2021 Physics Teaching Notes PDF

1 2021 PHYSICS TEACHING NOTES  2 TABLE OF CONTENTS 1 INTRODUCTION TO PHYSICS....................................................

1 2021 PHYSICS TEACHING NOTES  2 TABLE OF CONTENTS 1 INTRODUCTION TO PHYSICS........................................................................................................................ 9 FUNDAMENTAL QUANTITIES:..............................................................................................9 MEASUREMENT OF LENGTH...................................................................................................................... 11 VERNIER CALIPERS.................................................................................................................................. 11 MICROMETER SCREWGAUGE................................................................................................................. 14 ERRORS IN MEASUREMENT OF LENGTH................................................................................................. 16 TIME MEASUREMENT................................................................................................................................. 18 SIMPLE OSCILLATING PENDULUM.............................................................................................................. 19 FACTORS AFFECTING THE PERIOD OF THE SIMPLE PENDULUM............................................................. 21 SOURCES OF ERROR IN MEASUREMENT OF TIME.................................................................................. 21 MOTION...................................................................................................................................................... 23 DEFINITION OF TERMS............................................................................................................................ 23 GRAPHS OF MOTION............................................................................................................................... 24 DISTANCE TRAVELLED IN A SPEED/ VELOCITY-TIME GRAPH.................................................................. 26 EQUATIONS OF MOTION........................................................................................................................ 29 MOTION OF FALLING OBJECTS................................................................................................................ 31 MASS AND WEIGHT.................................................................................................................................... 35 RELATIONSHIP BETWEEN MASS AND WEIGHT....................................................................................... 36 CENTRE OF GRAVITY (C.G)/CENTRE OF MASS (CM)................................................................................ 36 STABILITY AND TOPPLING....................................................................................................................... 37 DENSITY...................................................................................................................................................... 40 RELATIVE DENSITIES OF LIQUIDS............................................................................................................ 41  3 FORCES........................................................................................................................................................ 44 SOME TYPES OF FORCE........................................................................................................................... 44 EFFECTS OF FORCE ON AN OBJECT......................................................................................................... 46 FORCE AND CHANGING SHAPE........................................................................................................... 46 EFFECTS OF FORCE ON MOTION......................................................................................................... 53 MOMENT OF A FORCE................................................................................................................................ 56 THE PRINCIPLE OF MOMENTS................................................................................................................. 56 FORCES ON A BEAM................................................................................................................................ 59 VECTORS AND SCALARS............................................................................................................................. 63 PARALLELOGRAM RULE.......................................................................................................................... 64 ENERGY, WORK AND POWER.................................................................................................................... 66 ENERGY................................................................................................................................................... 66 FORMS OF ENERGY............................................................................................................................. 66 PRINCIPLE OF CONSERVATION OF ENERGY........................................................................................ 67 ENERGY TRANSFORMATIONS............................................................................................................. 67 RENEWABLE AND NON-RENEWABLE ENERGY SOURCES.................................................................... 68 GRAVITATIONAL POTENTIAL ENERGY..................................................................................................... 72 KINETIC ENERGY...................................................................................................................................... 73 ENERGY INTERCHANGES: FALLING OBJECTS........................................................................................... 74 ENERGY EFFICIENCY................................................................................................................................ 75 WORK...................................................................................................................................................... 76 POWER (P).............................................................................................................................................. 77 PRESSURE.................................................................................................................................................... 80 PRESSURE DUE TO LIQUID...................................................................................................................... 81 ATMOSPHERIC PRESSURE....................................................................................................................... 82 U TUBE MANOMETER............................................................................................................................. 83 EFFECTS OF AIR PRESSURE...................................................................................................................... 84 WEATHER FORECAST.............................................................................................................................. 85  4 SIMPLE KINETIC MOLECULAR MODEL OF MATTER................................................................................... 87 STATES OF MATTER................................................................................................................................. 87 THE KINETIC THEORY OF GASES ASSUMPTIONS..................................................................................... 87 THE KELVIN TEMPERATURE SCALE.......................................................................................................... 88 BROWNIAN MOTION.............................................................................................................................. 89 GAS PRESSURE........................................................................................................................................ 89 THE BOYLE’S LAW.................................................................................................................................... 90 THERMAL PHYSICS...................................................................................................................................... 93 THERMAL EXPANSION OF MATTER......................................................................................................... 93 EXPANSION OF SOLIDS........................................................................................................................ 93 EXPANSION OF LIQUIDS...................................................................................................................... 94 THE UNUSUAL BEHAVIOUR OF WATER............................................................................................... 95 EXPANSION OF GASES......................................................................................................................... 95 COMPENSATIONS FOR THERMAL EXPANSION....................................................................................... 95 BIMETALLIC STRIP................................................................................................................................... 96 APPLICATION OF THERMAL EXPANSION................................................................................................. 97 TEMPERATURE............................................................................................................................................ 99 LIQUID-IN-GLASS THERMOMETER.......................................................................................................... 99 CLINICAL AND LABORATORY THERMOMETERS.................................................................................... 101 THERMOCOUPLE THERMOMETER........................................................................................................ 101 HEAT ENERGY AND CHANGE OF STATES................................................................................................. 103 MELTING AND BOILING......................................................................................................................... 103 EVAPORATION....................................................................................................................................... 103 BOILING................................................................................................................................................. 104 HEATING AND COOLING CURVES.......................................................................................................... 106 HEAT CAPACITY......................................................................................................................................... 107 SPECIFIC HEAT CAPACITY...................................................................................................................... 107 LATENT HEAT........................................................................................................................................ 109  5 TRANSFER OF THERMAL ENERGY............................................................................................................. 114 CONDUCTION........................................................................................................................................ 114 CONVECTION......................................................................................................................................... 116 CONVECTION CURRENTS.................................................................................................................. 116 APPLICATIONS OF CONVECTION....................................................................................................... 116 CONSEQUENCES OF CONVECTION............................................................................................ 117 RADIATION............................................................................................................................................ 118 GENERAL WAVES....................................................................................................................................... 124 GENERAL DESCRIPTION OF WAVES....................................................................................................... 124 CLASSES OF WAVES............................................................................................................................... 127 GENERAL PROPERTIES OF WAVES......................................................................................................... 128 THE ELECTROMAGNETIC SPECTRUM........................................................................................................ 131 LIGHT......................................................................................................................................................... 134 REFLECTION OF LIGHT........................................................................................................................... 134 REFRACTION OF LIGHT.......................................................................................................................... 138 LENSES....................................................................................................................................................... 146 SOUND...................................................................................................................................................... 151 MEASURING THE SPEED OF SOUND..................................................................................................... 152 REVERBERATIONS................................................................................................................................. 153 AUDIBLE FREQUENCIES......................................................................................................................... 154 CLASSES OF SOUNDS............................................................................................................................. 154 USES OF ULTRASOUND......................................................................................................................... 154 SOUND POLLUTION............................................................................................................................... 154 CHARACTERISITICS OF SOUND NOTES.................................................................................................. 155  6 MAGNETISM AND ELECTROMAGNETISM................................................................................................ 159 PROPERTIES OF MAGNETIC MATERIALS............................................................................................... 159 HARD AND SOFT MAGNETIC MATERIALS............................................................................................. 160 THEORY OF MAGNETS........................................................................................................................... 160 INDUCED MAGNETISM......................................................................................................................... 161 MAGNITIZATION METHODS.................................................................................................................. 162 DEMAGNETISATION.............................................................................................................................. 163 MAGNETIC FIELDS................................................................................................................................. 163 MAGNETIC SHIELDING.......................................................................................................................... 165 ELECTROMAGNETS................................................................................................................................... 166 STATIC ELECTRICITY.................................................................................................................................. 169 TESTING FOR A CHARGE....................................................................................................................... 170 LIGHTNING AND LIGHTNING CONDUCTOR........................................................................................... 172 ELECTRIC FIELD...................................................................................................................................... 173 USES OF STATIC ELECTRICITY..................................................................... Error! Bookmark not defined. CHARGING CONDUCTOR BY INDUCTION.............................................................................................. 174 CHARGING CONDUCTOR BY EARTHING............................................................................................... 175 CONDUCTORS AND INSULATORS.......................................................................................................... 175 ELECTRICITY CURRENT.............................................................................................................................. 180 ELECTRIC SYMBOLS............................................................................................................................... 180 ELECTRIC CURRENT............................................................................................................................... 181 ELECTRIC CURRENT IN A CIRCUIT.......................................................................................................... 182 ELECTROMOTIVE FORCE (EMF) AND POTENTIAL DIFFERENCE (PD), VOLTAGE (V).............................. 183 POTENTIAL DIFFERENCE OR VOLTAGE IN CIRCUITS.............................................................................. 184 ELECTRICAL RESISTANCE...............................................................................................186 RESISTOR AND RESISTOR CODES.............................................................................186 COMBINED RESISTANCE.......................................................................................................... 187 OHM’S LAW........................................................................................................................................... 190 FACTORS AFFECTING RESISTANCE.................................................................................................... 193 OHMIC AND NON OHMIC CONDUCTORS......................................................................................... 194  7 ELECTRICAL ENERGY AND POWER (P)................................................................................................... 198 CALCULATING COST OF ELECTRICITY.................................................................................................... 200 MAINS ELECTRICITY............................................................................................................................... 201 THE THREE PIN PLUG............................................................................................................................ 202 THE DANGERS OF MAINS ELECTRICITY................................................................................................. 202 SAFE USE OF ELECTRICITY..................................................................................................................... 204 ELECTROMAGNETIC EFFECTS................................................................................................................... 213 ELECTROMAGNETIC INDUCTION.......................................................................................................... 213 USES OF ELECTROMAGNETIC INDUCTION............................................................................................ 215 MUTUAL INDUCTION............................................................................................................................ 219 THE TRANSFORMER.......................................................................................................................... 219 THE TRANSFORMER EQUATION........................................................................................................ 221 POWER LOSS IN A TRANSFORMER.................................................................................................... 222 TRANSFORMERS AND THE NATIONAL GRID..................................................................................... 223 MAGNETIC EFFECT OF CURRENT.............................................................................................................. 226 THE MOTOR EFFECT.............................................................................................................................. 226 FIELD PATTERNS.................................................................................................................................... 226 FORCE ON A CURRENT-CARRYING CONDUCTOR.................................................................................. 228 D.C. MOTOR.......................................................................................................................................... 230  8 PRODUCTION AND DETECTION OF CATHODE RAYS................................................................................. 235 THERMIONIC EMISSION........................................................................................................................ 235 CATHODE RAY OSCILLOSCOPE.............................................................................................................. 236 ELECTRONIC SYSTEMS.............................................................................................................................. 239 ACTION AND USE OF CIRCUIT COMPONENTS....................................................................................... 239 POTENTIAL DIVIDER.......................................................................................................................... 239 THERMISTOR..................................................................................................................................... 240 LIGHT DEPENDENT RESISTOR (LDR):................................................................................................. 240 REED SWITCH.................................................................................................................................... 240 RELAY SWITCH................................................................................................................................... 241 CAPACITOR........................................................................................................................................ 241 DIODE................................................................................................................................................ 242 RADIOACTIVITY........................................................................................................................................ 246 ATOMIC STRUCTURE............................................................................................................................. 246 BACKGROUND RADIATION.................................................................................................................... 247 TYPES OF RADIATION............................................................................................................................ 247 PROPERTIES OF RADIATIONS................................................................................................................ 249 DETECTING RADIOACTIVITY.................................................................................................................. 251 RADIOACTIVITY AND HALF-LIFE............................................................................................................ 252 USES OF RADIOACTIVITY....................................................................................................................... 255 DANGERS OF RADIOACTIVE SOURCES.................................................................................................. 256 SAFETY PRECAUTIONS........................................................................................................................... 256 NUCLEAR ENERGY................................................................................................................................. 257  9 INTRODUCTION TO PHYSICS Physics is a science subject that deals with the study of matter, the energy that act on matter and the behaviour of matter when energy acts on them. BRANCHES F PHYSICS: 1. Mechanics 2. Electricity 3. General Physics 4. Optics 5. Wave 6. Magnetism 7. Nuclear Physics PHYSICAL QUANTITIES: These are properties of a substance or phenomenon that has a magnitude that can be determined and expressed from a reference point. CLASSIFICATION OF PHYSICAL QUANTITIES Physical quantities are classified into two: 1. Fundamental Quantities: Fundamental Quantities are basic quantities that do not depend on any other quantity. They are quantities that cannot be defined in terms of any other quantity. They are quantities that other quantities depend upon for their derivations. Examples of Fundamental Quantities, units and their symbols SI UNIT: Symbol of Unit Quantity unit symbol Other units Mass kilogram kg g, tonnes Length metre m cm, mm, km time second s h, min, years, decade  10 Derived Quantities: These quantities are derived or obtained from the fundamental quantities. They are dependent quantities that depend on the fundamental quantities for their derivations. QUANTITY UNITS speed/velocity m/s force/weight newtons (N) pressure Pascal (Pa) resistance ohms() emf/voltage volts(V) current amperes(A) charge coulombs(C) acceleration m/s2 power watt(W) energy/work joules(J) Heat capacity Jkg/K Temperature Kelvin (K) PREFIXES Prefix Symbol Value Prefix Symbol Value 18 exa E 10 deci d 10-1 peta P 1015 centi c 10-2 tera T 1012 milli m 10-3 giga G 109 micro μ 10-6 mega M 106 nano n 10-9 kilo k 103 pico p 10-12 hecto h 102 femto f 10-15 decka da 101 atto a 10-18  11 MEASUREMENT OF LENGTH Length is defined as the space or distance between 2 points. Units of length are related to metre by multiple of 10 Length can be measured using:  Rulers  Click wheel  Measuring tape  Surveyor’s sight These instruments are used to measure very long distances, for measuring small length of objects; we can use more accurate instruments like a VERNIER CALIPER and MICROMETRE SCREW GAUGE VERNIER CALIPERS A pair of vernier calipers can be used to measure: The thickness of solids and the external diameter of an object by using the external jaws. The internal jaws of the caliper are used to measure the internal diameter of an object. The tail of the vernier caliper is used to measure the depth of an object or a hole. Vernier calipers can measure up to a precision of ±0.01 cm. It has: a fixed scale (main scale) A moving (Vernier) scale)  12 How to measure using Vernier Caliper. First line on the moving scale reads the fixed scale of 2.0 Best aligns on moving scale at 0.05 1. Find the location on the Main Scale (MS) that line up (coincides) with the 0 mark of the Vernier Scale. OR take a reading on the main scale that come just before the zero mark of vernier scale. MS = 2 cm 2. Find the mark on the vernier scale (VS) that most closely aligns with any mark on the main scale. (Multiply it by 0.01 cm). TS = (5 x 0.01) = 0.05 cm 3. Add the two values together to get the total reading. (VR = MS +VS). Therefore the reading of the caliper is: 2.0 + 0.05 = 2.05 cm  13 EXERCISE 1: Find the readings of the vernier calipers below 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.  14 MICROMETER SCREWGAUGE A micrometer screw gauge has two scales: Main (Sleeve Scale) Circular (Thimble) scale. SLEEVESCALE: The main scale of a micrometer is calibrated in mm. The calibrations of the main scale of micrometer screw gauge vary depending on the range of measurement that the micrometer screw gauges are meant to measure. THIMBLE SCALE: The vernier scale has 50 equal divisions. Each division is obtained by dividing 5 by 10. How to measure using Vernier Caliper 1. The measure of the last marking showing on the upper scale (indicated by arrow A) is 11 mm. Check the lower scale. The last marking showing on the lower scale (indicated by arrow B) is to the left of arrow A. In this case, the number from the barrel is read as 11 mm. 2. Identify a division on the thimble scale that is in line with the datum line and multiply it by 0.01.The thimble reading yields 0.28 mm. (28 x0.01) 3. The sum and resulting measurement is: 11 mm + 0.28 mm = 11.28 mm.  15 EXERCISE Record the readings shown by the micrometer screw gauge below.  16 ERRORS IN MEASUREMENT OF LENGTH A. Parallax Error For accurate measurement, the eye must always be placed vertically above the mark being read. This is to avoid parallax errors which will give rise to inaccurate measurement. Correct position Wrong position Parallax errors affect the accuracy of the measurement. If you consistently used the incorrect angle to view the markings, your measurements will be displaced from the true values by the same amount. This is called systematic error. However, if you used different angles to view the markings, your measurements will be displaced from the true values by different amounts. This is called random error. B. Zero Error ZERO ERRORS OF VERNIER CALIPER When the jaws are closed, the vernier zero mark coincides with the zero mark on its fixed main scale. Before taking any reading it is good practice to close the jaws or faces of the instrument to make sure that the reading is zero. If it is not, then note the reading. This reading is called “zero error”. The zero error is of two types (i) positive zero error and (ii) negative zero error. Positive Zero Error: If the zero on the vernier scale is to the right of the main scale, then the error is said to be positive zero error and so the zero correction should be subtracted from the reading which is measured. Negative Zero Error: If the zero on the vernier scale is to the left of the main scale, then the error is said to be negative zero error and so the zero correction should be added from the reading which is measured. ZERO ERROR FOR MICROMETER SCREW GAUGE 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. 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.  17 Exercise 2: Assuming the jaws of the vernier calipers are tightly closed, find the zero error of the vernier calipers below. 1. 2. Zero Error = Zero Error = 3. 4. Zero Error = Zero Error = Example 3. Find the zero error and the correct reading of the vernier calipers below. 1. 2.  18 TIME MEASUREMENT It is the ordering or duration of events. The unit of time is second (s) which is defined as:  The particular frequency of electromagnetic spectrum given out by the common type of caesium atom The common devices to measure the time or duration of an event are clock and stopwatch. In stopwatch, each second is calibrated into one hundred part of a second called centisecond. EXERCISE Record the time shown by the stop clocks below a. b. c. d.  19 SIMPLE OSCILLATING PENDULUM A simple pendulum consists of inextensible string with a mass bob tied to it DEFINITION OF TERMS. a. AMPLITUDE (θ): is the angle between the rest position of the pendulum and one extreme. This is the maximum displacement of a pendulum from its rest position b. OSCILLATION: is a complete swing from one extreme to another and then back. That is from point P through R to Q and then back to P c. PERIOD (T): is the time taken to make a complete swing or oscillation 𝒐𝒔𝒄𝒊𝒍𝒍𝒂𝒕𝒊𝒐𝒏 𝑷𝒆𝒓𝒊𝒐𝒅 = 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒐𝒔𝒄𝒊𝒍𝒍𝒂𝒕𝒊𝒐𝒏𝒔 𝒕 𝑻= 𝑵 d. FREQUENCY(f): is the number of oscillations made per second 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒐𝒔𝒄𝒊𝒍𝒍𝒂𝒕𝒊𝒐𝒏𝒔 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 = 𝒕𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏 𝒃𝒚 𝑵 𝒐𝒔𝒄𝒊𝒍𝒍𝒂𝒕𝒊𝒐𝒏𝒔 𝟏 𝑭= 𝑻 e. Tension(T): Force on the string To find the amount of time it takes a pendulum to make a spin, time ~20 circles and then divide by the same number as the number of circles. The precession of time duration of an event can be improved by measuring the time for number of events and dividing time by total number of events. For example to measure the time period of a pendulum the time for ten swings should be recorded and dividing the total time by ten to get the time for one.  20 EXPERIMENT: DETERMINATION OF ACCELERATION OF FREE FALL (g) APPARATUS: - Inextensible string - pendulum bob - clamp -Stop clock - retort stand - ruler -graph sheet PROCEDURE: 1) Adjust the pendulum so that its length l is 100.0 cm 2) i. Displace the pendulum bob through a small angle (θ) and then release it so that it swings ii. Measure and record the time t20 for 20 oscillations, record as t1 and repeat. Record as t2. iii. Calculate average time (tav) 3) i. calculate the time T for one complete oscillation ii. Calculate T2 4) Repeat 2) and 3) for different lengths l of 90.0 cm, 80.0 cm, 70.0 cm, 60.0 cm, 50.0 cm, 40.0 cm and 30.0 cm TABLE OF RESULTS String length/cm t1/s t2/s tav/s T/s T2/s2 30.0 40.0 50.0 60.0 70.0 80.0 90.0  21 ANALYSIS  Plot a graph of T2(s2) against length(cm)  Draw a line of best fit  Calculate the gradient, G of the line of best fit G =………………………….  Use g = 40/G to find the acceleration of free fall g =………………………… FACTORS AFFECTING THE PERIOD OF THE SIMPLE PENDULUM a. Length of pendulum (l): the longer the length of string, the longer the period of the pendulum and vice versa. b. Gravitational field strength (g): the weaker the gravitational field strength, the shorter the period of the pendulum c. Angle of displacement (amplitude): the greater the angle of displacement, the longer the period. It affects the period to a smaller extent Note: Mass do not affect the period of the simple pendulum SOURCES OF ERROR IN MEASUREMENT OF TIME HUMAN REACTION TIME ERROR; this is an error whereby you start the stopwatch early or later when taking measurement. Some time is lost between the exact start and stop of the watch. To reduce this kind of error, we take many readings and do the average or take reading for more than one oscillation so as to increase the accuracy of the period ZERO ERROR: whereby the stopwatch do not start from zero or has not been reset. Instrument accuracy Rule 1 mm or 0.1 cm Micrometre screw gauge 0.01 mm Vernier caliper 0.1 mm, 0.01cm Stop watch 0.01 s or 1 ms  22 EXERCISE 1. The time taken for 10 oscillations is 20.00 s. What is the a) period of the pendulum period=……………………….. b) frequency of the pendulum frequency = …..………………….. 2. What is the accuracy of the metre rule? …………………… 3. What is the accuracy of the micrometer screw gauge? …………………… 4. Fig. 4.1 below shows a Simple Pendulum. Fig. 4.1 a) Define the term Period and Oscillation Oscillation……….………………………………………….……………………………………….. Period……………..…………………………………….……..……………………………….... b) The pendulum takes 8.0s to make 20 oscillations. i. Determine the period of the pendulum. ………………………… ii. calculate the frequency of the pendulum ………………………...  23 MOTION It is the state of an object at any given time. At any given time, an object/body may be:  at rest(stationery)  accelerating/decelerating  moving with constant speed DEFINITION OF TERMS a. DISTANCE: is the length between two points b. DISPLACEMENT (S): is the distance moved in a specified direction Both distance and displacement are measured in metres (m). Distance is a scalar and displacement is a vector quantity. c. AVERAGE SPEED: is distance travelled per unit time average speed(v) = distance time d. VELOCITY: The velocity of a body is its speed in a given direction. The airplane opposite may loop at a constant speed but its velocity changes as its direction of motion changes. SI UNIT: metres per second (m/s) Speed is a scalar and velocity is a vector quantity. u = initial velocity v = final velocity e. ACCELERATION: Is the rate of increase/change of velocity OR is the rate of change of speed in a stated/specified direction. a = change in velocity = (v – u) time t where: a = acceleration in metres per second squared (m/s2) v = final velocity in m/s u = initial velocity in m/s t = time taken in seconds (s) NOTE: Units of acceleration: m/s2 Deceleration is the negative of acceleration. 1. Speed and velocity: Often, but not always, speed can be used in the equation. 2. Change in velocity: = final velocity – initial velocity = v - u 3. Deceleration: This is where the speed is decreasing with time.  24 GRAPHS OF MOTION DISTANCE/DISPLACEMENT-TIME GRAPHS a. UNIFORM DISTANCE TIME GRAPH The slope or gradient of a distance-time graph is equal to the speed, 𝒔 = (∆𝒚/∆𝒙) Uniform/constant speed/velocity (negative) Distance/ Displacement (m) Rest/stationery Uniform/constant speed/velocity (positive) Time/s b. NON UNIFORM DISTANCE TIME GRAPH  25 VELOCITY/SPEED-TIME GRAPHS: The slope of a velocity-time graph represents acceleration, a = (∆y/∆x) a. Uniform motion Uniform/constant deceleration (Uniform decreasing speed) speed/ velocity (m/s) Constant/uniform speed Uniform/constant acceleration (uniform increasing speed) Time/s b. NON UNIFORM SPEED TIME GRAPHS  26 DISTANCE TRAVELLED IN A SPEED/ VELOCITY-TIME GRAPH The area the velocity time graph, gives the distance covered or moved by an object Examples 1. Calculate the distance travelled after 5 seconds from using the graph opposite. distance = area under the graph = area of triangle = ½ x base x height = ½ x 4s x 12m/s =24m 2. Calculate the acceleration and distance travelled using the graph shown below. Acceleration equals the slope of the graph = ∆y/ ∆x = (16 - 4) m/s / (10s) = 12 / 10 Acceleration = 1.2 m/s2 Distance travelled: This equals the area below the graph = area of rectangle + area of triangle = (20m/s x 5s) + (½ x 5s x (40 –20) m/s) = 1000m + 50m Distance travelled = 150m  27 EXERCISE 1. The graph below shows the motion of a part of a car journey. E Velocity (m/s) 10 D B 5 A 0 10 20 30 40 50 60 70 Time (s) a. Describe the motion of the car from point A to point E. ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… …………………………………………………………………………………………………… (b)What is the acceleration of the car between AB and CD? AB…………………….. CD= …………………………….. (c) between which two points is the car accelerating at the greatest rate?..………………………………………………………………………………………………….. (d)between which two points is the car travelling at a steady speed? …..……………………………………………………………………………………………….. (e) Between which two points is the acceleration getting bigger and bigger? ……………………………………………………………………………………………………  28 2. A car is travelling at a constant speed of 25 m/s for 10s. It then slows down until it comes to rest in 5s. Sketch a speed time graph for this motion Calculate the distance travelled over 15 seconds and the deceleration during the final five seconds. acceleration…………………………….. aistance……………………………  29 EQUATIONS OF MOTION There are four equations of motion: 1. v = u + at 2. s = (u +v) t 2 3. v2 = u2 + 2as 4. s = u t + 1 a t 2 2 synonym: suvat where: a = acceleration in metres per second squared (m/s2) v = final velocity in m/s u = initial velocity in m/s t = time taken in seconds in s s = distance/displacement in m QUESTIONS 1. A cheetah starts from rest, and accelerates at 2 m/s2 for 10 s. calculate, a. The final velocity Final velocity………………………….. b. The distance travelled distance……………………….. 5. Calculate the average speed of a car that covers 500m in 20s. 6. Sound waves travel at about 340m/s through air. How far will a sound wave travel in one minute? 7. Calculate the acceleration of a car that changes in velocity from 5m/s to 25m/s in 4 seconds. 8. Calculate the final velocity of a train that accelerates at 0.3m/s2 for 60 seconds from an initial velocity  30 HOMEWORK The following diagram shows the speed - time graph for a dog walking along a pavement. speed (mls) B 20 E 10 D A F G 0 2 4 6 8 10 12 14 Time (s) (i) Describe the motion of the dog between: (a) A and B………………………………………………………………………………………….. (b) B and C………………………………………………………………………………………….. (c) C and D……………………………………………………………………………………......... (d) D and E………………………………………………………………………………………...... (e) E and F………………………………………………………………………………………….. (f) F and G …………………………………………………………………………………………. (ii) (a) what is the velocity of the dog between D and E? ………………………….. (b) what is the velocity of the dog between E and F? ……………………………. 9. Sketch on the same set of axes distance-time graphs for: (a) a car moving at a steady speed, (b) a bus moving at a steady speed greater than the car, (c) a lorry increasing in speed from rest.  31 MOTION OF FALLING OBJECTS All objects near the earth’s surface are being acted upon by a force of gravity due to the earth. The force of gravity accelerates objects towards the earth at the same rate i.e. they have constant acceleration. This acceleration is called acceleration due to gravity or acceleration of free fall, denoted by the letter g Near the earth’s surface, g= 10 m/s2, at the moon is around 1.67 m/s2 and in space is 0 m/s2. FALLING BODIES IN THE ABSENCE OF AIR RESISTANCE: All bodies falling freely experience two forces being gravitational force and air resistance. If the air resistance is negligible, the acceleration of the object will be 10 m/s2.  The velocity of the object moving up will decrease by 10 m/s every second (g = -10 m/s2)  The velocity of the object moving down will decrease by 10 m/s every second (g = + 10 m/s2) Typical graph of object thrown vertical upwards Object moving upwards g = -10m/s2 Object moving downwards g = + 10m/s2  32 So the equations of motion will transform to: 1. v = u + gt 2. s = (u +v) t 2 3. v2 = u2 + 2gs 4. s = u t + 1 g t 2 2 where: g = acceleration in metres per second squared (10 m/s2) v = final velocity in m/s u = initial velocity in m/s t = time taken in seconds in s s = height in m FALLING BODIES IN THE PRESENCE OF AIR RESISTANCE When an object falls through air or some other fluid initially the only significant force acting on it is the downward pull of gravity (weight). As it falls, its velocity/speed increases and this causes air resistance (for objects falling in air) or force of viscosity (for objects falling in liquids). This two forces acts upward and opposes the downward movement of the object. Motion in air motion in liquid On Earth, it will initially accelerate downwards at 10 m/s2. As the object speeds up frictional forces such as air resistance become greater. Eventually the weight of the object balances the frictional forces (air resistance and force of viscosity). Resultant force on the object will be zero and the acceleration will also be zero. The object then moves at a constant speed called TERMINAL VELOCITY. TERMINAL VELOCITY is a constant/uniform speed at which two opposing forces acting on a falling object balances or are equal.  33 Typical graph Uses of terminal velocity in parachuting: A parachutist will have two different terminal velocities. Before opening the parachute it is about 60 m/s. Afterwards, due the much greater drag force, the terminal velocity is about 5 m/s EXERCISE 1. Galileo drops a stone from the leaning tower of Pisa, which is 45 m high, at what speed does the stone reach or hit the ground. ……………………………… 2. A car of mass 800 kg is travelling at 10 m/s. when the brakes are applied, it comes to rest in 8 m. what is the average force exerted by the brakes. …………………………………… 3. A skydiver is falling from an aeroplane. a. Name two forces acting on the diver …………………………………………………………………………………………………… …………………………………………………………………………………..……………..  34 b. State how each force changes as the sky diver speeds up. …………………………………………………………………………………………………… ………………………………………………………………………………..……………….. c. Why does the sky diver reach a steady speed (terminal velocity)? …………………………………………………………………………………………………… ……………….……………………………………………………..………………………… d. Describe and explain what happens when the sky diver opens the parachute. …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………….…..  35 MASS AND WEIGHT MASS: Is the amount of matter in an object. Mass is measured in kilograms (kg). The mass of an object is the same on the Moon as on the Earth. 1 kilogram is the mass of a piece of platinum-iridium alloy at the office of weights and measurements in Paris. 1kg =1000g MASS AND INERTIA Newton 1st Law of Motion All bodies resist a change in motion. A body will be in its state until an external force acts on it. This property of matter to resist change of its state of rest or change of its motion is called INERTIA. That is the reluctance or laziness of a body which is moving to stop moving or if moving to stop moving. The mass of an object is a measure of its inertia. The larger the mass, the larger the inertia is. The smaller the mass the smaller the inertia We can consider to cars;  A large truck: when it is moving, it is difficult to stop and if it is at rest, it becomes difficult (lazy)to move,  A van; has a small mass as compared to the truck, hence easy to stop and start moving Crumple zones, air bags and a collapsible steering wheel are designed to prevent passengers from being thrown out of the car or increase the time taken for a driver or passenger to change momentum to zero during a crash or collision or heavy braking. MASS AND WEIGHT Weight is the force of gravity on an object. It is measured in newtons (N). The weight of an object on the Moon is about one sixth (1/6) that on the Earth. The acceleration due to gravity, gravitational field strength (g): The acceleration due to gravity (g) varies with planet, moon and star and depends on the height of an object. This is an alternative way of measuring the strength of gravity. The gravitational field strength is equal to the gravitational force exerted per kilogram Near the Earth’s surface, g = 10 N/kg In most cases gravitational field strength in N/kg is numerically equal to the acceleration due to gravity in m/s2, hence they both use the same symbol ‘g’. Weight will differ from one location to another depending on the gravitational field strength of that place. In space, we there is no gravitational field strength, the weight or gravitational force on the object will be Zero (0 N)  36 RELATIONSHIP BETWEEN MASS AND WEIGHT 𝑤𝑒𝑖𝑔ℎ𝑡 = 𝑚𝑎𝑠𝑠 × 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝒘 = 𝒎𝒙𝒈 where: w = weight (N) m = mass (kg) g = gravitational acceleration (m/s2) NB: 1 N = 1 kgm/s2 CENTRE OF GRAVITY (C.G)/CENTRE OF MASS (CM) The centre of gravity of a body is that point at which the weight of the body acts. The centre of mass is a point in a body where the entire mass seems to be concentrated. The centre of mass and centre of gravity coincides. Centre of gravity is also sometimes called centre of mass. THE CENTRE OF GRAVITY OF A SYMMETRICAL BODY is along the axis of symmetry. NB: If suspended, a body will come to rest with its centre of gravity directly below the point of suspension so as to obtain equilibrium  37 FINDING THE CENTRE OF GRAVITY OF LAMINA or IRREGULAR OBJECT APPARATUS: card /lamina plumbline retort stand PROCEDURE  Pierce the card in at least two places.  Suspend the card from one of these holes.  Hang a plumbline from the point of suspension.  Using the plumbline as a reference draw a vertical line on the card.  Repeat for the other hole(s).  The centre of gravity is where the lines cross on the card. NOTE: A plumbline is an inextensible string with a small mass attached at one end STABILITY AND TOPPLING A body is stable as long as its centre of gravity remains vertically above its base. If this is not the case, the body will topple. CONDITION FOR TOPPLING: The vertical line through the centre of mass must lie outside the base of the object. Very stable Stable Unstable/topples FACTORS AFFECTING STABILITY A body will become most stable if it has a. A wide base b. Lowered center of mass Racing cars are designed with the above features to make them very stable. The double deck bus is also designed with a lowered center of mass, or else it will topple at some inclined roads  38 TYPES OF STABILITY/EQUILIBRIUM a) Stable equilibrium: if a body is slightly displaced from its original position and released, it returns to its original position b) Unstable equilibrium: if a body is slightly released from its rest or original position and released, it moves further away from its original positional. Its centre of gravity falls c) Neutral equilibrium: if the body is slightly released from its original position, it maintains the new position when displaced. The position of its centre of gravity remains the same.  39 Classwork 1. The table below gives a value for the acceleration due to gravity, g, on various planets. Use it to answer questions which follow. Planet g (m/s2) Pluto 0.5 Mars 4 Earth 10 Jupiter 26 A 30 000 kg Spacecraft leaves earth and visits all the planets listed above. Calculate the weight of the spacecraft in Pluto, Earth, Mars & Jupiter. Pluto……………………..N Earth……………..………N Mars……………………..N Jupiter..……..…………….N 2. A bus and a racing car are travelling at the same high speed in the same direction. They both approach a curve on the road at the same time. The bus overshoots the curve while the racing car negotiates the curve with ease. (i) State two attributes of the racing car which helped it to negotiate the curve............................................................................................................................................................................................................................................................... (ii) State a way in which road curves are constructed so as to minimise cases of vehicles overshooting it. ………………………………………………………………………………………..... 4. A truck and a small car are travelling along a straight road at the same speed. Both drivers see an obstacle on the road and apply the brakes at the same time. Which vehicle is likely to stop first? Give a reason for your answer. ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………..……  40 DENSITY It is defined as the mass per unit volume of a substance. The unit of density is kg/m3 or g/cm3. It is denoted by Greek symbol ρ (rhoo) and is calculated from the formula: 𝒎𝒂𝒔𝒔 𝐝𝐞𝐧𝐬𝐢𝐭𝐲 = 𝑽𝒐𝒍𝒖𝒎𝒆 𝒎 𝛒= 𝑽 Units: kg/m3 or g/cm3 Density of regularly shaped solid: The mass can be determined by top-pan balance and the volume by multiplying length, width and height. For cylindrical objects volume is area of cross section multiplied by length. Then the density found using the above equation. Density of irregularly shaped solid Mass of the solid is determined by top-pan balance. The volume of solid is obtained by subtracting the value before and after immersing the rock in a measuring cylinder containing water. This method is called displacement method. Density calculated using the above equation Density of liquid The mass of an empty beaker is found on a balance. A known volume of the liquid is transferred from burette or measuring cylinder into the beaker. The mass of beaker plus liquid is found and the mass of liquid is obtained by subtraction.  41 Density of air: The mass of a 500 cm3 round-bottomed flask full of air is found and then after removing the air with a vacuum pump; the difference gives the mass of air in the flask. The volume of air is found by filling the flask with water and pouring it into a measuring cylinder. RELATIVE DENSITIES OF LIQUIDS HYDROMETER A hydrometer consists of a sealed hollow glass tube with a wider bottom portion for buoyancy, a ballast such as lead or mercury for stability and a narrow stem with graduations for measuring. The stem is calibrated to give a numerical reading such as specific gravity. The liquid to test is poured into a container, often a graduated cylinder and the hydrometer is gently lowered into the liquid until it floats freely. The point at which the surface of the liquid touches the stem of the hydrometer correlates relative density. The hydrometer makes use of Archimedes’ Principle: A solid suspended in a fluid is buoyed by a force equal to the weight of the fluid displaced by the submerged part of the suspended liquid. The lower the density of the liquid, the deeper a hydrometer of a given weight sinks and vice versa. Hydrometers are calibrated differently for different uses  42 EXERCISE NB: 1 mL = 1 cm3 1. A gold-colored ring has a mass of 18.9 grams and a volume of 1.12 cm3. Is the ring pure gold? (The density of gold is 19.3 g/cm3.) …………………..… 2. What volume would a 0.871-gram sample of air occupy if the density of air is 1.29 g/L? ………………….. 3. Pumice is volcanic rock that contains many trapped air bubbles. A 225-gram sample occupied 236.6 cm3. What is the density of pumice? ……………………… Will pumice float on water? The density of water is 1.0 g/cm3. ………………………………………………………………………………………………………… 4. A cup of sugar has a volume of 237 cm3. What is the mass of the cup of sugar if the density is 1.59 g/cm3? …………………………. 5. Which has the greater mass, 1-liter of water or l litre of gasoline? The density of water is 1.00 g/ cm3 and that of gasoline is approximately 0.68 g/cm3. ………………………… 6. A crumpet recipe calls for 175 grams of flour. According to Julia Child's data, the density of flour is 0.620 g/cm3. How many cm3 of flour are needed for this recipe? …………………………  43 7. From their density values, decide whether each of the following substances will sink or float when placed in sea water, which has a density of 1.025 g/cm3. Gasoline 0.66 g/cm3__________ Asphalt l.2 g/cm3_________ Mercury 13.6 g/cm3__________ Cork 0.26 g/cm3__________ 8. A sample of lead is found to have a mass of 32.6 g. A graduated cylinder contains 2.8 cm3 of water. After the lead sample is added to the cylinder the water level reads 5.7 cm3. Calculate the density of the lead sample. …………………….….. 9. A piece of magnesium is in the shape of a cylinder with a height of 5.62 cm and a diameter of 1.34 cm. If the magnesium sample has a mass of 14.1 g, what is the density of the sample? ……………………… 10. 28.5 g of iron shot is added to a graduated cylinder containing 45.50 mL of water. The water level rises to the 49.10 mL mark, from this information, calculate the density of iron. ………………………..  44 FORCES A force is a push or a pull. A force can cause an object to:  speed up(accelerate)  slow down(decelerate)  change direction  change shape Force is measured in: newtons (N). It is measured with an instrument called newtonmeter. SOME TYPES OF FORCE 1. Gravitational: This is the attractive force exerted between bodies because of their masses. Bathroom scales measure weight. Weight is the gravitational force of the Earth on an object (w =mg).A mass of 1kg weighs about 10N on earth This force increases if either or both of the masses are increased and decrease if they are moved further apart. 2. Normal reaction or contact: This is the repulsive force that stops two touching bodies moving into each other. The word ’normal’ means that this force acts at 90° to the surfaces of the bodies. It is caused by repulsive molecular forces. 3. Air resistance or drag: This is the force that opposes the movement of objects through air. Drag is a more general term used for the opposition force in any gas or liquid. Objects are often streamlined to reduce this force. 5. Upthrust (buoyancy): This is the force experienced by objects when they are placed into a fluid (liquid or gas). An object will float on a liquid if the upthrust force equals its weight. 6. Magnetic force: Between magnets but also the force that allows electric motors to work. 7. Electrostatic: Attractive and repulsive forces due to bodies being charged.  45 8. Friction: This is the force that opposes motion. The kinetic energy of the moving object is converted to heat energy by the force of friction. Friction is needed for racing cars to grip the road, holding objects and for walking! Friction can cause: Wearing off of surface in contact Overheating of object in contact Slowing down of objects Friction can be minimised by Oiling or lubricating moving parts Streamlining Using rollers/wheels  46 EFFECTS OF FORCE ON AN OBJECT FORCE AND CHANGING SHAPE Force can change the shape of an object. A stretching force puts an object such as a wire or spring under tension. A squashing force puts an object under compression. Brittle materials such as glass do not change shape easily and break before noticeably stretching. Resilient materials do not break easily. Elastic materials return to their original shape when the forces on them are removed. Plastic materials retain their new shape. DETERMINATION OF HOOKE’S LAW Apparatus: spring masses ruler Retort stand mass hanger pin Experimental procedure: Arrange the apparatus as shown in diagram below 1. Place the weight holder only on the spring and note the position (lo) of the pin against the metre rule. 2. Add 1N (100g) to the holder and note the new position of the pin. 3. Calculate the extension of the spring using the equation: (e = l - lo) 4. Repeat stages 1 to 3 for 2N, 3N, 4N, 5N and 6N. DO NOT EXCEED 6N. 5. Plot a graph of Load/N against extension/mm 6. Calculate the gradient of the line to get force/spring constant (k)  47 RESULTS AND ANALYSIS Force/N New length(cm) Extension(cm) 1.0 2.0 3.0 4.0 5.0 Typical Graph: Force against extension graph CONCLUSION FROM THE GRAPH/RESULTS: Extension is directly proportional to the load. Hooke’s law Hooke’s law states that: The extension of a spring is directly proportional to the force used to stretch the spring PROVIDED the elastic limit or limit of proportionality is not exceeded. f α e force = force constant, k x extension, e f=ke where: force(f) is in newtons (N) e = extension k = spring constant  48 ‘Proportional’ means that if the force is doubled then the extension also doubles. The line on a graph of force against extension will be a straight and go through the origin. ELASTIC LIMIT The right hand spring has been stretched beyond its elastic limit. Up to a certain extension if the force is removed the spring will return to its original length. The spring is behaving elastically. If this critical extension is exceeded, known as the elastic limit, the spring will be permanently stretched. Hooke’s law is no longer obeyed by the spring if its elastic limit is exceeded. Force against extension graph if the elastic limit is exceeded for a stretching elastic band or spring Elastic rubber band elastic spring EXAMPLE 1. A spring of original length 150mm is extended by 30mm by a force of 4N. Calculate the length of the spring if a force of 12N is applied. 12N is three times 4N Therefore the new extension should be 3 x 30mm = 90mm New spring length = 150mm + 90mm = 240mm 2. The original length of a spring is 5cm and the spring constant is 2.5N/cm. Find the extension produced by a force of 50N by the same spring. ……………………….  49 IDENTICAL SPRINGS IN SERIES AND PARALLEL Series: in series each spring experience the same load hang on them. The extension on each spring is as if it was alone in the arrangement. 𝒏𝑭 The total extension is given by: 𝒆 = , where n is the number of springs. Extension, e is the 𝐤 total for the springs SPRINGS IN PARALLEL 𝑭 The total extension is given by: 𝒆 = , where n is the number of springs. Extension is for 𝐧𝐤 each spring.  50 Example 1. A spring has an original length of 6 cm. When a force of 2 N is hung on it, the new length becomes 10 cm. Calculate; a) The extension caused by a 2N force. …..…………………… b) The spring constant of the spring ……………………….. c) The new length of the spring ………………………….. Two identical springs to the above are arranged in series and a force of 6N hung on them. Calculate; d) The total extension produced by the springs ……………….………. e) The new length of each spring ……………………….. f) Total length of the springs ………………………..  51 2. A spring has a new length of 10 cm when a 4N force is hung on it. When the force is increased to 6N the new becomes 14 cm. b. Calculate the spring constant of the spring ……………………. c. What extension is produced by a force of 6N? …………………… d. What is the original- spring length? …………………….. Another identical spring is placed alongside (parallel) with the above spring and a force of 10N hung on them. e. What will be the extension on each spring? ………………………… f. What will be the total extension produced on each spring? ……………………. g. If the same spring were placed in series and the same force of 10N hung, what will be the extension on each spring, total extension by all springs and the new length of the springs? Extension……………..………….. Total extension…………………………. New length………………………  52 3. Two identical springs of length 8 cm are placed alongside each other with a mass of 400g If one spring produces an extension of 2 cm for a mass of 200g, what will be the new length of each spring when a mass of 400g is hung on the spring connected in parallel? ……………………….. 4. A spring extends by 10 cm when a mass of 100 g is attached to it. a) What is the spring constant? K=……………………… b) What will be the extension of this spring if the load is 75 g? …………………… c) If an identical spring were connected in parallel (do a sketch), i. what mass would need to be attached to produce an extension of 15 cm? ……………………… ii. What mass would be needed if two of these springs were placed in series (do a sketch) and an extension of 30 cm was required? …………………………  53 EFFECTS OF FORCE ON MOTION A force can cause: An object to move when push force is greater than the friction force. The plane will accelerate provided that the engine force is greater than the drag force. The brakes exert a resultant force in the opposite direction to the car’s motion causing the car to decelerate. Resultant force A number of forces acting on a body may be replaced by a single force which has the same effect on the body as the original forces all acting together. This overall force is called resultant force. It causes objects to speed up (accelerate) or down(decelerate). EXAMPLES NEWTON’S 2ND LAW OF MOTION: states that acceleration of an object is directly proportional to resultant force for a fixed mass. The resultant force, mass and acceleration of an object are related by the equation: 𝑹𝒆𝒔𝒖𝒍𝒕𝒂𝒏𝒕 𝒇𝒐𝒓𝒄𝒆 = 𝒎𝒂𝒔𝒔 × 𝒂𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏 𝑭 = 𝒎𝒂 Where: f = force (N) m =mass (kg) a = acceleration (m/s2)  54 EXAMPLE 1. Calculate the force required to cause a car of mass 1200 kg to accelerate by 5 m/s2. F=ma = 1200 kg x 5 m/s2 = 6000 N 2. Calculate the acceleration produced by a force of 200N on a mass of 4kg. F=ma a=F÷m = 200N ÷ 4kg acceleration = 50 m/s2 Car forces When a vehicle travels at a steady speed the frictional forces balance the driving force. To slow the car the engine force is reduced by releasing the throttle and the frictional force is increased by applying the brakes. Stopping a car The total distance required to stop a car, the stopping distance, is equal to the thinking distance plus the braking distance. Factors affecting stopping distance 1. The reaction time of the driver: This will increase if the driver is tired, distracted or has consumed alcohol or drugs. Increasing reaction time increases the thinking distance. 2. The speed of the car: The greater the speed the greater will be both the thinking and braking distances. Doubling the speed increases the overall stopping distance by about four times. 3. The mass of the car and its contents: The greater the mass the greater will be the braking distance. 4. The condition of the road: Wet and icy roads will cause the braking distance to increase. 5. The condition of the vehicle: Worn brakes or worn tyres will both increase the braking distance.  55 EXERCISE 1. A Saturn V Moon rocket has a mass of 3.0 x106 kg. The thrust at lift off is 3.3 x107 N. Find a. The weight of the rocket ……………………… b. The resultant or unbalanced force force at lift off....................................1] c. The acceleration at lift off ……………………….. d. The apparent weight of the rocket in orbit. ……………………….. 2. A ball is thrown vertically upwards at 20 m/s. ignoring air resistance and taking g = 10 N/kg or 10 m/s2, calculate a. How high it goes ……………………. b. The time taken to reach its highest point ……………………. c. Time taken to return to its starting point. ……………………. 3. When a force of 6 N is applied to a block of mass 2 kg, it moves along a table at constant velocity. a. What is the frictional force …………………… b. When the force is increased to 10 N, what is i. The resultant force ….………………. ii. The acceleration ………………….. iii. The velocity, if it accelerate from rest for 10 s..............................  56 MOMENT OF A FORCE Moment of a force: Also known as the turning effect of a force. It is a product of the applied force and perpendicular distance of applied force from the pivot/fulcrum. Examples of application of moments  Levers (force multipliers)  Opening a door/window  Tightening a nut The moment of a force about any point is defined as: 𝒎𝒐𝒎𝒆𝒏𝒕 = 𝑨𝒑𝒑𝒍𝒊𝒆𝒅 𝒇𝒐𝒓𝒄𝒆 𝒙 𝒑𝒆𝒓𝒑𝒆𝒏𝒅𝒊𝒄𝒖𝒍𝒂𝒓 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇 𝒂𝒑𝒑𝒍𝒊𝒆𝒅 𝒇𝒐𝒓𝒄𝒆 𝒇𝒓𝒐𝒎 𝒕𝒉𝒆 𝒑𝒊𝒗𝒐 𝒎 = 𝒇𝒙𝒅 Unit: newton-metre (Nm) Moments can be either CLOCKWISE or ANTICLOCKWISE Example Calculate the moment exerted with the claw hammer if the person exerts a force of 80N and distance d equals 25cm. moment = F x d = 80N x 25cm = 80N x 0.25m = 20 Nm CLOCKWISE THE PRINCIPLE OF MOMENTS When an object is not turning (e.g. balanced/equilibrium): The total clockwise moment equals the total anticlockwise moment If the ruler above is balanced: 𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒 𝑚𝑜𝑚𝑒𝑛𝑡 = 𝑎𝑛𝑡𝑖𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒 𝑚𝑜𝑚𝑒𝑛𝑡 𝑾𝟐 𝒙 𝒅𝟐 = 𝑾𝟏 𝒙 𝒅𝟏  57 EXAMPLES 1. On a see-saw Mary, weight 600N balances John, weight 200N when she sits 1.5m away from the pivot. How far from the pivot is John? Applying the principle of moments: Mary’s weight x distance = John’s weight x distance 600N x 1.5m = 200N x distance 900 ÷ 200 = d John is 4.5m from the pivot 2. Calculate the weight of the beam, W0 if it is balanced W 1 = 6N; d1 = 12 cm; d0 = 36 cm. Applying the principle of moments: W1 x d1 = W0 x d0 6N x 12 cm = W0 x 36 cm W0 = 72 / 36 W0 the weight of the beam = 2N EXERCISE 1. A spanner was used to undo a nut. A force of 20 N was applied at a distance of 20 cm from the nut. Calculate the moment of the force being used. …..……………….. 2. A uniform metre rule of mass 100 g balances at the 40 cm mark when a mass X is placed at the 10 cm mark. What is the value of X? X = ………………….  58 3. If the ruler in the diagram below is balanced, what is the weight W 25 cm 15 cm 25 cm W 4N 1N n W =……………...... 4. The ruler below is balanced at their centre of gravity. What is weight of the X? 20 cm 25 cm X 4N X =………….……… 5. What is the value of Y if the ruler is in equilibrium 20 cm 40 cm 25 cm W 1N 2N Y=…………………..  59 FORCES ON A BEAM Newton’s 3rd law of motion states that: forces always occur in pairs. Each force has the same size but acts in opposite directions. Example 2: Tyre-road friction A car is able to move forwards due to friction acting between its tyres and the road. The force of friction of the road on the tyre acts in the forward direction and is equal but in the opposite direction to the force of friction of the tyre on the road. The law is often expressed as: “To every action there is an equal and opposite reaction” For parallel forces, if the beam balances (in equilibrium), 2 conditions must be satisfied: 1. The sum of the forces in one direction must be equals the forces in opposite direction, that is the resultant force must be Zero 2. The law of moments must apply, meaning that the resultant moment must be Zero  60 Example 1. A mass of 60 kg is placed on a 6m long plank whose weight can be neglected. The plank is supported at two points A and B as shown below, what is the resultant force at each support or pivot R + S = 600N and taking moments about pivot A, 600N x 1m = S x (1m +3m) 600Nm = 4Sm S = 600Nm/4m S =150N Therefore: R + S = 600N R + 150N = 600N R = 600N – 150N R = 450N EXERCISE 1. Calculate the reaction Q and P in the diagrams below P………………………….. Q………………………..  61 4. A body of mass 50 kg is resting on a 10m long beam. The beam is in equilibrium when supported by two pivots as shown below find the reaction of each pivot. X…………………………………….. Y………………………………….. COUPLES If parallel forces act on the same body, they form a couple which will cause a rotation e.g. a steering wheel. Equal and opposite parallel forces form what we call a torque.  62 5. Fig. 5.1 shows apparatus for investigating moments of forces. Fig. 5.1 The uniform metre rule shown in Fig. 5.1 is in equilibrium. (a) Write down two conditions for the metre rule to be in equilibrium. Condition 1.............................................................................................................................................................................................................................................................................................. condition 2......................................................................................................................................................................................................................................................................................... (b) Show that the value of the reading on the spring balance is 8.0 N. ………………………. (c) The weight of the uniform metre rule is 1.5N. Calculate the force exerted by the pivot on the metre rule. magnitude of force = ………………………………… direction of force =………………………………  63 VECTORS AND SCALARS All physical quantities (e.g. speed and force) are described by a magnitude and a unit. VECTORS – also need to have their direction specified. Examples: displacement, velocity, acceleration, force. SCALARS – do no