Transcript The realm of physics

The realm of physics
What is Physics?
• Physics is the study of fundamental interactions of
our universe.
• There are 4 types of interactions:
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–
–
–
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)
Measuring
• Define measuring:
– 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
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 …
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 2 350 000s use 106s etc
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
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
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.
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): 10 -15 m
– extent of the visible universe: 10+25 m
• Mass
– mass of electron neutrino: less than 10-36 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
Interactions
Type
Affects to
Relative
strength to
gravity
Distance
Gravitational
all bodies with
mass
1
∞
Weak Nuclear Force
all known
fermions (subnuclear
particles)
1025
10−18
Electromagnetic
electric
charges
1036
∞
Strong Nuclear Force
protons and
neutrons
(quarks)
1038
10−15
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)
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 5873.5m 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.
SIGNIFANT figures
• The amount of significant figures includes all
digits except:
– leading and trailing zeros (such as 0.0024 (2 sig.
figures) and 24000 (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
Rules for identifying significant figures
• All non-zero digits are considered significant
– such as 14 (2 sig. figures) and 12.34 (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 2.3400 (5 sig. figures)
• How many significant numbers?
– 0.00002340?
– 0.00023400?
– 0.00000234?
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:
– 0.00002340 = 2,340x10-5
– 0.00023400 = 2,3400x10-4
– 0.00000234 = 2,34x10-6
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
Examples of units
• Density:
– 𝐝𝐞𝐧𝐬𝐢𝐭𝐲 =
• Acceleration:
𝐦𝐚𝐬𝐬
𝐯𝐨𝐥𝐮𝐦𝐞
– 𝐚𝐜𝐜𝐞𝐥𝐞𝐫𝐚𝐭𝐢𝐨𝐧 =
• Force:
→
𝐤𝐠
𝐦𝟑
𝐬𝐩𝐞𝐞𝐝
𝐭𝐢𝐦𝐞
= 𝐤𝐠 𝐦−𝟑
=
𝐝𝐢𝐬𝐭𝐚𝐧𝐜𝐞
𝐭𝐢𝐦𝐞
𝐭𝐢𝐦𝐞
→
𝐦
𝐬
𝐬
= 𝐦 𝐬 −𝟐
– 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
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
1=100
1m
SI
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
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)
– to transform metres to kilometres we calculate
–
3.2 𝑘𝑚
10−3 𝑘𝑚 𝑚−1
= 3200 km
UNCERTAINITIES IN
MEASUREMENTS
UNCERTAINITY in measurement
• There are three sources of uncertainity and errors in
mesurement:
I. Uncertainity of gauges (instruments)
–
–
–
–
II.
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
III. Measured object itself
–
Object never stays exactly the same. It changes and makes
measuring uncertain.
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
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
• Wider graph makes measuring less precise
• Getting peak of graph closer the reference
value makes measuring more accurate
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.
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 = 0.009 ± 0.005 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 ...?
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 =
0.00312
– m = 0.009 ± 0.005 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.
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 = 170.85 mm2 = 1,7x102 mm2 (2 sign. fig)
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
𝐁∆𝐀 + 𝐀∆𝐁
∆ 𝐀/𝐁 =
𝐁𝟐
Absolute mistake in powering and rooting:
∆ 𝑨𝒏 = 𝐧𝐀∆𝐀
𝟏
𝒏
∆ 𝑨 = 𝐀∆𝐀
𝒏
UNCERTAINITIES IN CALCULATED
RESULTS
• To calculate fractional (or pe
• 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
𝒔
𝒗=
𝒕
𝒔
𝒗=
𝒕
• The best value: 𝑣 =
• Highest value 𝑣 =
• Lowest value 𝑣 =
300𝑚
25𝑠
305𝑚
24.5𝑠
= 12 ms −1
= 12.4 ms −1
295𝑚
25.5𝑠
= 11.6 ms−1
• Absolute mistake: ∆𝑣 =
• Fractional uncertainity:
𝑡∆𝑠+𝑠∆𝑡
∆𝑣
𝑣
𝑡2
=
=
0.44
12
25s∙5m+300m∙0.5s
(25x25)s2
= 0.44ms −1
= 0.037 = 0.037 ∙ 100% = 3.7%
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
𝐦
830.0 ± 0.05 g and 𝝆 = and 𝑽 = 𝒂𝟑
𝐕