Physics and Physical Measurement The Realm of physics Measurement and uncertainties

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Why does that matter? Must have a consistent set of units agreed upon. (SI system) – SI has 7 fundamental units w/ lots of combinations. How far off were you? – Need an appreciation for the magnitude of things. (masses, time, distances, forces…)

1.1.2 State the ranges of magnitude of distances, masses and times that occur in the universe, from smallest to greatest. Distances Sub-nuclear particles = m Extent of the visible universe = m Distance from Earth to Moon = 3.84 x 10 5 km Radius of Earth = 6380km = 10 7 m Diameter of a nucleus = m

1.1.2 State the ranges of magnitude of distances, masses and times that occur in the universe, from smallest to greatest. Masses Rest mass of and electron = kg The universe = kg Mass of the Earth = 5.97 x kg Mass of the Moon = 7.35 x kg Mass of an electron = 9.11 x kg

1.1.2 State the ranges of magnitude of distances, masses and times that occur in the universe, from smallest to greatest. Times Passage of light across a nucleus = s Age of the universe = s Light to travel from Sun to Earth = 8min = 10 2 s Period for one orbit of Earth = 365day = 10 7 s Time between vibrations of Cesium = s

1.1.2 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: – Visible universe= m – The age of the universe= s – The total mass of the universe= kg The atom: – The diameter of an atom = m – The diameter of the nucleus = m

Upper and lower measurements Size of proton m (lower) Speed of light in a vacuum 3 x10 8 m/s Age of universe s If quarks are the fundamental unit then their mass would give us the lower limit, but they hide in protons and our best guess is kg. This is also the approximate mass of an electron at rest.

1.1.3 Stating ratios of quantities as differences of orders of magnitude m/ m= is known as a difference of five orders of magnitude. The ratio of the diameter of the hydrogen atom to its nucleus is about times or 10 5 times, or a difference of 5 orders of magnitude.

1.1.3 Stating ratios of quantities as differences of orders of magnitude Example The rest mass of a proton is about 1.67x kg. The rest mass of an electron is about 9.1x10 31 kg. How many orders of magnitude bigger is the mass of the proton than that of the electron?

1.1.3 Stating ratios of quantities as differences of orders of magnitude Example Solution 1x kg and 10x kg (1x kg) = 3 orders of magnitude Realize that the proton is not 3 times more massive it is 10 3 times more massive or 1000 times more massive.

1.1.3 Stating ratios of quantities as differences of orders of magnitude Practice 2 The length of a football pitch is about 100m. The distance from the earth to the moon is about 384x10 6 m. How many orders of magnitude larger is the distance from earth to the moon than the length of a football pitch?

1.1.3 Stating ratios of quantities as differences of orders of magnitude Practice 2 solution Football pitch = 10 2 Earth to moon = = 6 orders of mag Or 1,000,000 times larger

1.1.3 Stating ratios of quantities as differences of orders of magnitude Practice 3 The mass of the Sun is 1.99 x kg. The mass of the Earth is 5.98x10 24 kg. How many orders of magnitude more massive is the Sun than the Earth?

1.1.3 Stating ratios of quantities as differences of orders of magnitude Practice 3 Solution Sun = Earth = = 5 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 high is a two storey house in meters? – What is the diameter of your pupil? – How many times does your heart beat in an hour when you are relaxed? – What is the weight of an apple in Newtons? –

About 6m about 2-4mm / 4-8mm about beats/min about 1N

1.1.4 Estimate approximate values of everyday quantities to one or two significant figures and/or to the nearest order of magnitude. Practice 7 Estimate the thickness of a page in your book.

Fundamental Units Metermlength Kilogramkgmass Secondstime AmpereAelectric current KelvinKtemperature Molemolamount of matter Candelacdintensity of light

Mechanics and Derived Units Mechanics is the study of matter, forces, and energy. With combinations of the first three base units (m, kg, and s), all other units for mechanics can be developed. Name one not listed…. NewtonNforce or weight kg m s -2 JouleJenergy or work kg m 2 s -2 WattWpower kg m 2 s -3 PascalPapressure kg m -1 s -2

Derived Units Find the symbol, concept, and broken down base units for each of the following: Hertz Coulumb Ohm Tesla Weber Becquerel

HertzHzfrequencys -1 CoulombCElectric charge As OhmΩelectrical resistance kg m 2 s -3 A -2 TeslaTmagnetic fluxWb m -2 WeberWbmagnetic flux(T m 2 ) or kg m -2 s -2 A Becquerel Bqradioactivitys -1

HertzHzfrequencys -1 CoulombCElectric charge As OhmΩelectrical resistance kg m 2 s -3 A -2 TeslaTmagnetic fluxWb m -2 WeberWbmagnetic flux(T m 2 ) or kg m -2 s -2 A Becquerel Bqradioactivitys -1

Problems 1.Give units for the following expressed as derived and base units: a.Forceb. Kinetic energy 2.Check if these equations work by substituting units into them. a.Power= work/time or energy/time b.Power = force x velocity

Answers 1. a. N or kg m s -2 b.J or kg m 2 s a. W: J s -1 or W: (kg m 2 s -2 )s -1 or W: kg m 2 s -3 b. W: N x (m s -1 ) or W: (kg m s -2 )x (m s -1 ) or W: kg m 2 s -3

Problems 3. Which one of the following units is a unit of energy? a. eVb. W s -1 c. W m -1 d. N m s Which on of the following lists a derived unit and a fundamental unit? AAmpereSecond BCoulombKilogram CCoulombNewton DMeterkilogram

Answers 3.eV 4.B

Other Units NameSymbolConcept LiterLvolume Minute, hour, year, etc.Min, h, y, etc.Time Kilowatt-hourkWhEnergy ElectronvolteVEnergy Degrees celsius oCoCtemperature DecibeldBLoudness Unified atomic mass unitUMass of nucleon

Problem 5.Convert these units to SI: a. Yearb. 100 o C c. kWhd. eV

Modifying SI Units SI units can be modified by the use of prefixes. PrefixAbbreviationValue TeraT10 12 GigaG10 9 MegaM10 6 Kilok10 3 centic10 -2 millim10 -3 microμ10 -6 nanon10 -9 picop femtof10 -15

Problems 6.Change J to scientific notation and MJ. 7.A popular radio station has a frequency of Hz. Change this to scientific notation and MHz. 8.The average wavelength of white light is 5.0x m. What would this be in nanometers? 9. The time taken for light to cross a room is about 1 x10 -8 s. Change this into microseconds.

Answers x 10 6 J or 2.36 MJ x 10 6 Hz or 1.09 MHz nm μs

10.Estimate the speed with which human hair grows. 11.If all the people on earth were to hold hands in a straight line, how long would the line be? How many times would it wrap around the earth? 12.How many revolutions do the wheels of a car make before it is junked (wheel radius is 30cm,250,000km total)

Answers About 4 x m/s About 9 x 10 9 m, about 200 times About 10 8

Uncertainty and Error There are two types of errors: Random and systematic Random errors can be reduced by repeating measurement many times. Systematic errors can be reduced by repeating measurement using a different method or different apparatus and comparing the results.