Physics and Physical Measurement

1. Physics and Physical Measurement The Realm of physics Measurement and uncertainties

2. The Realm of Physics • Range of magnitudes of quantities in our universe: • Visible universe= 1025 m • The age of the universe= 1018 s • The total mass of the universe= 1050 kg • The atom: • The diameter of an atom = 10-10 m • The diameter of the nucleus = 10-15 m

3. Upper and lower measurements • Planck length 10-35 m (lower) • Speed of light in a vacuum 3 x108 m/s • Time = distance/ speed • Time= 10-35 m/ 108 m/s • Time= 10-43 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 10-30 kg. This is also the approximate mass of an electron at rest.

4. Stating ratios as differences in magnitude • 10-10m/ 10-15 m= 105 • 105 is known as a difference of five orders of magnitude. What is the order of magnitude of the diameter of a proton? A. 10-12 m B. 10-15 m C. 10-18 m

5. Estimating Approximate Values • Estimate the value of these everyday quantities to one or two significant figures. • 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?

6. Fundamental Units • Meter 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

7. 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. • Newton N force or weight kg m s-2 • Joule J energy or work kg m2 s-2 • Watt W power kg m2 s-3 • Pascal Pa pressure kg m-1 s-2

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

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

10. Answers 1. a. N or kg m s-2 • J or kg m2 s-2 2. a. W: J s-1 or W: (kg m2 s-2 )s-1 or W: kg m2 s-3 b. W: N x (m s-1 ) or W: (kg m s-2 )x (m s-1 ) or W: kg m2 s-3

11. Problems 3. Which one of the following units is a unit of energy? a. eV b. W s-1 c. W m-1 d. N m s-1 4. Which on of the following lists a derived unit and a fundamental unit?

12. Answers • eV • B

13. Other Units

14. Problem • Convert these units to SI: a. Year b. 100 oC c. kWh d. eV

15. Modifying SI Units • SI units can be modified by the use of prefixes.

16. Problems • Change 2360000J to scientific notation and MJ. • A popular radio station has a frequency of 1090000Hz. Change this to scientific notation and MHz. • The average wavelength of white light is 5.0x 10-7 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.

17. Answers • 2.36 x 106 J or 2.36 MJ • 1.09 x 106 Hz or 1.09 MHz • 500 nm • 0.01 μs

18. 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.