Topic 1 – Physics and physical measurement Use the syllabus and this REVISION POWERPOINT when studying for examinations

Order of magnitude The number of atoms in 12g of carbon is approximately We can say to the nearest order of magnitude that the number of atoms in 12g of carbon is (6 x is 1 x to one significant figure) This can be written as 6 x 10 23

Small numbers Similarly the length of a virus is 2.3 x m. We can say to the nearest order of magnitude the length of a virus is m.

Ranges of sizes, masses and times You need to have an idea of the ranges of sizes, masses and times that occur in the universe.

You have to LEARN these! Size m to m (subatomic particles to the extent of the visible universe) Mass kg to kg (electron to the mass of the Universe) Time s to s (time for light to cross a nucleus to the age of the Universe)

A common ratio – Learn this! Hydrogen atom ≈ m Proton ≈ m Ratio of diameter of a hydrogen atom to its nucleus = / = 10 5

Estimation For IB you have to be able to make order of magnitude estimates.

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

SI Base Units QuantityUnit distancemetre timesecond currentampere temperaturekelvin quantity of substancemole luminous intensitycandela masskilogram Can you copy this please? 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.m 2.s -2 (W = Force x distance) 1 W = kg.m 2.s -3 (Power = energy/time) Guess what

Prefixes PowerPrefixSymbolPowerPrefix Symbol attoa10 1 dekada femtof10 2 hectoh picop10 3 kilok nanon10 6 megaM microμ10 9 gigaG millim10 12 teraT centic10 15 petaP decid10 18 exaE Don’t worry! These will all be in the formula book you have for the exam.

Examples 3.3 mA = 3.3 x A 545 nm = 545 x m = 5.45 x m 2.34 MW = 2.34 x 10 6 W

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!) 22.0 ± 0.5 V

Individual measurements When using a digital scale, the uncertainty is plus or minus the smallest unit shown ± 0.01 V

Repeated measurements When we take repeated measurements and find an average, we can find the uncertainty by finding the difference between the average and the measurement that is furthest from the average.

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 ± 0.01 cm This is a precise result (high number of significant figures, small range of measurements)

Accuracy Height of man = ± 0.01cm This is a precise result, but not accurate (near the “real value”) because the man still had his shoes on.

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 or “zero” 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.

Uncertainties If the average height of students at BSH is 1.23 ± 0.01 m We say the absolute uncertainty is 0.01 m The fractional uncertainty is 0.01/1.23 = The percentage uncertainty is 0.01/1.23 x 100 = 0.8%

Combining uncertainties When we find the volume of a block, we have to multiply the length by the width by the height. Because each measurement has an uncertainty, the uncertainty increases when we multiply the measurements together.

Combining uncertainties When multiplying (or dividing) quantities, to find the resultant uncertainty we have to add the percentage (or fractibnal) uncertainties of the quantities we are multiplying.

Combining uncertainties Example: A block has a length of 10.0 ± 0.1 cm, width 5.0 ± 0.1 cm and height 6.0 ± 0.1 cm. Volume = 10.0 x 5.0 x 6.0 = 300 cm 3 % uncertainty in length = 0.1/10 x 100 = 1% % uncertainty in width = 0.1/5 x 100 = 2 % % uncertainty in height = 0.1/6 x 100 = 1.7 % Uncertainty in volume = 1% + 2% + 1.7% = 4.7% (4.7% of 300 = 14) Volume = 300 ± 14 cm 3 This means the actual volume could be anywhere between 286 and 314 cm 3

Combining uncertainties When adding (or subtracting) quantities, to find the resultant uncertainty we have to add the absolute uncertainties of the quantities we are multiplying.

Combining uncertainties One basketball player has a height of 196 ± 1 cm and the other has a height of 152 ± 1 cm. What is the difference in their heights? Difference = 44 ± 2 cm

Who’s going to win Bush = 48 ± 5 % = between 43 and 53 % Gore = 52 ± 5 % = between 47 and 57 % We can’t say! (If the uncertainty is greater than the difference)

Error bars X = 0.6 ± 0.1 Y = 0.5 ± 0.1

Gradients

Minimum gradient

Maximum gradient

y = mx + c

E k = ½mv 2

y = mx + c E k = ½mv 2 E k (J) V 2 (m 2.s -2 )

Period of a pendulum T = 2π l g

Period of a pendulum T = 2π l g T (s) l ½ (m ½ )

Period of a pendulum T = 2π l g T 2 (s) l (m)