Physical Quantities, Units and Prefixes (and a bit on taking measurements too!)

1. Physical Quantities, Units and Prefixes (and a bit on taking measurements too!) B A One of these images shows measurements that is ‘accurate, but not precise’ and one shows measurements that are ‘precise, but not accurate’ Which is which? We will revisit this later in the lesson.

2. Mr. Mason • Lessons: Wednesday P1&2, Friday P5&6

3. You will need a folder to keep your current work and assessments in. • To get the best grades you can, youll need to do work at home beyond homework. • Before each class, you must have read the double page spread in the textbook. • http://www.physics-oasis.co.uk/timetable_ASphysics.html • If you need any help, my room is C5 (Here!) • Or email me on nick.mason@oasisenfield.org

4. Lesson 2 Objectives from 1.1.1 Physical quantities and units • Candidates should be able to: • (a) explain that some physical quantities consist of a numerical magnitude and a unit; • (b) use correctly the named units listed in this specification as appropriate; • (c) use correctly the following prefixes and their symbols to indicate decimal sub-multiples or multiples of units: pico (p), nano (n), micro (μ), milli (m), centi (c), kilo (k), mega (M), giga ,(G), tera (T); • (d) Make suitable estimates of physical quantities included within this specification.

5. Physical Quantities

6. PHYSICAL QUANTITIES Physics is a fascinating science. It deals with times that range from less than 10-22s, the half-life of helium 5 to 1.4 x1010 years, the probable ’age’ of our Universe.

7. Temperatures Physicists study temperatures from within a billionth of a degree above absolute zero to almost 200 million degrees, the temperature in the plasma in a fusion reactor

8. Mass and length An investigation of the mass of a quantum of FM radio radiation (2.3x10-42 kg) and the ‘size’ of a proton (1.3x10-15 m) all fall within the World of Physics!

9. Number and Unit • It is vital to realise that all the quantities mentioned above contain a number and then a unit of measurement. • Without one or other the measurement would be meaningless. • Imagine saying that the world record for the long jump was 8.95 (missing out the metres) or that the mass of an apple was kilograms (missing out the 0.30)!

10. In 60 Seconds, List as many units as you can!

11. 7 base units • All units used in Physics are based on the International System (SI) of units which is based on the following seven base units.

12. The base units the first 3 • Mass - measured in kilograms • The kilogram (kg): this is the mass equal to that of the international prototype kilogram kept at the Bureau International des Poids et Mesures at Sevres, France. • Length - measured in metres • The metre (m): this is the distance travelled by electromagnetic waves in free space in 1/299,792,458 s. • Time - measured in seconds • The second: this is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of caesium 137 atom.

13. The last 4 • Electric current - measured in amperes. • The ampere: this is that constant current which, if maintained in two parallel straight conductors of infinite length and of negligible circular cross section placed 1 metre apart in a vacuum would produce a force between them of 2 x 10 -7 N. • Temperature - measured in Kelvin • The Kelvin: this is 1/273.16 of the thermodynamic temperature of the triple point of water. • Luminous intensity - measured in candelas • The candela: this is the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540x1012 Hz that has a radiant intensity of 1/683 watt per steradian • Amount of substance - measured in moles • The mole: this is the amount of substance of a system that contains as any elementary particles as there are in 0.012 kg of carbon-12.

14. The base units

15. How many are there?

16. You should be asking • How many of what? • It's simply a collection of different animals - you cannot add them together! 

17. Adding units • It is most important to realise that these units are for separate measurements – you can’t add together quantities with different units. • For example five kilograms plus twenty-five metres has no meaning.

18. Multiplying units • Units can be multiplied just like quantities. • For example: • Mass x Length • (kg) x (m) • (kg m)

19. Dividing Units Remember: 1/s = s-1 • Dividing Units works just the same • For example: • Speed = Distance / Time • Distance is measured in (m) • Time is measured in (s) • = (m) / (s) • = (m/s) or (ms-1) • Speed is measured in (ms-1)

20. 1) Area = Length (m) x Width (m). What are the units of Area? • 2) Acceleration = Velocity (ms-1) / Time (s) What are the units of acceleration? • 3) Charge = Current (A) x time (s). What are the units for charge in base units?

21. Check that the following are dimensionally correct 1. s=ut + 1/2 at2 Dimensions of s= Dimensions of ut = Dimensions of 1/2 at2 = 2. Show that F= mv2/r is dimensionally homogeneous for the movement of mass m in a circle. 3. Show that E= mc2 is dimensionally homogeneous . Practice Questions

22. Answers • 1) (m) • 2) (kg m s-2) • 3) (kg m2 s-2)

23. Summary • Some physical quantities consist of a numerical magnitude and a unit • You can only add/ subtract similar units. • Units can be multiplied or divided • Seven base units. This means they cannot be expressed in any other combination of units. • Use correctly the named units listed in this specification as appropriate

24. Powers of Ten

25. Powers of ten • In Physics we often deal with very small or very large numbers and it is important to understand how these may be represented. • http://htwins.net/scale2/

26. Prefixes are used with the unit symbols to indicate decimal multiples or submultiples. What would these mean if you found them in front of a unit ?

27. Use of your calculator. • It is important to understand how to use your own calculator; they can all be slightly different. This is especially true when dealing with powers of ten. • Remember that 5.4x104 is keyed in as 5.4 EXP 4 but that 105 (One followed by FIVE noughts) is keyed in as 1 EXP 5 and NOT 10 EXP 5. • (Some calculators have an EE key in place of the EXP)

28. Use the most suitable prefix • Distance a finger nail grows in 1s 10-9 m • Distance across an atom 10-10 m • Wavelength of yellow light 6x10-7 m • Diameter of a human hair 5x10-6 m • World record long jump (man 2007) 8.95 m • Height of an adult 1.75 m • Length of a marathon (approximately) 40 000 m Extension: Find out what prefix would be most suitable for these measurements • Distance light travels in a year 1016 m • Radius of the observable universe 1025 m • ‘Diameter’ of a sub nuclear particle 10-15 m

29. How Science works: Takingmeasurements

30. Taking measurements When you take measurements there may be some variation in the readings. For example: If you time the fall of a paper parachute over a fixed distance, the times may vary slightly. 10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s Let’s look at these results more closely. Why is there a difference between these results?

31. Taking measurements The results were: 10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s What is the Range of these results?

32. Taking measurements : Range The results were: 10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s Find the minimum value and the maximum value Range = max – min = 10.4 – 9.9 = 0.5 s

33. Taking measurements : Mean The results were: 10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s What is the mean (or average) of these results?

34. = 10.1 s =50.6 5 Taking measurements : Mean The results were: 10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.3 s Add up the 5 numbers: 10.1+10.2+9.9+10.0+10.4= 50.6 There are 5 items, so divide by 5: Mean (or average) = Why is the mean recorded to 3 significant figures?

35. Taking measurements : Mean The results were: 10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s Why is it a good idea to calculate the mean of your results? Because it improves the reliability of your results. Your results will be more reliable.

36. Accuracy & Precision

37. Definitions Accuracy and Precision …sound the same thing… …is there a difference??

38. B A One of these images shows measurements that is ‘accurate, but not precise’ and one shows measurements that are ‘precise, but not accurate’ Which is which? .

39. B A ‘accurate, but not precise’ ‘precise, but not accurate’ .

40. Definitions : Accuracy In your experiments, you need to consider the accuracy of your measuring instrument. For example: An expensive thermometer is likely to be more accurate than a cheap one. It will give a result nearer to the true value. It is also likely to be more sensitive.So it will respond to smaller changes in temperature.

41. Definitions : Precision As well as accuracy, precision is also important. Precision is connected to the smallest scale division on the measuring instrument that you are using. For example:

42. Definitions : Precision For example, using a ruler: A ruler with a millimetre scale will give greater precision than a ruler with a centimetre scale.

43. Definitions : Precision A precise instrument also gives a consistent reading when it is used repeatedly for the same measurements. For example:

44. A = 6 g B = 2 g Definitions : Precision For example, 2 balances: A beaker is weighed on A, 3 times: The readings are: 73 g, 77 g, 71 g So the Range is: It is then weighed on B, 3 times: The readings are: 75 g, 73 g, 74 g So the Range is: Balance B has better precision. Its readings are grouped closer together.

45. 0 true value Accuracycompared withPrecision Suppose you are measuring the length of a wooden bar: The length has a true value And we can take measurements of the length, like this: Let’s look at 3 cases…

46. 0 true value 0 0 Accuracycompared withPrecision Precise (grouped) but not accurate. Accurate (the mean) but not precise. Accurate and Precise.

47. Learning Outcomes You should now understand: • The meaning of ‘variation’ and ‘range’, • How to calculate the mean (or average), • and why this improves the reliability of your results, • The difference between ‘accuracy’ and ‘precision’.

48. Percentage Difference • This is a method of comparing experimental values of a quantity to the accepted precise measurement • Percentage difference= • (experimental value-accepted measurement) x100% • accepted measurement • It tells you how accurate you were • E.g. g = 9.81m/s2 , measured 10.82 m/s2 • Percentage difference = (10.82-9.81)/9.81 x 100%= 10.3% • Not very accurate.

49. How did you do? • Greater than 20% - rubbish • Greater than 10%, less than 20% Poor • Greater than 5% less than 10% very good • Less than 5% - excellent.