Measurement and Physical Quantities PDF

MEASUREMENT AND PHYSICAL QUANTITIES PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 1  MEASUREMENT AND PHYSICAL QUANTITIES TOPIC 1: Measurement and Physical Quantities TOPIC OBJECTIVES UNIT CONTENT...

MEASUREMENT AND PHYSICAL QUANTITIES PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 1  MEASUREMENT AND PHYSICAL QUANTITIES TOPIC 1: Measurement and Physical Quantities TOPIC OBJECTIVES UNIT CONTENT SUGGESTED LEARNING SUGGESTED Learners should be able to: (Skills, attitudes ACTIVITIES AND NOTES RESOURCES and knowledge) 1.0 1. measure physical quantities; Length, area, Experiments on measuring A ruler, Vernier MEASUREMENTS 2. read an instrument scale to volume, mass, length, time, mass. callipers, micro AND PHYSICAL the nearest fraction of a time, temperature. Determining area and volume. meter screw QUANTITIES division Liquids, regular, Determining density gauge, balance, 3. determine density of regular irregular objects. experimentally for liquids, thermometer, 1.1 and irregular objects S.I. units. regular and irregular objects. stop-watch, Measurements 4. express quantities in terms of Newton, joule Relating density to flotation measuring S.I. units; watt, volt and and sinking. cylinder, force 5. Derive other units from base others. Deriving units from base units. meter units Physical Quantities  Physical Quantities  Scalar vs. Vector Quantities  SI units and Prefixes  Standard Form  Significant Figures (s.f.) Measurement of Length  General information  Vernier Calipers  Micrometer Screw Gauge Measurement of Time  General information  Pendulum  Ticker Tape Timer Physical Quantities Content  Base Quantity  Derived Quantity — Like your height and weight, any physical quantity must have a numerical magnitude and a unit. Base Quantity — In total, there are SEVEN basic physical quantities, or base quantities. — Base quantities are expressed in base units. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 2  MEASUREMENT AND PHYSICAL QUANTITIES Base Quantity SI unit Name Abbreviation Name Symbol Length l meter m Mass m kilogram Kg Time t second s Electric current I ampere A Temperature T kelvin K Luminous intensity Iv candela Cd Amount of n mole mol substance Derived Quantity — Derived quantities are defined in terms of the basic quantities through equations. — Derived quantities are expressed in derived units. — SI units for derived quantities are obtained from the basic SI units through equations (see the table below how it is done). — Examples of derived quantities: Physical quantity Symbol for unit How the unit is derived by equation speed m/s or ms-1 speed = distance / time = m/s 3 volume m volume = length x width x height =mxmxm =m3 — There are also derived units with names of scientists and symbols for their units e.g. Newton (N), Pascal (Pa), Watt (W), Joule (J), Coulomb (C), Ohm (Ω) etc. — The table that follows shows how some derived quantities are derived from base quantities. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 3  MEASUREMENT AND PHYSICAL QUANTITIES Scalar Quantity vs Vector Quantity (Scalars vs vector Quantity) — Scalar quantities are quantities with magnitude (size) only.  Scalars are added by normal addition. — Vector quantities are quantities with both magnitude (size) and direction.  Vectors are added by taking into account their direction. — Examples of scalars and vectors: Scalar Quantities Vector Quantities Speed Distance Mass Velocity Displacement Energy Work Done Density Acceleration Force Power Pressure volume Weight Friction Temperature Heat Capacity Resistance Moment Gravitational Field Current Potential e.m.f Electric Field Magnetic Field Difference Vector diagrams — In a vector diagram, vectors are often represented with an arrowed line. — The direction of the arrow is the direction of the vector and the length of the line represents the size of the vector. — A single vector called resultant vector (R) represents the individual vectors combined in terms of magnitude and direction. — A resultant vector is indicated by a double-headed arrow while individual vector is a single-headed arrow.  Example: The velocity of a particle can be stated as: “speed of particle = 5.0 m/s and it is moving at an angle of 40° above the horizontal”. Addition of Vectors — Involves magnitude and direction. Addition of Parallel forces PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 4  MEASUREMENT AND PHYSICAL QUANTITIES Addition of non-parallel forces Three methods 1) Trigonometric method 2) Parallelogram Method (Graphical method) 3) Tip-to-Tail Method (a.k.a. Head-to-tail method) Example Find the resultant force R at point P due to F1 and F2 which are at right angles to each other. Method 1: Trigonometric Method PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 5  MEASUREMENT AND PHYSICAL QUANTITIES Using Pythagoras’ Theorem for right angled triangle: R2 = (F1)2 + (F2)2 R is at an angle θ above the horizontal 2 2 2 R =4 +5 tan θ = = R=√ R=√ θ = tan-1 ( ) R = 6.40 N θ = 38.7 Therefore, Resultant force, R = 6.40 N at 38.7 above the 5N force.  Remember that a vector should have both magnitude and direction. So in this case 6.40 N is the magnitude and ‘38.7 above the 5N force’ is the direction. Method 2a: Parallelogram method (Graphical Method) Parallelogram Method. To use this method, draw the vectors (F1 and F2) so that they extend from the same point and use the same scale. Use the vectors as two sides of a parallelogram and complete the figure by adding the two missing sides. The diagonal of the parallelogram measured to scale using a ruler is the Resultant vector (R) as shown in the diagram. Angle θ (measured by a protractor) gives the direction of the resultant vector. Resultant = R at θo to the horizontal. Or Resultant = R at θo above the F2 force. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 6  MEASUREMENT AND PHYSICAL QUANTITIES Example Find the resultant force R at point P due to F1 and F2 which are at right angles to each other. F1 = 4N and F2 = 5N. Step 1: Select an appropriate scale E.g. 1 cm to 2 N. Step 2: Draw a parallelogram of vectors to scale. In this case: F1 => 8cm, F2 => 10cm Step 3: Measure the length of diagonal to find R. In this case: R => 12.8 cm Since 1cm is representing 2N R = 12.8/2 = 6.4 N Step 4: Use the protractor to measure angle θ. In this case θ = 39 Therefore, Resultant force, R = 6.4 N at 39 above the 5N force. Resolution of Vectors A single vector may be resolved, or broken down, into its components. Vectors are commonly resolved into horizontal and vertical components so that trigonometric relationships can be used. The sum of the components is the original vector. Consider a vector F at an angle to the horizontal. To find the components, draw a horizontal vector (Fx) and a vertical vector(Fy). PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 7  MEASUREMENT AND PHYSICAL QUANTITIES The component vectors form a right-angled triangle. Therefore, you can solve for the magnitude of each component using trigonometric (Soh Cah Toa or ChaShoTao). Example: A force is exerted at an angle of 30° with the horizontal. If the magnitude of the force vector is 20N, what are the vertical and horizontal components? PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 8  MEASUREMENT AND PHYSICAL QUANTITIES SI Units and Prefixes Content  Why SI Units  Common Prefixes  Order of Magnitude  Unit Conversion Units There are two common systems of units: S.I. units (Systeme International d’Unites) e.g. metre, kilogram, second. The British engineering system (a.k.a. Imperial system of units) e.g. foot, pound, inch. Why SI units? It provides a standard measurement system because there are too many measurement systems around the world which would create confusion. Common prefixes — Prefixes are very useful in expressing physical quantities that are either very large or very small. — For example, we prefer to estimate the area of Singapore as 716.1 km2 instead of 716100000 m2. Prefix Symbol Factor giga G 109 mega M 106 kilo k 103 deci d 10-1 centi c 10-2 milli m 10-3 micro µ 10-6 nano n 10-9 Unit conversion — For simple unit conversion, you can simply multiply or divide by the appropriate power of the ten found in the above table. For example: 4567.8 km to m 4567.8 km = 4567.8 x 103 m = 4567800 m 4567.8 cm to km 4567.8 cm = 4567.8 x 10-2 m = 4567.8 x 10-2 ÷ 103 = 0.045678 km PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 9  MEASUREMENT AND PHYSICAL QUANTITIES For derived unit conversion, you have to do the following conversion step by step: For example: (i) 123.4 km/h = ? m/s 123.4 km/h = (123.4 x 103 m)⁄(3600 s) = 34.3 m/s [Steps: convert 123.4 km to 123.4 x 103 m on numerator and 1 h to 3600 s on denominator]. (ii) 345.6 g/cm3 = ? kg/m3 345.6 g/cm3 = (345.6 x 10-3 kg)⁄((10-2)3 m3) = 345600 kg/m3 [Steps: convert 345.6 g to 345.6 x 10-3 kg on numerator and 1 cm3 = (10-2)3 m3 (as 1 cm = 10-2 m) on denominator]. Standard Form Very often, we prefer to express the physical quantities that are very large or very small in the standard form. In standard form, the number is written as, A x 10n, where 1 ≤ A < 10 and n is an integer. For example: 12300000 m = 1.23 x 107 m as the decimal point has been moved 7 places to the left to get the number to be 1.23. 0.0000123 m = 1.23 x 10-5 m as the decimal point has been moved 5 places to the right to get the number to be 1.23. Significant Figures (s.f.) Rules 1) All non-zero digits (1, 2, 3, 4, 5, 6, 7, 8, 9) are significant. 2) Zeros between non-zero digits are significant. 3) Zeros before the first non-zero digit are not significant. 4) In a decimal, zeros after non-zero digits are significant. 5) In an integer, zeros after non-zero digits may or may not be significant. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 10  MEASUREMENT AND PHYSICAL QUANTITIES Examples s.f. Remarks 456 3 1.345 4 Rule 1 10204 5 1.406 4 Rule 2 0034 2 0.00546 3 Rule 3 1.30 3 1.400 4 Rule 4 1300 2,3,4 Rule 5 Reasons for being 2 or 3 s.f, Round off 1296 to 2 s.f. => 1300 Round off 1296 to 3 s.f. => 1300  Note that for rule (5), we can express an integer in standard form to avoid this ambiguity. i.e 1300 = 1.3 x 103 (2s.f) = 1.30 x 103 (3s.f) = 1.300 x 103 (4s.f)  Also, note that in Physics, all the final answer should be in 2 or 3 s.f. Measurement of Length SI unit: meter (m). Instruments: Meter Rule, Tape, Vernier Calipers, Micrometer Screw Gauge Instruments Meter Tape Vernier Micrometer Screw Rule Calipers Gauge Range Up to 100 Several Up to 15 cm Less than 1 cm cm meters Precision 0.1 cm 0.1 cm 0.01 cm 0.01 mm Example of Breath of Length of Diameter of Diameter of hair usage book wall coin Errors to take Parallax error Parallax error and Zero error note Parallax Error To avoid parallax error, you must position your eye directly above the marking when taking the reading. Two examples are shown below. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 11  MEASUREMENT AND PHYSICAL QUANTITIES  Zero error will be discussed in more details in respective instruments. Vernier Calipers Content  Structure  How to Use  Zero Error Structure of Vernier Calipers — Vernier Caliper consists of a main scale and a sliding vernier scale. — It is used to measure both the internal and external diameters as well as the depth of an object as shown in the diagram below. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 12  MEASUREMENT AND PHYSICAL QUANTITIES Functions of parts of a Vernier caliper How to use and read a vernier caliper Step 1: Check for zero error. This will be covered in more details later. Here, we assume there is no zero error. Step 2: Place the object into the correct place for measuring by using the inside jaws, outside jaws or tail as shown in the above diagram. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 13  MEASUREMENT AND PHYSICAL QUANTITIES Try these questions PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 14  MEASUREMENT AND PHYSICAL QUANTITIES Zero Error When using Vernier Calipers, we have to check for zero error. This is to check whether two zero marks coincide with each other before measuring anything (jaws are in contact with each other). For reading on zero error, we have to read it from the vernier scale. How to correct zero error on a Vernier caliper reading PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 15  MEASUREMENT AND PHYSICAL QUANTITIES Try these questions Micrometer Screw Gauge Content  Structure  How to Use  Zero Error Structure of Micrometer Screw Gauge — Micrometer Screw Gauge consists of a main scale and a thimble scale. — It is used to measure diameter of hair, wire or anything less than 1 cm. — It can measure to a precision of 0.01 mm. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 16  MEASUREMENT AND PHYSICAL QUANTITIES How to use and read a micrometer screw gauge? Step 1: Check for zero error. (This will be covered in more details later. Here, we assume there is no zero error). Step 2: Place the object between anvil and spindle, and turn the thimble until the anvil and spindle grip the object. Then turn the ratchet until it starts to click for careful tightening as shown in the above diagram. Step 3: Read the main scale at the edge of the thimble. This is the sleeve reading. In this case, the sleeve reading is 4.5 mm. Step 4: Find a mark on the circular scale that aligns with the datum line of the main scale. This is the thimble reading. In this case, it is 0.22 mm. Step 5: Actual reading = Sleeve reading + thimble reading. i.e. 4.5 + 0.22 = 4.72 mm Worked example: PRECAUTIONS WHEN USING A MICROMETER SCREW GAUGE 1. Check for zero error. 2. Clean anvil and spindle ends as thickness of dirt affects/adds to the reading 3. Do not tighten screw too much to avoid damaging micrometer screw gauge or gripped object. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 17  MEASUREMENT AND PHYSICAL QUANTITIES Zero Error When using Micrometer Screw Gauge, we have to first check for zero error. This is to check whether zero mark on thimble (circular) scale coincides with datum line on the main scale and reading on main scale is 0 when we are not measuring anything (that is when anvil is in contact with spindle). For reading on zero error, we have to read it from thimble (circular) scale. Tape measure Advantages of using a tape measure to measure length can be very long can be used to measure bent lines can be used to measure circumference portable Try these questions PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 18  MEASUREMENT AND PHYSICAL QUANTITIES Read the following micrometer screw gauge scales and come up with the actual reading in each case. Measurement of Time — SI unit: second (s) — Instruments: Stopwatch, pendulum clock and ticker tape timer. — Precision for most stopwatches (including analogue stopwatch) is 0.1 s. — Digital stopwatch can have a precision of 0.01 s. Pendulum: A timing apparatus consisting of a bob mounted so that it swings freely under the influence of gravity. — What u must now is that: PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 19  MEASUREMENT AND PHYSICAL QUANTITIES — One complete oscillation is a to and fro movement of a body when it has returned to its original position and is moving in the same original direction. — Amplitude, a, is the maximum displacement from the resting position. — Period, T, is the time taken to make one complete oscillation. — One complete oscillation: one complete to-and-fro motion, — like A -> B -> C -> B -> A — Frequency, f, is the number of oscillations produced in one second. The Period (T) of pendulum is affected by (1) Length of pendulum, l (2) Gravitational field strength, g The Period (T) is not affected by (1) Mass of pendulum bob (2) Angle of release Note that the period of pendulum is indeed affected by the angle of release, but by a very small amount. Therefore, to minimize this, we normally release the pendulum from an angle less than 10O such that it won’t affect the period of pendulum. This means whenever we talk about angle of release for pendulum, we assume it is a small angle. Also, note that the formula stated above is only valid for a small angle of release. SIMPLE PENDULUM EXPERIMENT 1. Inference : When the length of a simple pendulum increases, the period of oscillation also increases. // The period of pendulum is affected by the length of the thread. 2. Hypothesis : The longer the length of a simple pendulum, the longer will be the period of oscillation 3. Aim : To find the relationship between the length of a simple pendulum and the period of oscillation. 4. Variable : a) Manipulated variable : Length, l b) Responding variable : Period, T. c) Fixed variable : Mass of pendulum bob. 5. Materials/ Apparatus : Retort stand, pendulum bob, thread, metre rule, stop watch. 6. FUNCTIONAL DIAGRAM PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 20  MEASUREMENT AND PHYSICAL QUANTITIES 7. Procedure : a) Set up the apparatus as shown in Figure above.// A small brass or bob was attached to the thread. The thread was held by a clamp of a the retort stand. b) The length of the thread , l was measured by a metre rule, starting with 90.0 cm. The bob of the pendulum was displaced through an angle less than 10O and released. c) The time for 20 complete oscillations was taken using a stop watch. To account for human timing error, the whole process was repeated for three times. The average time (t) was calculated by averaging: t = The period of oscillation (T) was calculated by using, T = d) The experiment was repeated using different lengths such as 80.0 cm. 70.0 cm, 60.0 cm, 50.0 cm and 40.0 cm. Length of Time taken for 20 Period of T2 string, l / m oscillation, t (s) oscillation (s2 ) t1 t2 t3 Average, t T 0.40 25.2 25.1 25.3 25.2 1.26 1.59 0.50 28.1 28.3 28.2 28.2 1.41 1.99 0.60 31.0 31.0 31.0 31.0 1.55 2.40 0.70 33.5 33.6 33.7 33.6 1.68 2.82 0.80 35.8 35.9 35.7 35.8 1.79 3.20 0.90 38.2 37.9 38.2 38.1 1.91 3.65 1.00 39.7 39.8 39.9 39.8 1.99 3.96 PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 21  MEASUREMENT AND PHYSICAL QUANTITIES 8. Plotting the graph Length (l) vs Period squared (T2) Notes on plotting the graph  The graph should be labeled by a heading.  All axes should be labeled with quantities and their respective units.  The manipulated variable (l) should be plotted on the x-axis while the responding variable (T2 ) should be plotted on the y-axis.  Odd scales such as 1:3, 1:7 , 1:9 or 1 :11 should be avoided in plotting graph.  Make sure that the transference of data from the table to the graph is accurate. Plot points using a cross (+). Use a sharp pencil.  Draw a line of best fit. - the line that passes through most of the points plotted such that it is balanced by the number of points above and below the straight line.  make sure that the size of the graph is large enough, which is, not less than half the size of the graph paper or ( > 8 cm by 10 cm ). 10. How to improve the accuracy of the experiment. a) The bob of the pendulum was displaced through a small angle b) The amplitude of the oscillation of a simple pendulum is small. c) The simple pendulum oscillate in a vertical plane only. d) Switch off the fan to reduce air resistance. 11. Precautions of the pendulum experiment a. avoid conical oscillation b. ensure firm support c. avoid draught PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 22  MEASUREMENT AND PHYSICAL QUANTITIES d. zero error should be noted with respect to metre rule and corrected. e. avoid parallax error with respect to the instruments(metre rule) 12. Conclusion The length of simple pendulum (I) is directly proportional to the square of the period of oscillation (T2). // T2 is directly proportional to l (the straight line graph passing through the origin) 13. Discussion 1. 1.Use the graph to state the relationship between length of simple pendulum (I) and the square of the period of oscillation (T2). 2. Use the results to find the relationship between length (l) and the period (T) of a pendulum.  As length decreases the period also decreases. 3. (a) State the two factors which affect the period (T) of a pendulum.  Length of pendulum (l)  Acceleration due to gravity /gravitational field strength (g) (b) The period does not depend on the mass of the bob. (c) that is, the period (T) of a pendulum is dependent on length and acceleration due to gravity but is independent of (not affected by)the mass of the bob. 4. If the pendulum experiment was performed on the Moon it will be observed that the time (t) for 20 Oscillations will be much longer than on Earth as gravitational field strength on the Moon is smaller than that on Earth. So we can conclude that the period of pendulum is affected by the gravitational field strength. Ticker Tape Timer — The Ticker Tape Timer is a piece of apparatus that we use to measure very small time intervals. — The tape is pulled under a vibrating arm by a moving object e.g. trolley, toy car etc. — The vibrating arm makes dots on a paper tape. The amount of dots depends on its frequency. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 23  MEASUREMENT AND PHYSICAL QUANTITIES Using a ticker-timer to measure speed, velocity and acceleration It will be noted that the dots pulled at different velocities will be as follows; — We have to count the number of SPACES and not the number of dots themselves to measure the time taken. — The first dot at the direction of movement is the starting dot. — NB. Usually the first few dots are ignored as motion is not steady at first when the trolley starts moving, then counting starts after a few dots. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 24  MEASUREMENT AND PHYSICAL QUANTITIES  Most ticker-timers operate at a frequency (f) of 50Hz i.e. 50 cycles per second hence they make 50 dots per second.  Time interval between two consecutive dots is given as: Time interval = 1/f (This comes from the formula f = 1/T i.e. frequency = 1/Period) Therefore Time interval = 1/50 seconds = 0.02 seconds. This time is called a tick. The distance is measured in ten-tick intervals hence time becomes: Time = 10 x time interval =10×0.02 = 0.2 seconds. In short: Time = 1/f x 10 = 1/50 x 10s = 0.2 s NB. You will also meet ticker tape timers of different frequencies e.g. 40Hz (40 dots per second), 50Hz (50 dots per second) etc. Try this question Calculate the time intervals and hence the time for the ten-tick intervals of the following ticker tape timers. (a) 40Hz ticker tape timer. (b) 100Hz ticker tape timer Solution (a) Time interval = 1/f = 1/40 s = 0,025 s Time = 10 x 0.025 s = 0.25 s (b) Time interval = 1/f = 1/100 s = 0.01 s Time = 10 x 0.01 s = 0.1 s Worked examples 1) A ticker tape timer makes 40 dots in 1 second. The result of an experiment to find the average speed of a toy car is shown below. What is the average speed of the toy car? Answer: PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 25  MEASUREMENT AND PHYSICAL QUANTITIES Time = 1/f x 10 = 1/40 x 10 s = 0.25 s Speed = distance/time = 0.6m/0.25s = 2.4 m/s 2) A tape is pulled steadily through a ticker-timer of frequency 50 Hz. Given the outcome below, calculate the velocity with which the tape is pulled. Solution Distance between two consecutive dots = 5cm = 0.05m Frequency of the ticker-timer = 50Hz Time taken between two consecutive dots = 1/50 = 0.02 seconds Therefore, velocity of tape = 0.05m/0.02s = 2.5 m/s 3) The tape below was produced by a ticker-timer with a frequency of 100Hz. Find the acceleration of the object which was pulling the tape. Solution 0.5 cm = 0.005 m 2.5 cm = 0.025 m Time between successive dots= 1/100 = 0.01 seconds Initial velocity (u) = 0.005m/0.01s = 0.5 m/s Final velocity (v) = 0.025m/0.01s = 2.5 m/s Since there are 5 dot spaces, Time taken = 5 × 0.01s = 0.05 s Therefore, acceleration= v-u/t = 2.5-0.5/0.05 = 40 m/s2 DENSITY AND FLOTATION PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 26  MEASUREMENT AND PHYSICAL QUANTITIES — Density is mass per unit volume. — Density is calculated using the formula: Density = ρ= — SI Unit: kg m–3 — A solid will float in a liquid if the density of the solid is less than the density of the liquid — As such, if an object is denser than the liquid, the object will sink in the liquid. To measure the density of a regularly-shaped block 1. To find the mass - weigh it on an electronic balance. In this case let’s assume the mass of block = 36.7g 2. To find the volume: Volume = length × width × height In this case the volume is 5 × 2 × 1 = 10 cm3. 3. To get the density, substitute values in the formula ρ =. In this case ρ = = = 3.67g/cm3 To measure the density of an irregularly-shaped small stone PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 27  MEASUREMENT AND PHYSICAL QUANTITIES 1. To find the mass - weigh it on an electronic balance. Let’s assume mass of stone in this case was found to be 41.2g 2. To find the volume: Tie the stone with a string. Using the string lower the stone gently into a graduated cylinder containing water and note the new volume. To get the volume of the stone simply subtract the initial volume from the final volume. In this case, volume = 90 – 75 = 15 cm3. 3. To get the density, substitute values in the formula ρ =. In this case ρ = = = 2.75g/cm3 Precautions:  If there are any trapped bubbles flick the walls of the measuring cylinder with a finger so as to displace the bubbles.  Carefully lower the stone in using a string so there is no splash  Read volume below the meniscus.  Eye level and point of reading should be perpendicular to avoid parallax error. To measure the density of an irregularly-shaped large stone 1. To find the mass - weigh it on an electronic balance. Let’s assume mass of stone in this case was found to be 218.3g. 2. To find the volume: Fill an overflow can (Eureka can) up to the top and place an empty graduated cylinder under the spout. Carefully lower the stone in using a string so there is no splash. Note the level of water that has flown into measuring cylinder. PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 28  MEASUREMENT AND PHYSICAL QUANTITIES The volume of the stone = displaced water volume. 3. To get the density, substitute values in the formula ρ =. In this case the density can be obtained in kg/m3 as follows: 218.3g = 0.218kg 125cm3 to m3 = 125/106 = 0.000125 =1.25 x 10-4 m3 ρ= = 1.74 x 10-5 kg/m3 PHYSICS MADE SIMPLE compiled by TARUVINGA G  +263 772 980 253 Page 29