Topic 1.1 (PPT) Units _ Measurements Grade 10 Physics.pptx

IGCSE PHYSIC

1. Topic 1.1 :Units & Measurements

2. Main Sections of Topic 1.1 What are physical quantities? What are fundamental quantities? What are derived quantities? What are prefixes? How to derive units of derived quantities? Difference between Scalar & Vector quantities. How to measure length? What is parallax error? How to measure volume ?

3. Contents Rate yourself out of 5 at we have finished learning this topic to check your understanding. Sr. Learning Outcome Rating 1 Describe physical quantities 2 Understand prefixes. 3 Describe scalars and vectors 4 Use and describe the use of rules and measuring cylinders to find a length or a volume 5 Understand that a micrometer screw gauge is used to measure very small distances 6 Use and describe the use of clocks and devices, both analogue and digital, for measuring an interval of time 7 Obtain an average value for a small distance and for a short interval of time by measuring multiples (including the period of a pendulum)

4. What Standard We Will Use? We will follow the International System of Units – also known as the SI standard That means we’ll need to convert other measures to our standard

5. What are Physical Quantities? There are two types of Physical Quantities Fundamental Derived Quantities

6. What are Fundamental Physical Quantities?

7. What are Fundamental Physical Quantities? 7 SI base units : those from which all others are derived Physical Quantity Unit Abreviation Length Meter m Mass Kilogram Kg Time Seconds S Temperature Kelvin K Current Ampere A Amount of substance Mole Mol

8. What are Derived Physical Quantities? SI derived unit”: derived from base units Except the 7 Fundamental Units, the others are called Derived units . Unlimited number of derived units! Some examples?

9. What are Derived Physical Quantities? Some examples Area Volume Speed Force Frequency Time period

10. What are Derived Physical Quantities? Some examples Area (m 2 ) Volume (m 3 ) Speed (m/s) Force (kg·m / s 2) Frequency (s -1 ) Time period (s)

11. Examples of Derived Physical Quantities Physical Quantity: Velocity=Speed/Time Unit: m/s, m s -1 Physical Quantity : Force: mass X acceleration Unit: 1N=1kg∙m ∙s -2

12. Examples of Derived Physical Quantities  

13. Examples of Derived Physical Quantities  

14. Conversion of Units The SI Unit of length is metre (m) The SI Unit of weight is kilograms (kg) The SI Unit of volume is cubic metres (1cubic metre=1000L)

15. What are Prefixes? Prefixes are useful for expressing units of  physical quantities  that are either very big or very small. Some of the Greek prefixes and their symbols to indicate decimal sub-multiples and multiples of the SI units are:

16. Other Common prefixes

17. SI units and their prefixes

18. SI units and their prefixes

19. Vectors and scalars

20. Displacement and velocity A runner completes one lap of an athletics track. 400 m What is her final displacement? If she ends up exactly where she started, her displacement from her starting position is zero . What is her average velocity for the lap, and how does it compare to her average speed? What distance has she run?

21. Vector equations An equation is a statement of complete equality. The left hand side must match the right hand side in both quantity and units. In a vector equation , the vectors on both sides of the equation must have equal magnitudes and directions . Take Newton’s second law, for example: force = mass × acceleration Force and acceleration are both vectors, so their directions will be equal. Mass is a scalar: it scales the right-hand side of the equation so that both quantities are equal. Force is measured in newtons (N), mass in kilograms (kg), and acceleration in ms -2 . The units on both sides must be equal, so 1 N = 1 kgms -2 .

22. Scalar or vector?

23. Scientific Notation Numbers written using base 10 a x 10 b a is between 1 and 9 Has one significant digit before decimal place The remaining significant digits are right of decimal place Significant digits add more accuracy

24. Scientific Notation Numbers written using base 10 a x 10 b a is between 1 and 9 Has one significant digit before decimal place The remaining significant digits are right of decimal place Significant digits add more accuracy Examples: 12000 = 0.0001203 = 1.203 ×10 - 4 1.2×10 4

25. Practice question What is 20000m in cm? Express 20000m in standard form. Express 0.0002m in standard form.

26. Measuring Length SI Units for Length is meters. Length is fundamental Quantity

27. Measuring Length Length and distance can be measuring using following instruments: Meter rule Meter Tape Vernier Caliper Micrometer

28. What is Least Count? The smallest value that can be measured by the measuring instrument is called its  least count .

29. Measuring Length

30. Using Meter Rule to Measure Length A metre rule is the most commonly used instrument that can measure lengths upto 1 metre. Its accuracy is 1mm so it cannot accurately measure lengths smaller than 1mm. Useful to take quick measurements between 5cm to 95cm. When taking observations: Position eyes directly above the markings to avoid parallax error Note several readings then take average In case of wear and tear of ruler, if zero marking is not visible, measure from next visible marking and subtract it from the final result.

31. Exam Style Question

32. Exam Style Question

33. What is Parallax Error? A parallax error is the perceived shift in an object's position as it is viewed from different angles. The error is most easily noticed by looking at a nearby object with one eye closed, then looking at it through the other eye. The apparent motion of the object is the parallax shift, and it is responsible for a small, but noticeable, error common to optical equipment.

34. What is Parallax Error?

35. How to avoid Parallax Error? Parallax error can be avoided by keeping line of sight perpendicular to the scale.

36. Exam Style Question

37. Micrometer Screw Gauge

38. Micrometer Screw Gauge Equipment:  It is made up of a main scale and a thimble scale and can measure objects up to 5 cm in length. The smallest marking is usually 1 mm on the main scale (sleeve) and 0.01 mm on the thimble scale (thimble). The thimble has a total of 50 markings representing 0.50 mm. It has: an anvil and a spindle to hold the object a ratchet on the thimble for accurate tightening (prevent over-tightening) Accuracy:  ± 0.01 mm

39. How to use Micrometer

40. How to read a micrometer: Thimble is turned until the object is gripped very gently Read the main scale on the sleeve for the 1 st of decimal (4.5mm) For the 2 nd place of decimal, look at the circular scale on the thimble. Find a marking on the circular scale that is in line with the horizontal line of the main scale. (0.12mm) To get the correct reading, simply add up the two decimal numbers. (4.62mm

41. What is the reading here?

42. Exam Style Question

43. Zero Error  

44. Zero Error

45. Positive Zero Error If the zero marking on the thimble is  below  the datum line, the micrometer has a positive zero error. Whatever reading we take on this micrometer we would have to subtract the zero correction from the readings.

46. How to read with Postive Zero Error

47. The reading on the bottom is the measurement obtained and the reading at the top is the zero error. Find the actual measurement. (Meaning: get rid of the zero error in the measurement or take into account the zero error) Measurement with zero error : 1.76 mm Zero error : + 0.01 mm (positive because the zero marking on the thimble is below the datum line) Measurement without zero error :  1.76–(+0.01)=1.75 1.76–(+0.01)=1.75 mm

48. Negative Zero Error If the zero marking on the thimble is  above  the datum line, the micrometer has a negative zero error. Whatever readings we take on this micrometer we would have to add the zero correction from the readings.

49. Measurement of Volume Volume : The amount of space occupied by a substance Symbol : V SI Unit : cubic metre (m 3 ) Measuring Device : Measuring Cylinder is usually used to measuring volume. Conversion: 1cm 3 =1ml therefore 1000cm 3 =1000 ml 1L=1000cm3=1000 ml 1m 3 =1000000cm 3

50. Exam Style Question

51. What is a Meniscus? A  meniscus  occurs because of surface tension in the liquid and must be read at eye level. For a concave meniscus , the correct  volume  will be read at the bottom of the curve. For a convex  meniscus , the opposite is true and the correct reading will be at the top of the curve.

52. How to read Meniscus in Lab Measurements? For a concave meniscus , the correct  volume  will be read at the bottom of the curve. For a convex  meniscus , the opposite is true and the correct reading will be at the top of the curve.

53. Exam Style Question

54. Exam Style Question

55. How to read volume of Irregular Shaped Objects?

56. How to read volume of Irregular Shaped Objects?

57. Exam Style Question

58. Exam Style Question

59. Measurement of Time Clocks: can be used to measure time intervals in seconds, minutes and hours. The least count is 1s. Stopwatches : can be used to measure time intervals to a precision of 0.1s and 0.01s. Pendulum : a simple pendulum uses regular swings (oscillations) of the bob to measure time intervals.

60. Exam Style Question

61. Exam Style Question

62. Simple Pendulum A simple pendulum makes use of the regular swings(oscillations) of the for measuring time.. Oscillation : Journey from one extreme position to other and then back to first. Period (T) : Time takes for one complete oscillation is time period.

63. Simple Pendulum How to measure time period accurately? Note time taken for 20 oscillations by using stop watch and divide it by 20. What factors affect pendulum Time Period? How length affects time periods?

64. Simple Pendulum Experiment Design an experiment to investigate the relationship between Length of Pendulum vs Period of Pendulum

65. Exam Style Question

66. Exam Style Question- Solution

67. Scalars and Vectors In physics, there are two types of quantities: Scalars (e.g. distance, mass, temperature). Measurements with size but no direction. Only need to give a magnitude and units . Vectors (e.g. force, velocity, acceleration) Must have magnitude, units and direction . (MUD)

68. Vectors and scalars

69. Working with Vectors Vectors can be worked with Algebraically – calculations Or Vector Diagrams – scale diagram The first step when solving any vector problems is to draw a simple sketch. Force is a Vector

70. Think of Vectors as Arrows X Tip Tail Direction is very important so we put an arrowhead in the direction that the vector is going. This is sometimes called the Tip of a vector. The other end is usually called the Tail. Length of the line represents magnitude And the arrow represents direction.

71. +2 N -1 N -3 N Up, Right, North and East and can be taken as positive directions. Think of Vectors as Arrows + + Up, North Bearing 0 Right, East Bearing 90 Down, South Bearing 180 Left, West Bearing 270 - -

72. Equal vectors have same Direction & Magnitude All these Vectors are identical Same Magnitude Same Line of Action This allows us to move them around to add together.

73. Forces are Vectors Vectors must be Added Tip to Tail R = a + b a + b = R = a + b The Resultant is the sum of two or more Forces . SP Notes p 8 To add two vectors, place the tail of the second vector at the head of the first. The sum of the vectors is called Resultant vector or Net Vector. The Resultant vector always has the direction of where we start our vector diagram to where we finish.

74. + = F 1 = +10 N F 2 = +50 N F R = F 1 + F 2 = +60 N F 1 = +10 N F 2 = -30 N + = F R = F 1 + F 2 = -20 N Vectors must be Added Tip to Tail R = a + b

75. Adding Forces – 2 Dimensions  

76. Adding Vectors

77. Vector Sum Vectors must be Added Tip to Tail R = A + B The result is the Resultant Vector F R Or Net Vector F N Or Sum of Vectors

78. Find Resultant Force In IGCSE only need same line of action vectors F 3 = 12 N F 1 = 8 N F 2 = 2 N Resultant Force See SP Notes p 11 2 D Vectors

79. When subtracting Vectors must add the Negative. Cannot subtract vectors. a - b = R = a - b a + - b R = a – b = a + (-b) = Subtracting Vectors

80. Subtracting Vectors When subtracting Vectors must add the Negative. Cannot subtract vectors.

81. Constructing Resultant Forces

82. Equilibrium Net Force is Zero If there is no resultant force on a body it either remains at rest or continues at constant speed in a straight line.

83. Exam Style Question

84. Exam Style Question- Solution

85. Exam Style Question

86. Exam Style Question- Solution

87. Exam Style Question

88. Free-body diagrams FREE-BODY DIAGRAM: Shows all of the forces acting ON an object. Weight acting vertically down from the centre of mass All forces where it is contact with other objects Vectors should have lengths approximately proportional to their magnitudes. Free body diagrams only include the forces that act on one object. This makes it easy to work out whether the forces on it are balanced or not, and whether the object will accelerate. Applied Force Frictional Force

89. Equilibrium means Forces are Balanced Net Force is Zero If there is no resultant force on a body it either remains at rest or continues at constant speed in a straight line. Resultant Force = 0 N Balanced forces. If R esultant force = 0 => A cceleration = 0 => V elocity remains constant => E quilibrium see Equilibrium ppt

90. Problem A street lamp is fixed to a wall by a metal rod and a cable. Which vector triangle represents the forces acting at point P?

91. Problem – Vertical Equilibrium A weight of 7.0 N hangs vertically by two strings AB and AC, as shown For the weight to be in equilibrium, the tension in string AB is T 1 and in string AC it is T 2 . T1=5.4N; T2=4.0N

92. Vertical Forces Question A student sets up the apparatus shown in the diagram below in order to find the resultant of the two tensions T 1 and T 2 acting at P. When the tensions T 1 , T 2 and T 3 are balanced, the angles between T 1 and the vertical and T 2 and the vertical are as marked on the diagram. Draw a scale diagram of the forces T 1 and T 2 . Use the diagram to find the resultant of the two forces.

93. Velocity Vectors River bank River bank 1. ) A boat is capable of moving at 4 ms -1 through still water. It heads towards the opposite bank of a river which flows at 3 ms -1 a) What is the resultant velocity of the boat relative to the bank?     b) If the river is 60 m wide, how long does it take to cross the river?        c) How far downstream does the boat move? 5 ms -1 at 53 15s 45m