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The realm of physics

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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)

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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

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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 …

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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 m – Instead s use 10 6 s etc

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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

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number of molecules in the sun Mass of the sun kg Chemical composition of the sun: 25% He and 75% H 100% of H 2 Molar mass of matter of sun 2 g mol -1 ≈ kg mol -1 Avogadro’s number 6x10 23 mol -1 ≈ mol -1

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

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

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Interactions TypeAffects toRelative strength to gravity Distance Gravitationalall bodies with mass 1∞ Weak Nuclear Forceall known fermions (sub- nuclear particles) −18 Electromagneticelectric charges ∞ Strong Nuclear Forceprotons and neutrons (quarks) −15

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Differences of orders Using ranges of magnitude makes it easy to compare quantities Example: – Diameter of Sun is 10 9 m and diameter of Earth is 10 7 m – How big is the difference between these diameters ? – 10 9 /10 7 =10 2 (100) times or difference is of 2 orders of magnitude Calculate the difference of orders between – mass of electron ( kg) and mass of universe ( kg) – extent of the visible universe: m and diameter of neutrino ( m)

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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.

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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

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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? – ? – ? – ?

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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

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fundamental units in the SI system NameSymbolConcept meter (or metre)mlength kilogramkgmass secondstime ampereAelectric current kelvinKtemperature molemolamount of matter candelacdintensity of light We can develop all other units with combination of these fundamental units

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Examples of units

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SI PREFIXES PREFIXABBRE-VIATIONVALUEEXAMPLE ExaE m = 1 Em TeraT m = 1 Tm GigaG m = 1 Gm MegaM m = 1 Mm Kilok m = 1 km Hectoh m = 1 hm Decada m = 1 dam SI1= m detsid ,1 m = 1 dm centic ,01 m = 1 cm millim ,001 m = 1 mm microμ m = 1 μm nanon m = 1 nm pikop m = 1 pm femtoF m = 1 fm

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HOW TO transform units

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UNCERTAINITIES IN MEASUREMENTS

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UNCERTAINITY in measurement There are three sources of uncertainity and errors in mesurement: I.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 II.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.

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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

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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

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

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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.

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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...?

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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 = – 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.

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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 cm 2 = 1x10 3 cm 2 (1 sign. fig) Sample2 – a=3.35 mm (3 sign. fig) – b=51 mm (2 sign. fig) – A = 3.35 x 51 = mm 2 = 1,7x10 2 mm 2 (2 sign. fig)

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UNCERTAINITIES IN CALCULATED RESULTS

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To calculate fractional (or pe

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CALCULATE

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