Chapter 1 Physical Quantities Measurement PDF

TOPIC 1.0 Physical Quantities and Measurement  SUBTOPIC 1.1 1.2 1.3 1.4 Describe base quantities, derived quantities and the International System (SI) of units De...

TOPIC 1.0 Physical Quantities and Measurement  SUBTOPIC 1.1 1.2 1.3 1.4 Describe base quantities, derived quantities and the International System (SI) of units Define the physical quantities 1.11 A quantity that is measurable is call a ‘Physical 1.12 Quantities’ Numerical Values & Units give quantities meaning  SUBTOPIC Define the physical quantities 1.1 1.2 1.3 1.4 1.11 1.12 Physical Quantities Base quantities Derived quantities  SUBTOPIC Define the physical quantities 1.1 1.2 1.3 1.4 1.11 Base Quantities Physical quantity that can not be derived from 1.12 other physical quantities. Derived Quantity Physical quantity is a combination of more than two base quantities.  SUBTOPIC 1.1 1.2 1.3 1.4 BASE QUANTITY SI UNIT (SYMBOL) (SYMBOL) Define the physical quantities 1.11 Length (l ) Meter (m) Mass (m) Kilogram (kg) 1.12 Time (t) Second (s) Temperature (θ) Kelvin (K) Electric current (I) Ampere (A) Luminous Intensity Candela (cd) Amount of substance Mole (Mol) Base quantities and their respective SI units  SUBTOPIC Define the physical quantities 1.1 1.2 1.3 1.4 Derived Quantities & Their Units 1.11 (In Terms Base Quantities & Base Unit) Relationship 1.12 Derived Symbo Relationship to Derived with base quantity l base quantities unit units 1 Area A Length x breadth mxm m2 Length x breadth 2 Volume V mxmxm m3 x height displacement m 3 Velocity, Speed v ms-1 Time s Velocity change ms-1 4 Acceleration a ms-2 Time s 𝑘𝑔𝑚 5 Momentum p Mass x Velocity 𝑘𝑔𝑚𝑠 −1 𝑠  SUBTOPIC 1.1 1.2 1.3 1.4 Relationship Derived Relationship with Derived Symbol to base Define the physical quantities quantity base units unit quantities 1.11 Mass kg 6 Density ρ kgm-3 Volume m3 1.12 𝑘𝑔𝑚𝑠 −2 Mass x 7 Force F 𝑘𝑔 𝑥 𝑚𝑠 −2 (newton, Acceleration N) 𝑘𝑔 𝑥 𝑚𝑠 −2 = 𝑘𝑔𝑚−1 𝑠 −2 𝑚2 𝐹𝑜𝑟𝑐𝑒 8 Pressure P or, pascal, Pa 𝐴𝑟𝑒𝑎 𝑁 = 𝑁𝑚−2 𝑚2 𝑘𝑔𝑚𝑠 −2 𝑥 𝑚 = Force x 𝑘𝑔𝑚2 𝑠 −2 9 Work W Displacemen joule, J or, t 𝑁 𝑥 𝑚 = 𝑁𝑚  SUBTOPIC Define the physical quantities 1.1 1.2 1.3 1.4 Example 1 1.11 The area of a square is the product of two lengths. 1.12 Write the area of the square in term of its derived quantity and its respective unit. Solution Area = length x length = mxm = m2  SUBTOPIC 1.1 1.2 1.3 1.4 Example 2 Define the physical quantities 1.11 The mass and volume of an object are 4 kg and 2 m3 respectively. 1.12 What is the density of the object? (Given the density is mass per unit volume) Solution 𝑚𝑎𝑠𝑠 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 𝑣𝑜𝑙𝑢𝑚𝑒 4 𝑘𝑔 = 3 2𝑚 𝑘𝑔 = 2 3 𝑚  SUBTOPIC Define the physical quantities 1.1 1.2 1.3 1.4 Example 3 1.11 Base on the following information, classify the given 1.12 physical quantities into base and derive quantities. Sam brought 4.0 kg of meat and cut into pieces of 20 cm3 cubes. He cooked the meat in an oven with temperature of 120C for 30 minute. He served the meat in a plate with a total area 0f 200 cm2.  SUBTOPIC Define the physical quantities 1.1 1.2 1.3 1.4 1.11 Solution 1.12 Base Quantity Derived Quantity Mass = 4 kg Volume = 20 cm3 Temperature = 120C Area = 200 cm2 Time = 30 minute  SUBTOPIC 1.1 1.2 1.3 1.4 Define scalar and vector quantities Define the physical quantities 1.11 Scalar Quantity Physical quantities that possess 1.12 MAGNITUDE or SIZE only Example mass, temperature, time distance, speed and density Vector Quantity Physical quantities that possess both MAGNITUDE and DIRECTION Example displacement, velocity, acceleration, momentum and force.  SUBTOPIC 1.1 1.2 1.3 1.4 Describe consistency, accuracy and sensitivity Define measurement and errors in Consistency 1.2.1 Measurements are said to be consistent when the values of the measurements are close to each other. 1.22 measurement Accuracy Accuracy is the degree of how close a measurement is to the true and actual value of the physical quantity Sensitivity The sensitivity of an instrument is its ability to detect small changes in the quantity that is being measured. Define measurement and errors in measurement SUBTOPIC 1.1 1.2 1.3 1.4 1.2.2 1.21  SUBTOPIC 1.1 1.2 1.3 1.4 Convert Metric Units and Customary Units Solve problems of unit conversion Prefixes 1.3.1 Prefix are used to deal with i. very large numbers ii. very small numbers A prefix is written in front of the symbol without spacing Example 30 kg, 15 MN, 1.5 µF, 1 TByte ……  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 1.3.1 List of prefixes and multiplication factor  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 Scientific Notation (Standard Form) 1.3.1 Used to deal with i. Very large number ii. Very small number Can be written as A x 10n , where 1 ≤ A  10, n = integer  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 Example of the usage standard form as follows. 1.3.1 i. The distance between the sun and the Pluto which is 5 890 000 000 000 meters 𝟓. 𝟖𝟗 𝒙 𝟏𝟎𝟏𝟐 𝒎 ii. The weight of proton is 0.000 000 000 000 000 000 000 000 001 67 kilogram 𝟏. 𝟔𝟕 𝒙 𝟏𝟎−𝟐𝟕 𝒌𝒈  SUBTOPIC 1.1 1.2 1.3 1.4 Example 4 Solve problems of unit conversion 1.3.1 Convert 30,000,000 W into: i. SI prefix form. ii. Standard form. Solution i. Prefix Prefix for Mega is 106 meaning 1 million. Hence, Power = 30.0 x 106 W, can be rewritten as, Power = 30.0 (x 106) W = 30.0 MW  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 Solution 1.3.1 ii. Standard Form A x 10n , 1 ≤ A < 10, A = 3.0 n = 7 (it shows how many places to move the decimal point). Now this power can be rewritten in the form of standard form as shown below: Power = 3.0 x 107 W  SUBTOPIC 1.1 1.2 1.3 1.4 Example 5 Solve problems of unit conversion 1.3.1 The diameter of a cell is 0.000002 m. Convert into i. SI prefix form. ii. Standard form. Solution i. Prefix Rewrite 0.000002 m to 2.0 x 10-6. As we have seen in the Table 1.3, prefix for micro is x 10-6 Hence, Diameter = 2.0 x 10-6 m, can be rewritten as, Diameter = 2.0(x 10-6) m = 2.0 m  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 Solution 1.3.1 ii. Standard Form A x 10n , 1 ≤ A < 10, A = 2.0 n = -6 (it shows how many places to move the decimal point). Now this power can be rewritten in the form of standard form as shown below: Diameter = 2.0 x 10-6 m  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 1.3.1 Conversion Of Units 1 1 h = 60 min 1 min = h 60 1 1 min = 60 s 1s= min 60 1 1s= h 1 h = 3600 s 3600 1 1 m = 100 cm 1 cm = m 100 1 1g= kg 1kg = 1000 g 1000  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 1.3.1 Method 1 Conversion Of Unit Method 2  SUBTOPIC 1.1 1.2 1.3 1.4 Method 1 Solve problems of unit conversion 1.3.1 x (multiplication factor) Prefix Base Unit ÷ (multiplication factor)  SUBTOPIC 1.1 1.2 1.3 1.4 Example 6 Solve problems of unit conversion 1.3.1 Convert 100 cm to m Solution x 10-2 = 100 cm m ÷ 100 = 100 x 10−2 ÷ 100 m = 1m  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 Method 2 1.3.1 Using unit cancellation One of the easiest ways to keep control of your units in any science problem. It doesn't matter what the units are, the process is the same.  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 STEP 1 : 1.3.1 Draw up a set of ‘railroad tracks’ STEP 2 : Write each conversion factor into the following columns in such a way that the units cancel out, and leaving the units you want. 5 cm 10-2 m 1 cm  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 1.3.1 STEP 3 The multiply or divided all the conversion factor depending on whether they are above or below the line Result = 5 x 10-2 m = 0.05 m  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 Convert: 1.3.1 i. 15 cm2 to m2 𝑘𝑚 𝑚 ii. 110 to ℎ 𝑠 𝑚 𝑘𝑚 iii. 340 to 𝑠 ℎ 𝑔 𝑘𝑔 iv. 1 3 to 3 𝑐𝑚 𝑚  SUBTOPIC 1.1 1.2 1.3 1.4 Convert: Solve problems of unit conversion i. 15 cm2 to m2 1.3.1 Solution x (10-2)2 15 cm2 m2 ÷ (100)2 = 15 x 10 -4 ÷ 100 m2 = 15 x 10 -4 x 100 x 1m2 = 15 x 10-4 m2  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 1.3.1 Convert: 𝑘𝑚 𝑚 ii. 110 to ℎ 𝑠 Solution 𝑘𝑚 1000 𝑚 1ℎ = 110 𝑥 𝑥 ℎ 1 𝑘𝑚 3600 𝑠 𝑚 = 30.56 𝑠  SUBTOPIC 1.1 1.2 1.3 1.4 Convert: Solve problems of unit conversion 1.3.1 𝑚 𝑘𝑚 iii. 340 to 𝑠 ℎ Solution 𝑚 0.001 𝑘𝑚 1𝑠 = 340 𝑥 𝑥 1 𝑠 1𝑚 ℎ 3600 𝑚 0.001 𝑘𝑚 1𝑠 = 340 𝑥 𝑥 1 𝑠 1𝑚 ℎ 3600 𝑚 0.001 𝑘𝑚 3600 𝑠 = 340 𝑥 𝑥 𝑠 1𝑚 ℎ 𝑘𝑚 = 1224 ℎ  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 1.3.1 Convert: 𝑔 𝑘𝑔 iv. 1 to 𝑐𝑚3 𝑚3 Solution 𝑔0.001 𝑘𝑔 1 𝑐𝑚3 =1 𝑥 𝑥 𝑐𝑚3 1𝑔 10−6 𝑚3 𝑘𝑔 = 1000 3 𝑚  SUBTOPIC Solve problems of unit conversion 1.1 1.2 1.3 1.4 1.3.1 Customary Units The customary system of measurement, also called the U.S. Customary System, is based on the English system of measurement. Solve problems of unit conversion SUBTOPIC 1.1 1.2 1.3 1.4 1.3.1  SUBTOPIC 1.1 1.2 1.3 1.4 Customary Units Solve problems of unit conversion 1.3.1  SUBTOPIC 1.1 1.2 1.3 1.4 Practice Question Solve problems of unit conversion 1.3.1 Change the following quantities to the units shown. 1. 4 yd = ft 2. 108 in = ft 3. 32 oz = lb 4. 3T = oz 5. 20 qt = gal 6. 28c = qt  SUBTOPIC 1.1 1.2 1.3 1.4 Measurements (Understanding) Interpret readings of measurement tools 1.4.1 Meter rules Measure length from a few cm up to 1 m 1.4.2 Accurate up to 0.1 cm (or 1 mm) Precautions to be taken when using a ruler i. Make sure the object is in contact with the ruler ii. Avoid parallax error  SUBTOPIC 1.1 1.2 1.3 1.4 to be taken when using using a ruler: ure that the object is in contact with the ruler. parallax error. Interpret readings of measurement tools 1.4.1 1.4.2 o avoid parallax error How to avoid parallax error  SUBTOPIC 1.1 1.2 1.3 1.4 State the measurement reading from vernier calipers usage Vernier Callipers Interpret readings of measurement tools 1.4.1 Measure length from 1 mm to 100 mm Accurate up to 0.01 cm (or 0.1 mm) 1.4.2  SUBTOPIC 1.1 1.2 1.3 1.4 State the measurement reading from vernier calipers usage Example 7 Interpret readings of measurement tools 1.4.1 1.4.2 What are the reading of the two vernier callipers?  SUBTOPIC 1.1 1.2 1.3 1.4 State the measurement reading from vernier calipers usage Solution Interpret readings of measurement tools 1.4.1 1.4.2 The ‘0’ mark lies between 3.7 and 3.8  SUBTOPIC 1.1 1.2 1.3 1.4 State the measurement reading from vernier calipers usage Interpret readings of measurement tools 1.4.1 Reading of the vernier callipers 1.4.2 = main scale reading + vernier scale reading = 3.7 cm + 0.05 cm = 3.75 cm  SUBTOPIC 1.1 1.2 1.3 1.4 State the measurement reading from vernier calipers usage Interpret readings of measurement tools 1.4.1 1.4.2  SUBTOPIC 1.1 1.2 1.3 1.4 State the measurement reading from vernier calipers usage Example 8 Interpret readings of measurement tools 1.4.1 The figure below show another pair of vernier callipers with a zero error of -0.04 cm. 1.4.2 Then the vernier callipers is used to measure the internal diameter of the boiling tube. What is the internal diameter of the tube?  SUBTOPIC 1.1 1.2 1.3 1.4 State the measurement reading from vernier calipers usage Interpret readings of measurement tools 1.4.1 1.4.2  SUBTOPIC 1.1 1.2 1.3 1.4 48 State the measurement reading from micrometer screw gauge usage Interpret readings of measurement tools MICROMETER 1.4.1 Measure length from 0.10 mm to 25.00 mm Accurate up to 0.001 cm (or 0.01 mm) 1.4.2 Micrometer Screw Gauge  SUBTOPIC 1.1 1.2 1.3 1.4 49 State the measurement reading from micrometer screw gauge usage Example 9 Interpret readings of measurement tools 1.4.1 1.4.2 The figure above shown two sets of raading of a micrometer screw gauge. Determine the reading.  SUBTOPIC 1.1 1.2 1.3 1.4 State the measurement reading from micrometer screw gauge usage Solution Interpret readings of measurement tools 1.4.1 1.4.2  SUBTOPIC 1.1 1.2 1.3 1.4 State the measurement reading from micrometer screw gauge usage Interpret readings of measurement tools Solution 1.4.1 1.4.2  SUBTOPIC Interpret readings of measurement tools 1.1 1.2 1.3 1.4 PART FUNCTION 1.4.1 Anvil and spindle To grip the object to be measured 1.4.2 To limit the pressure exerted on the Ratchet stop object to be measured by rotating it until a ‘click’ sound is heard To be rotated to tighten the anvil and Thimble spindle Function Of Each Part of Micrometer Screw Gauge  SUBTOPIC Interpret readings of measurement tools 1.1 1.2 1.3 1.4 1.4.1 Main Scale and Vernier of A Micrometer Screw Gauge 1.4.2 Main scale has two rows of marking on opposite side upper scale lower scale The different between one division on the upper scale and one division on lower scale is 0.50 mm The thimble scale is subdivided into 50 equal division, one division is 0.01mm  SUBTOPIC 1.1 1.2 1.3 1.4 Describe random error and systematic error Systematic Error Interpret readings of measurement tools 1.4.1 Errors in measurements due to the condition of the measuring instrument or the state of the 1.4.2 environment in which the measurement are taken. The reading taken is always bigger than the actual value or it is always smaller than the actual value. Systematic errors can be caused by the zero error of the instrument and the instrument is being incorrectly calibrated.  SUBTOPIC Interpret readings of measurement tools 1.1 1.2 1.3 1.4 1.4.1 Systematic error are error that may be due to 1.4.2 Personal error of the observer Wrong assumptions Incorrect calibration of the measuring instrument Zero Error, which is cause by incorrect position of the pointer when an instrument is not in use.  SUBTOPIC Interpret readings of measurement tools 1.1 1.2 1.3 1.4 Type of Zero Error 1.4.1 Positive zero error Negative zero error 1.4.2 Zerro error Define as non-zero reading shown by instrument while it is not measuring any object To get a true reading, we need to subtract the zero error from the observed reading. True Reading = Obtained Reading – Zero Error  SUBTOPIC Interpret readings of measurement tools 1.1 1.2 1.3 1.4 1.4.1 Random Error Occurs due to mistakes made by observer when 1.4.2 taking the measurement. A common random error is caused by incorrect positioning of eye (parallax error). Also occur when there is a sudden change of environmental factors like temperature, lighting or air circulation  SUBTOPIC 1.1 1.2 1.3 1.4 Example of micrometre reading and their zero error Interpret readings of measurement tools 1.4.1 1.4.2  SUBTOPIC 1.1 1.2 1.3 1.4 Example of Vanier calliper reading and their zero error Interpret readings of measurement tools 1.4.1 1.4.2