐬 𝐯𝐨𝐥𝐮𝐦𝐞 → 𝐤𝐠 𝐦 𝟑 =𝐤𝐠 𝐦 −𝟑
Acceleration:
𝐚𝐜𝐜𝐞𝐥𝐞𝐫𝐚𝐭𝐢𝐨𝐧= 𝐬𝐩𝐞𝐞𝐝 𝐭𝐢𝐦𝐞 = 𝐝𝐢𝐬𝐭𝐚𝐧𝐜𝐞 𝐭𝐢𝐦𝐞 𝐭𝐢𝐦𝐞 → 𝐦 𝐬 𝐬 =𝐦 𝐬 −𝟐
Force:
𝐟𝐨𝐫𝐜𝐞=𝐦𝐚𝐬𝐬 𝐱 𝐚𝐜𝐜𝐞𝐥𝐞𝐫𝐚𝐭𝐢𝐨𝐧 → ?
If the concepts becomes too complex, we gige them new units:
Force unit called N (newton) etc
These units are derived units

18. SI PREFIXES PREFIX ABBRE-VIATION VALUE EXAMPLE Exa E 1015
1015 m = 1 Em
Tera T
1012
1012 m = 1 Tm
Giga G
109
109 m = 1 Gm
Mega M
106
106 m = 1 Mm
Kilo k
103
1000 m = 1 km
Hecto h
102
100 m = 1 hm
Deca da
101
10 m = 1 dam SI
1=100
1 m
detsi d
10-1
0,1 m = 1 dm
centi c
10-2
0,01 m = 1 cm
milli m
10-3
0,001 m = 1 mm
micro μ
10-6
10-6 m = 1 μm
nano n
10-9
10-9 m = 1 nm
piko p
10-12
10-12 m = 1 pm
femto F
10-15
10-15 m = 1 fm

19. HOW TO transform units Transform 5500 metres to kilometres
there are 1000 metres in 1 kilometre (103 m/km or 103 m km-1)
to transform metres to kilometres we calculate
5.5×103 𝑚 103 𝑚 𝑘𝑚 −1 =5.5 km
Transform 3.2 kilometres to metres
there are 10-3 metres in 1 kilometre (10-3 km/m or 10-3 km m-1)
3.2 𝑘𝑚 10 −3 𝑘𝑚 𝑚 −1 =3200 km

20. UNCERTAINITIES IN MEASUREMENTS

21. UNCERTAINITY in measurement
There are three sources of uncertainity and errors in mesurement:
Uncertainity of gauges (instruments)
scale partitions of instruments are not exactly equal
pointers (and scale partitions) of gauges have certain width what makes measuring uncertain
volatility of sensors makes measuring uncertain
rounding in digital instruments makes measuring uncertain
Measurement procedures
errors in reading scale
parallax in reading scale
distruption of reading procedure or instruments
imperfect methods of measuring
Measured object itself
Object never stays exactly the same. It changes and makes measuring uncertain.

22. RANDOM AND SYSTEMATIC ERRORS
A RANDOM ERROR, is an error which affects a reading at random. Sources of random errors include:
The observer being less than perfect
The readability of the equipment
External effects on the observed item
A SYSTEMATIC ERROR, is an error which occurs at each reading. Sources of systematic errors include:
The observer being less than perfect in the same way every time
An instrument with a zero offset error
An instrument that is improperly calibrated

23. How precise? How accurate?
During a lots of measurings the same quantity we get quite lot of different measurements.
Due the measuring errors, some of these measurements are more, some less close to true (reference) value of measured quantity
We can draw the graph of measurements –graph shows number of measurements witch have the same value

24. Wider graph makes measuring less precise
Getting peak of graph closer the reference value makes measuring more accurate

25. PRECISION AND ACCURACY
A measurement is said to be accurate if it has little systematic errors.
A measurement is said to be precise if it has little random errors.

27. UNCERTAINITIES IN measurements
When marking the absolute uncertainty in a piece of data, we simply add ± 1 (or 0.1 or 0.05 eg. one significant figure) of the smallest significant figure:
Samples:
l = 3.21 ± 0.01  the best value is 3.21m, the lowest value is 3.20m and the highest value is 3.22m
m = ± g  the best value is 0.009g, the lowest value is 0.004g and the highest value is 0.014g
t = 1.2  ± 0.2 s  the best value is ..., the lowest value is ... and the highest value is ...?
V = 12 ± 1V  the best value is ..., the lowest value is ... and the highest value is ...?

28. UNCERTAINITIES IN measurements
To calculate the fractional uncertainty of a piece of data we simply divide the uncertainty by the value of the data.
Samples:
l = 3.21 ± 0.01  fractional uncertainity is 0.01/3.21 =
m = ± g  fractional uncertainity is 0.005/0.009 = 0.556
t = 1.2  ± 0.2 s  fractional uncertainity is ...?
V = 12 ± 1V  fractional uncertainity is ...?
To calculate the percentage uncertainty of a piece of data we simply multiply the fractional uncertainty by 100.

29. NUMBERS OF SIGNIFICANT FIGURES IN CALCULATED RESULTS
The number of significant figures in a result should mirror the precision of the input data.
When we dividing and multiplying, the number of significant figures must not exceed that of the least precise value.
Sample1:
Area of rectangle = width x length (A = axb)
a=25 cm (2 sign. fig);
b=40cm (1 sign. fig);
A = 25 x 40 = 1000 cm2 = 1x103 cm2 (1 sign. fig)
Sample2
a=3.35 mm (3 sign. fig)
b=51 mm (2 sign. fig)
A = 3.35 x 51 = mm2 = 1,7x102 mm2 (2 sign. fig)

30. UNCERTAINITIES IN CALCULATED RESULTS
A=A±ΔA and B=B±ΔB are the measurements with absolute mistakes
Absolute mistake in compounding and subtraction:
∆ 𝐀±𝐁 =∆𝐀+∆𝐁
Absolute mistake in multiplication and dividing:
∆ 𝐀 𝐱 𝐁 =𝐁∆𝐀+𝐀∆𝐁
∆ 𝐀/𝐁 = 𝐁∆𝐀+𝐀∆𝐁 𝐁 𝟐
Absolute mistake in powering and rooting:
∆ 𝑨 𝒏 =𝐧𝐀∆𝐀
∆ 𝒏 𝑨 = 𝟏 𝒏 𝐀∆𝐀

31. UNCERTAINITIES IN CALCULATED RESULTS
To calculate fractional (or pe

32. 𝒗= 𝒔 𝒕 if it moved 300 ± 5 meters in 25.0 ± 0.5 seconds Calculate:
the best value for the speed of the car,
the highest and lowest values for the speed of the car
absolute mistake and fractional uncertainity of the speed of the car,
if it moved 300 ± 5 meters in 25.0 ± 0.5 seconds
𝒗= 𝒔 𝒕

33. 𝒗= 𝒔 𝒕 The best value: 𝑣= 300𝑚 25𝑠 =12 m s −1
Highest value 𝑣= 305𝑚 24.5𝑠 =12.4 m s −1
Lowest value 𝑣= 295𝑚 25.5𝑠 =11.6 m s −1
Absolute mistake: ∆𝑣= 𝑡∆𝑠+𝑠∆𝑡 𝑡 2 = 25s∙5m+300m∙0.5s (25x25) s 2 =0.44m s −1
Fractional uncertainity: ∆𝑣 𝑣 = =0.037=0.037∙100%=3.7%

34. CALCULATE
Calculate the best, highest and lowest values of resistance of the conductor, absolute mistake and fractional uncertainity of resistance, if the electric current is I=2.5±0.25A, voltage is V=10±0.5V and 𝐈= 𝐕 𝐑
Calculate the best, highest and lowest values of density of material of the cube, absolute mistake and fractional uncertainity of density, if the edge length of cube is 3.00±0.25 cm and the mass of the cube is ± 0.05 g and 𝝆= 𝐦 𝐕 and 𝑽= 𝒂 𝟑