Topic 1 – Physics and Physical measurement Use the syllabus particularly when studying for examinations
Order of magnitude We can express small and large numbers using exponential notation The number of atoms in 12g of carbon is approximately 600000000000000000000000 This can be written as 6 x 1023
Order of magnitude We can say to the nearest order of magnitude (nearest power of 10) that the number of atoms in 12g of carbon is 1024 (6 x 1023 is 1 x 1024 to one significant figure)
Small numbers Similarly the length of a virus is 2.3 x 10-8 m. We can say to the nearest order of magnitude the length of a virus is 10-8 m.
Size The smallest objects that you need to consider in IB physics are subatomic particles (protons and neutrons). These have a size (to the nearest order of magnitude) of 10-15 m.
Size The largest object that you need to consider in IB physics is the Universe. The Universe has a size (to the nearest order of magnitude) of 1025 m.
Mass The lightest particle you have to consider is the electron. What do you think the mass of the electron is? 10-30 kg! (0.000000000000000000000000000001 kg)
Mass The Universe is the largest object you have to consider. It has a mass of …. 1050 kg (100000000000000000000000000000000000000000000000000 kg)
Time The smallest time interval you need to know is the time it takes light to travel across a nucleus. Can you estimate it? (Time = distance/speed) 10-24 seconds
Time The longest time ? The age of the universe. 12 -14 billion years 1018 seconds
You have to LEARN THESE! Size 10-15 m to 1025 m (subatomic particles to the extent of the visible universe) Mass 10-30 kg to 1050 kg (mass of electron to the mass of the Universe) Time 10-23 s to 1018 s (time for light to cross a nucleus to the age of the Universe)
A common ratio – Learn this! Hydrogen atom≈ 10-10 m Proton ≈ 10-15 m Ratio of diameter of a hydrogen atom to its nucleus = 10-10/10-15 = 105
Estimation For IB you have to be able to make order of magnitude estimates.
Estimate the following: (to the nearest order of magnitude) • The mass of an apple
Estimate the following: (to the nearest order of magnitude) • The mass of an apple • The number of times a human heart beats in a lifetime.
Estimate the following: (to the nearest order of magnitude) • The mass of an apple • The number of times a human heart beats in a lifetime. • The speed a cockroach can run. A fast South American one!
Estimate the following: (to the nearest order of magnitude) • The mass of an apple 10-1 kg • The number of times a human heart beats in a lifetime. • The speed a cockroach can run.
Estimate the following: (to the nearest order of magnitude) • The mass of an apple 10-1 kg • The number of times a human heart beats in a lifetime. 70x60x24x365x70=109 • The speed a cockroach can run.
Estimate the following: (to the nearest order of magnitude) • The mass of an apple 10-1 kg • The number of times a human heart beats in a lifetime. 70x60x24x365x70=109 • The speed a cockroach can run. 100 m.s-1
The SI system of units There are seven fundamental base units which are clearly defined and on which all other derived units are based: You need to know these, but not their definitions.
The metre • This is the unit of distance. It is the distance traveled by light in a vacuum in a time of 1/299792458 seconds.
The second • This is the unit of time. A second is the duration of 9192631770 full oscillations of the electromagnetic radiation emitted in a transition between two hyperfine energy levels in the ground state of a caesium-133 atom.
The ampere • This is the unit of electrical current. It is defined as that current which, when flowing in two parallel conductors 1 m apart, produces a force of 2 x 10-7 N on a length of 1 m of the conductors. Note that the Coulomb is NOT a base unit.
The kelvin • This is the unit of temperature. It is 1/273.16 of the thermodynamic temperature of the triple point of water.
The mole • One mole of a substance contains as many molecules as there are atoms in 12 g of carbon-12. This special number of molecules is called Avogadro’s number and equals 6.02 x 1023.
The candela (not used in IB) • This is the unit of luminous intensity. It is the intensity of a source of frequency 5.40 x 1014 Hz emitting 1/683 W per steradian.
The kilogram • This is the unit of mass. It is the mass of a certain quantity of a platinum-iridium alloy kept at the Bureau International des Poids et Mesures in France. THE kilogram!
SI Base Units You HAVE to learn these! Note: No Newton or Coulomb
Derived units Other physical quantities have units that are combinations of the fundamental units. Speed = distance/time = m.s-1 Acceleration = m.s-2 Force = mass x acceleration = kg.m.s-2 (called a Newton) (note in IB we write m.s-1 rather than m/s)
Some important derived units (learn these!) 1 N = kg.m.s-2 (F = ma) 1 J = kg.m2.s-2 (W = Force x distance) 1 W = kg.m2.s-3 (Power = energy/time) Guess what
Prefixes Don’t worry! These will all be in the data book you have for the exam. Power Prefix Symbol Power Prefix Symbol 10-18 atto a 101 deka da 10-15 femto f 102 hecto h 10-12 pico p 103 kilo k 10-9 nano n 106 mega M 10-6 micro μ 109 giga G 10-3 milli m 1012 tera T 10-2 centi c 1015 peta P 10-1 deci d 1018 exa E
Examples 3.3 mA = 3.3 x 10-3 A 545 nm = 545 x 10-9 m = 5.45 x 10-7 m 2.34 MW = 2.34 x 106 W
Checking equations For example, the period of a pendulum is given by T = 2π l where l is the length in metres g and g is the acceleration due to gravity. In units m = s2 = s m.s-2
Errors/Uncertainties In EVERY measurement (as opposed to simply counting) there is an uncertainty in the measurement. This is sometimes determined by the apparatus you're using, sometimes by the nature of the measurement itself.
Individual measurements When using an analogue scale, the uncertainty is plus or minus half the smallest scale division. (in a best case scenario!) 4.20 ± 0.05 cm
Individual measurements When using an analogue scale, the uncertainty is plus or minus half the smallest scale division. (in a best case scenario!) 22.0 ± 0.5 V
Individual measurements When using a digital scale, the uncertainty is plus or minus the smallest unit shown. 19.16 ± 0.01 V
Repeated measurements When we take repeated measurements and find an average, we can estimate the uncertainty by finding the difference between the highest and lowest measurement and divide by two.
Repeated measurements - Example Pascal measured the length of 5 supposedly identical tables. He got the following results; 1560 mm, 1565 mm, 1558 mm, 1567 mm , 1558 mm Average value = 1563 mm Uncertainty = (1567 – 1558)/2 = 4.5 mm Length of table = 1563 ± 5 mm This means the actual length is anywhere between 1558 and 1568 mm
Precision and Accuracy The same thing?
Precision A man’s height was measured several times using a laser device. All the measurements were very similar and the height was found to be 184.34 ± 0.01 cm This is a precise result (high number of significant figures, small range of measurements)
Accuracy Height of man = 184.34 ± 0.01cm This is a precise result, but not accurate (near the “real value”) because the man still had his shoes on.
Accuracy The man then took his shoes off and his height was measured using a ruler to the nearest centimetre. Height = 182 ± 1 cm This is accurate (near the real value) but not precise (only 3 significant figures)
Precise and accurate The man’s height was then measured without his socks on using the laser device. Height = 182.23 ± 0.01 cm This is precise (high number of significant figures) AND accurate (near the real value)
Precision and Accuracy • Precise – High number of significent figures. Repeated measurements are similar • Accurate – Near to the “real” value
Random errors/uncertainties Some measurements do vary randomly. Some are bigger than the actual/real value, some are smaller. This is called a random uncertainty. Finding an average can produce a more reliable result in this case.
Systematic/zero errors Sometimes all measurements are bigger or smaller than they should be. This is called a systematic error/uncertainty.
Systematic/zero errors This is normally caused by not measuring from zero. For example when you all measured Mr Porter’s height without taking his shoes off! For this reason they are also known as zero errors/uncertainties. Finding an average doesn’t help.