The realm of physics

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)

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

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 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

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: 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

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

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

UNCERTAINITIES IN MEASUREMENTS

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.

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 ∆ 𝐀/𝐁 = 𝐁∆𝐀+𝐀∆𝐁 𝐁 𝟐 Absolute mistake in powering and rooting: ∆ 𝑨 𝒏 =𝐧𝐀∆𝐀 ∆ 𝒏 𝑨 = 𝟏 𝒏 𝐀∆𝐀

UNCERTAINITIES IN CALCULATED RESULTS To calculate fractional (or pe

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

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. 44 12 =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 830.0 ± 0.05 g and 𝝆= 𝐦 𝐕 and 𝑽= 𝒂 𝟑