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Topic 1 – Physics and Physical measurement Use the syllabus particularly when studying for examinations

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Ranges of sizes, masses and times

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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 10 23

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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 10 24 (6 x 10 23 is 1 x 10 24 to one significant figure)

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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.

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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.

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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 10 25 m.

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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)

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Mass The Universe is the largest object you have to consider. It has a mass of …. 10 50 kg (100000000000000000000000000000000000000000000000000 kg)

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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

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Time The longest time ? The age of the universe. 12 -14 billion years 10 18 seconds

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You have to LEARN THESE! Size 10 -15 m to 10 25 m (subatomic particles to the extent of the visible universe) Mass 10 -30 kg to 10 50 kg (mass of electron to the mass of the Universe) Time 10 -23 s to 10 18 s (time for light to cross a nucleus to the age of the Universe)

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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 = 10 5

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

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Estimate the following: 1.The mass of an apple (to the nearest order of magnitude)

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Estimate the following: 1.The mass of an apple 2.The number of times a human heart beats in a lifetime. (to the nearest order of magnitude)

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Estimate the following: 1.The mass of an apple 2.The number of times a human heart beats in a lifetime. 3.The speed a cockroach can run. (to the nearest order of magnitude) A fast South American one!

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Estimate the following: 1.The mass of an apple 10 -1 kg 2.The number of times a human heart beats in a lifetime. 3.The speed a cockroach can run. (to the nearest order of magnitude)

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Estimate the following: 1.The mass of an apple 10 -1 kg 2.The number of times a human heart beats in a lifetime. 70x60x24x365x70=10 9 3.The speed a cockroach can run. (to the nearest order of magnitude)

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Estimate the following: 1.The mass of an apple 10 -1 kg 2.The number of times a human heart beats in a lifetime. 70x60x24x365x70=10 9 3.The speed a cockroach can run. 10 0 m.s -1 (to the nearest order of magnitude)

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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.

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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.

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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.

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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.

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The kelvin This is the unit of temperature. It is 1/273.16 of the thermodynamic temperature of the triple point of water.

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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 Avogadros number and equals 6.02 x 10 23.

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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 10 14 Hz emitting 1/683 W per steradian.

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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!

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SI Base Units QuantityUnit distancemetre timesecond currentampere temperaturekelvin quantity of substancemole luminous intensitycandela masskilogram You HAVE to learn these! Note: No Newton or Coulomb

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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)

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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

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Prefixes PowerPrefixSymbolPowerPrefixSymbol 10 -18 attoa10 1 dekada 10 -15 femtof10 2 hectoh 10 -12 picop10 3 kilok 10 -9 nanon10 6 megaM 10 -6 microμ10 9 gigaG 10 -3 millim10 12 teraT 10 -2 centic10 15 petaP 10 -1 decid10 18 exaE Dont worry! These will all be in the data book you have for the exam.

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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 10 6 W

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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= s 2 = s m.s -2

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Errors/Uncertainties

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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.

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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

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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

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Individual measurements When using a digital scale, the uncertainty is plus or minus the smallest unit shown. 19.16 ± 0.01 V

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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.

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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

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Precision and Accuracy The same thing?

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Precision A mans 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)

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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.

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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)

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Precise and accurate The mans 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)

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Precision and Accuracy Precise – High number of significent figures. Repeated measurements are similar Accurate – Near to the real value

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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.

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Systematic/zero errors Sometimes all measurements are bigger or smaller than they should be. This is called a systematic error/uncertainty.

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Systematic/zero errors This is normally caused by not measuring from zero. For example when you all measured Mr Brockmans height without taking his shoes off! For this reason they are also known as zero errors/uncertainties. Finding an average doesnt help.

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Uncertainties In the example with the table, we found the length of the table to be 1563 ± 5 mm We say the absolute uncertainty is 5 mm The fractional uncertainty is 5/1563 = 0.003 The percentage uncertainty is 5/1563 x 100 = 0.3%

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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.

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

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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

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

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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

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

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Gradients

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Minimum gradient

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Maximum gradient

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y = mx + c

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Hookes law F = kx F (N) x (m)

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

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Which of the following is the odd one out? Mass Speed Force Temperature Distance Elephant DO NOW!

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Which of the following is the odd one out? Mass Speed Force Temperature Distance Elephant DO NOW!

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Scalars Scalar quantities have a magnitude (size) only. For example: Temperature, mass, distance, speed, energy.

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Vectors Vector quantities have a magnitude (size) and direction. For example: Force, acceleration, displacement, velocity, momentum.

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Representing vectors Vectors can be represented by arrows. The length of the arrow indicates the magnitude, and the direction the direction!

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Representing velocity Velocity can also be represented by an arrow. The size of the arrow indicates the magnitude of the velocity, and direction...well represents the direction! When discussing velocity or answering a question, you must always mention the direction of the velocity (otherwise you are just giving the speed).

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Adding vectors When adding vectors (such as force or velocity), it is important to remember they are vectors and their direction needs to be taken into account. The result of adding two vectors is called the resultant.

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Adding vectors For example; 6 m/s4 m/s 2 m/s 4 N 5.7 N Resultant force

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How did we do that? 4 N 5.7 N 4 N

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Scale drawing You can either do a scale drawing 4 cm 1 cm = 1N θ = 45° θ

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Or by using pythagorous and trigonometry 4 N Length of hypotenuse = 4 2 + 4 2 = 32 = 5.7 N Tan θ = 4/4 = 1, θ = 45°

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Subtracting vectors For example; 6 m/s4 m/s 10 m/s 4 N 5.7 N Resultant velocity Resultant force

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Subtracting vectors For example; 4 N 5.7 N

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Resolving vectors into components It is sometime useful to split vectors into perpendicular components

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Resolving vectors into components

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Tension in the cables? 10 000 N ? ? 10°

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Vertically 10 000 = 2 X ? X sin10° 10 000 N ? ? 10° ? X sin10°

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Vertically 10 000/2xsin10° = ? 10 000 N ? ? 10° ? X sin10°

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? = 28 800 N 10 000 N ? ? 10° ? X sin10°

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