CSEC PHYSICS MANUAL OF ESSENTIAL NOTES By Kevin Jared Hosein Based purely on syllabus requirements. Worked example questions and practice questions at the back. Complete list of formulae and laws at back. 1 PHYSICS, SECTION A (1/2) : MEASUREMENTS AND STATICS QUANTITIES AND UNITS The SI (Standard International) unit system is the most widely used system in measurement and comprises seven fundamental units. A fundamental quantity, also called a base quantity, is known as one that is independent from the others and usually cannot be expressed using other quantities. A derived quantity is one that is a combined product of different fundamental ones, e.g. ‘speed’ is derived from distance (length) and time, two base quantities. ‘Area’ and ‘volume’ are derived from multiple lengths. The table below shows units the seven“fundamental quantities”. Quantity Symbol Unit Name Measuring Instrument Length l Metre (m) Metre rule Measuring tape Vernier caliper Micrometer screw gauge Mass M Kilogram (kg) Scale balance / Triple beam balance Time T Second (s) Stopwatch Electronic Current I Ampere (A) Ammeter Temperature T or ϴ Kelvin (K) Thermometer Amount of a Substance n Mole (mol) --------- Luminous Intensity L Candela (cd) --------- This table shows a few derived quantities. Quantity Unit Unit Breakdown Measuring Instrument Volume m3 mxmxm Measuring cylinder / Burette Force N kg m/s2 Force-metre / Spring balance Speed m/s m÷s Ticker tape timer Pressure Pa (kg m/s2)/m2 Barometer / Manometer 2 ENSURING ACCURACY WHEN TAKING MEASUREMENTS 1. Avoiding parallax errors – These occur when the experimenter is not viewing the readings at eye level. Not doing this can cause inaccurate data to be recorded. When possible, equipment should always be placed on a level surface. Sometimes perpendicular aids must be constructed from set squares in order to read instruments accurately. 2. Avoiding zero errors – Before using an instrument, it is important that it is calibrated to read zero at the start of the experiment. Scales and stopwatches have an option to reset to zero while the gauges on ammeters and voltmeters must be checked beforehand. 3. Human response time – When taking readings with stopwatches, for example, the actual time for the experimenter to start and stop the stopwatch causes a delay and accounts for a slight error in measurement. This is why it is important to repeat an experiment multiple times. The table below shows a list of some unit prefixes that denote the magnitude (size) of the unit. Prefix Symbol Power SI Unit Conversion Example Mega M 10+6 5.0MJ = 5.0 x 106 J = 5000000 J Kilo k 10+3 4.52km = 4.52 x 103 m = 4520 m Centi c 10-2 300cm = 3 x 10-2 m = 3 m Milli m 10-3 6.8 ms = 6.8 x 10-3 s = 0.0068 s Micro µ 10-6 4500 μA = 4500 x 10 -6 A = 0.0045 A 3 STANDARD FORM & UNIT CONVERSION Standard form is a means of expressing large numbers in simple ways using integer powers and usually three significant figures. Note that the decimal point goes after the first significant figure. For e.g. 54880N in standard form (to 3 s.f.) will be written as 5.49 x 104 N. 0.006483J in standard form (to 3 s.f.) will be 6.48 x 10-3 J. How to convert km/h to m/s How to convert m/s to km/h Convert 108km/h to m/s Convert 18m/s to km/h THE SCIENTIFIC METHOD The scientific method is a process for creating setups of situations to examine factors of the real world and gather data from testing. This data can then be analyzed and replicated by other scientists to further study the models and draw reasoning from them. It was first used by scientists such as Isaac Newton and Galilei Galileo. The scientific method has FOUR main steps: 1. OBSERVATION - Which can be made visually or through apparatus. 2. HYPOTHESIS - A statement made that has to be proven true or false. It has to be testable. 3. METHODOLOGY - Formulating a method to test the hypothesis and gather data. May have to be repeated several times to validate results under various conditions. 4. ANALYSIS - Determining whether or not the results conform to the hypothesis and formulating a theory based on them. PERIOD OF A PENDULUM One of the first major experiments in Physics was Galileo’s determination for the acceleration due to gravity on Earth, also known as g. This was done using a pendulum with strings of varying lengths. 4 Example question: Complete the table and plot a graph of T2 vs. L. Length, L (m) Time for 20 oscillations, t(s) Period, T (s) Period Squared, T2 (s2) 0.10 12.96 0.65 0.42 0.20 18.00 0.90 0.81 0.30 22.00 1.10 1.21 0.50 28.28 1.41 1.99 0.60 31.10 1.56 2.43 Now calculate the acceleration due to gravity, g, using this formula. Put the unit for your answer as m/s2 as that is the unit for acceleration. (π = 3.14) 5 SCALARS AND VECTORS Quantity Definition Examples Scalar A quantity that has magnitude but NO direction. Distance, speed, area, volume, density Vector A quantity that has BOTH magnitude and direction. Displacement, velocity, acceleration, force, momentum Parallel and antiparallel vectors: We just add the vectors to form a single vector called a RESULTANT. A single vector may also be the resultant of two other vectors, e.g. an airplane’s overall flight direction is a combination of the engines’ thrust, gravity and the wind. Opposite direction vectors (antiparallel) are viewed as negative. Draw the resultant vectors for the two examples below. NON-PARALLEL VECTORS Draw and measure the resultant forces for both diagrams below. Question: An airplane is flying east in still air at 92m/s. A heavy north-east wind starts to blow at 36m/s at 45o. Using a scale of 1cm:10m/s, draw a vector diagram to show the resultant velocity of the plane. Measure the angle the plane deviated from its original path. 6 MASS AND WEIGHT Quantity Definition Example Mass The amount of matter contained in an object. It is a measure of an object’s INERTIA or resistance to change in motion. A truck has more mass than a car and thus, would resist a change in motion more than a car would. It would take longer to speed up and require more force on its brakes. Weight The force exerted on a body’s mass by gravity. An astronaut on the Moon would have the same mass on Earth but less weight, because the Moon’s gravitational field is weaker. Note the formula for weight: CENTRE OF GRAVITY AND STABILITY Objects balance at a point called the centre of gravity. The centre of gravity of an object can be defined as THE POINT AT WHICH THE WEIGHT OF A BODY ACTS. The force of weight acts downward from the centre of gravity. Imagine it as a straight line vector pointing down from that position. Objects or systems that are stable tend to have most of their mass deposited much LOWER than unstable ones. They are said to have a low centre of gravity. Observe the shapes below. An irregular lamina’s centre of gravity can be found by boring holes and hanging a plumbline from each hole The purpose of the plumbline is to see which points are vertically below the hole. By marking the lines, an intersection will be noticed. This is the lamina’s 7 centre of gravity. FORCES Forces enable masses to overcome inertia, i.e. they are able to cause a change in an object’s acceleration, deceleration or direction (even shape and size, but NOT mass) Forces are measured in Newtons (N) which can be derived as 1N = 1 kg m/s2. Type of Force Description GRAVITY Pulls objects towards the centre of the Earth. WEIGHT The effect of gravity on an object’s mass. FRICTION The resistance an object experiences when rubbing a surface. BUOYANCY / UPTHRUST The upward force exerted by a fluid. ELECTROSTATIC Attraction due to charged particles called electrons stored in an object. MAGNETIC An attraction or repulsion caused by north and south poles. REACTION The force that always acts opposite to another, e.g. the forward push from swimming while pushing the water backward. TENSION An upward force exerted on a string or rope attached to a load. CENTRIPETAL The pull towards a central point for an object moving in a circle. NUCLEAR The attraction holding the nucleus of an atom together. ● Forces may be CONTACT or NON-CONTACT. They may also be ABSORBED, such as by kneepads worn by athletes, cyclist helmets, bubblewrap packaging and cellphone cases. When a force is absorbed, its impact is decreased. ● All moving objects on Earth experience some form of resistance, whether from the surface they are on (friction) or the medium that they are in, such as the atmosphere (called air resistance or drag). In this example, the two “resistant forces” are equal to the applied forward thrust of the car. This will give an overall resultant or net force of 0 Newtons. This doesn’t mean the car will stop. This means that the object is in EQUILIBRIUM and is moving at a constant velocity. Therefore, we can say that if a force is absent, there will be no change in motion or direction. 8 9 AIR RESISTANCE & TERMINAL VELOCITY Observe the panels below: 1. As he falls, GRAVITY initially pulls him down. 2. AIR RESISTANCE acts upwards, making his ACCELERATION DECREASE (NOT decelerate). 3. Eventually, the air resistance will be equal to his weight. He will then be held at EQUILIBRIUM and fall at a CONSTANT SPEED. Acceleration stops at this point. This balanced velocity is referred to as TERMINAL VELOCITY. 4. When he opens the parachute, he decelerates (velocity decreases) as the parachute has a wide surface area that increases his air resistance. 5. As his velocity decreases, his air resistance also decreases until the forces are balanced again. He falls at a safe terminal velocity, no longer accelerating. 6. When he hits the ground, the ground causes a sudden deceleration that brings him to rest. The ground hits him back with a REACTION FORCE to stop him. FREEFALL When an object is accelerating due to gravity only, it is said to be in freefall. If on Earth, this is to be taken as 10 m/s2 (rounded off from 9.81m/s2) this means that with each second, the velocity increases by 10 m/s. So, after 5s in freefall, the velocity would be 50 m/s. 10 . LEVERS A lever is a type of simple machine. Machines are designed to make work easier, which means that they can either: 1. Modify or transmit forces and motion 2. Convert different types of energy into mechanical energy All machines have an input and an output. The input force is usually referred to as the EFFORT and the output as the LOAD. Levers have a point of rotation that these forces will turn about. This point of rotation is referred to as the PIVOT or FULCRUM. The greater the distance from the fulcrum, the greater magnitude of turning force the effort would have. This turning force is sometimes referred to as a MOMENT or a TORQUE. There are THREE classes of levers. On the diagrams below, label the effort, load and fulcrum and determine which class of lever each is. Class Placement First Fulcrum between effort and load. Second Load between effort and fulcrum. Third Effort between load and fulcrum. 11 PRINCIPLE OF MOMENTS The drawing depicts Odie trying to balance Garfield, whom is heavier. Let’s also say that the two of them are at a balance or equilibrium. How far would Odie have to be from the pivot to balance Garfield? Each above is creating a turning force or MOMENT. Moments are determined about the turning point or fulcrum, so any distances used in calculation must be measured from the fulcrum. Note the formula for calculating a moment: Moment = Force x Distance Unit = Nm Using the figures shown, what is the force applied to the effort end of the wheelbarrow? F1D1 (load) = F2D2 (effort) 600 x 1.2 = F2 x (1.8 + 1.2) 720 = 3 F2 F2 = 720 ÷ 3 = 240 N Reena, Mark and Sharon, sit on a seesaw fashioned from a log resting on a pivot. Each of them has the same weight of 500N. Mark sits 0.4m away from the pivot and Sharon sits 0.8m away from the pivot. For the seesaw to be in equilibrium, calculate the distance Reena has to sit to balance Mark and Sharon. 12 HOOKE’S LAW However, when a load (F) is attached, the spring extends. This extension is noted as x. The total length of the spring is now given as (L0 + x). When an object changes shape due to the action of a force upon it, the object is said to experience DEFORMATION. On the diagram, the initial length of the spring is noted as L0. This is when no weight is attached. As the weight of the load is increased, the extension will increase. If the weight is doubled to 2F, the extension will double to 2x. The constant (k) can be obtained by finding the gradient of an extension-force graph. To put it simply, k represents the “stiffness” of the spring. A bigger ‘k’ value would require more force to extend the spring. HOWEVER, there is a point where the proportionality will stop if too much weight or force is applied to the spring. This is called the LIMIT OF PROPORTIONALITY. Beyond this point is the ELASTIC LIMIT, where further extension can cause permanent deformation of the spring. Example question: The initial length of a spring is 10mm. A 20N weight is attached and it has a length of 14mm. What is the extension and length of the spring if 50N were attached? 13 DENSITY AND ARCHIMEDES’ PRINCIPLE Density is defined as MASS PER UNIT VOLUME. However, Cube A is considered denser because it has more MASS. Cube A has twice as much mass in it than Cube B. Therefore, we can say that Cube A is twice as dense than B. Cube B can be made denser by: 1. Adding more mass. 2. Decreasing its volume (compacting it). Note these two objects. They are both cube containers of the same size and volume. Note the formula and units for density: Archimedes’ Principle states that: THE UPWARD FORCE THAT IS EXERTED ON AN OBJECT IMMERSED IN A FLUID IS EQUAL TO THE WEIGHT OF FLUID DISPLACED. 14 15 RELATIVE DENSITY Relative density is a given ratio of the density of a substance in reference to the density of another substance (usually the medium it is kept in). It is one of few quantities with NO UNIT. For e.g. if the block below had a mass of 6000kg and was kept in a container of mercury, what would be its relative density is mercury had a density of 13,600kg/m3? SINKING AND FLOATING Whether or not an object sinks or floats depends on two things: the density of the object, and the density of the medium the object is held in. There are usually two forces that act on the object at this point: a downward force (WEIGHT) and an upward force known as UPTHRUST. NOTE: The density of pure water is given as 1000 kg/m3 or 1 g/cm3. Since seawater has salt and other substances, its density would be slightly higher. 16 PHYSICS. SECTION A (2/2): DYNAMICS AND ENERGETICS DISTANCE AND DISPLACEMENT Distance is the HOW MUCH GROUND AN OBJECT HAS COVERED. The magnitude is of importance, not the direction, therefore distance is noted as a SCALAR quantity. Displacement is the OVERALL CHANGE IN POSITION OF AN OBJECT IN A STRAIGHT LINE BETWEEN ITS ORIGIN AND DESTINATION. Both magnitude and direction are importance. It is therefore a VECTOR. Looking at the example to the left, if a person ran from A to B and then B to C, they would have travelled a distance of 7m but a displacement of 5m. DISPLACEMENT-TIME GRAPHS Displacement-time graph simply show an object’s position as time passes. Observe the graph below. It shows that after 5 seconds, the object is 25m away from the starting position. From 5s to 10s, the object has not moved since its position is still 25m away. For the last 2.5s, the object has returned to its starting position. Calculating the gradient of a line in the graph gives the object’s VELOCITY. 17 SPEED AND VELOCITY Quantity Definition Formula Unit Category Speed (s) Distance travelled per unit time time. s=d m/s or ms-1 SCALAR Displacement travelled per unit time. v=x m/s or ms-1 VECTOR Velocity (v) t t ACCELERATION When the velocity of an object is changing, it has an acceleration. It can either speed up or slow down or change direction. A positive acceleration denotes that the velocity has increased over time. A negative acceleration (or deceleration) denotes that velocity has decreased over time. Acceleration is therefore defined as the CHANGE IN VELOCITY OVER TIME. It is a VECTOR quantity. Note the formula and unit for acceleration below: VELOCITY-TIME GRAPHS These graphs above represent an object’s change in velocity as time passes. HOWEVER, note that the lines are straight for the left figure and curved for the right figure. The acceleration in graph A is said to be UNIFORM while graph B is said to be NON-UNIFORM. Since the line is getting less and less steep in the right figure, the acceleration can be said to be at a decreasing rate. 18 Observe the LEFT figure for now. Aside from the appearance of the graph and general idea of motion, other quantities can also be deduced and calculated from the graph: ● The ACCELERATION can be obtained by calculating the gradient of the slope. ● The DISPLACEMENT can be obtained by calculating the area under the required portion of the graph. If the displacement for the entire journey is required, we need to find the area of a trapezium in this case, which is given by the following formula: Example Question (Graphwork) 1. Calculate the gradients of B and D, and the displacement of BCD. Example question: Plot the events on the graph. Label the points. A – The driver begins at 10m/s and keeps going at constant velocity for 20 seconds. B – He takes 10 seconds to decelerate uniformly until he comes to rest. C – He remains at rest for 10 seconds. D – He accelerates in reverse for 10 seconds until he is at -10m/s. E – He reverses at a constant velocity of -10m/s for 20 seconds. F – He decelerates for 10 seconds until he is at rest again. 19 20 NEWTON’S THREE LAWS OF MOTION Before Isaac Newton’s laws of motion were made known, many people ascribed to Aristotle’s Law of Motion, which basically stated that “Nothing moves unless you push it. An object’s speed is proportional to the force applied to it.” We learned previously that this is not true because: A force is not required to keep an object moving. If there was no friction, an object would keep moving forever. Newton’s Three Laws are stated below: Law What the Law States Example 1st An object at rest remains at rest, or an object in motion remains in motion at a constant velocity, unless an unbalanced force acts upon it. A trolley will stay where it is unless someone pulls or pushes it. It cannot move unless a force is applied to it. The force on a body is directly proportional to its acceleration. A trolley with more mass will need a greater force to get it to accelerate at the same rate as a trolley with less mass. 2nd (F = ma) 3rd Every action force has an equal and opposite reaction force. If a Body A acts on Body B, then B exerts an equal and opposite force on A. Similarly, if a trolley is moving, a force will be needed to stop it. This force could be friction, air resistance or the reaction force from a collision. In order to swim forward, a person must push the water backwards. Pushing the water back is the “action” while the water pushing the body forward is the “reaction”. Think about how Newton’s Laws apply to the following situations: 1. 2. 3. 4. 5. A rocket or airplane being able to propel itself upward or forward. A child jumping on a trampoline. Why an astronaut would need to tie themselves to an object while doing repairs in space. Why a loaded truck is harder to stop than an empty one Why seatbelts or deployable airbags are necessary in cars 21 LINEAR MOMENTUM AND IMPULSE Linear momentum is defined as THE PRODUCT OF AN OBJECT’S MASS AND VELOCITY. Momentum is a VECTOR quantity, since it has a direction. The force that produces a change in momentum of a body is called an IMPULSE. Note the formulas and units for momentum and impulse: Scenario A: The white ball hits the 8-ball, transferring all its momentum to it, and comes to a stop. The 8-ball then moves at the same velocity as the white ball. Scenario B: The two balls move at a combined mass. Since the combined mass is exactly twice as large, the resultant velocity will be halved,. The law of conservation of linear momentum states that: IN A CLOSED SYSTEM, THE TOTAL MOMENTUM BEFORE COLLISION IS EQUAL TO THE TOTAL MOMENTUM AFTER COLLISION. 22 LINEAR MOMENTUM AND COLLISION The previous examples dealt with one moving object colliding with a stationary object. However, what would happen if we had a question like this: PROBLEM 1: A car, heading east at 24m/s, of mass 1200kg collides with a 4000kg truck, heading west at 5m/s. If the wreckage moves as a combined mass, what is the velocity and direction it moves at? First, calculate the total momentum in the system before collision. This momentum should be equal to the momentum of the wreckage after collision. The wreckage’s mass is the sum of both vehicles. (Recall that one of the values for velocity must be negative, since it is in an opposing direction) The direction of the wreckage will move at will be in the direction of whichever vehicle had a higher momentum. In this case, it will be EAST. PROBLEM 2: Two American football players collide into each other. Calculate the velocity the first player will push the second. 23 FORMS OF ENERGY Energy is simply defined as the CAPACITY FOR DOING WORK. The unit for energy is Joule (J). A Joule is defined as the work needed to move 1N by a 1m distance, so 1J = 1Nm. . The table below describes some of the many different types of energy: Type of Energy Description Example CHEMICAL Released during chemical reactions or transformation. Batteries, food, fossil fuels, metabolism. ELECTRICAL The flow and movement of electrons. Power lines, lightning. KINETIC or MECHANICAL Occurs during physical collisions and movement. A rolling ball. A falling object. GRAVITATIONAL POTENTIAL (GPE) The energy possessed by a body by virtue of its position, such as its height. An airplane in mid-air. A car on a cliff. ELASTIC POTENTIAL Energy that is stored within an object experiencing deformation. Compressed spring. Slingshot. Catapult. ELECTROMAGNETI C Held in waves such as light, X-rays and radio. Transmitters, TV screens. NUCLEAR Released during the splitting (fission) of an atom or the combining (fusion) or two atoms. Splitting of Uranium in nuclear reactors. SOUND Associated with the vibrations of matter to produce various pitches and tones. Vocal cords. Music. Tyres screeching. THERMAL Energy that can be stored or transferred across molecules through kinetic energy. Heat from friction. Wasted energy from appliances. Note the energy transfers in the following: (i) a car being driven on a straight road (ii) burning match (iii) slingshot (iv) object falling from shelf (v) radio (vi) in a football being kicked (vii) acoustic guitar 24 (viii) wheels after brakes are applied (ix) lithium-ion batteries (x) a sprinter racing up a hill 25 ENERGY AND POWER Energy can either be released or stored. Energy that is used or released to produce some type of change is termed WORK DONE. Work has the same unit as energy. HOWEVER, even though energy can be stored, work cannot, so these terms should not be used interchangeably. Note the formula for work below: POWER refers to THE RATE OF ENERGY CONVERSION, OR WORK DONE OVER TIME. For example, if there are two sprinters of the same mass (70kg) who run the same 100m dash, but sprinter A completes the race in 1 minute, while sprinter B completes it in 1.5 minutes, BOTH sprinters did the same work, but sprinter A had more power than B, since he did the work in less time. Note the formula and unit for power below: INPUT, OUTPUT & EFFICIENCY EFFICIENCY refers to THE PERCENTAGE OF USEFUL OUTPUT COMPARED TO TOTAL SUPPLIED INPUT. Most objects will not convert 100% of one type of energy to another type. A fraction of the energy is always lost due to heat, for example. When these energy losses are reduced, machines are said to be more energy-efficient. For example, fluorescent lights tend to lose much less heat than filament lights, which heat up very quickly. As a result, fluorescent lights are more efficient and last much longer. Note the formula for efficiency below: 26 ENERGY IN A PENDULUM When the pendulum swings from positions 1 to 5, it is converting kinetic to GPE. Note what happens at: 1 – Maximum GPE, minimum KE 2 – GPE converting to KE 3 – Minimum GPE, maximum KE 4 – KE converting to GPE 5 – Maximum GPE, minimum KE KINETIC ENERGY (KE) This is the energy possessed by an object IN MOTION OR DURING COLLISION. Note its formula: GRAVITATIONAL POTENTIAL ENERGY (GPE) This is the energy possessed by an object BY VIRTUE OF ITS POSITION OR HEIGHT. Note its formula: KE AND GPE CONVERSION When an object is falling (assuming no air resistance) or sliding down a slope, the following is noted: For situations that account for resistance or friction, energy loss is accounted for, e.g. A cyclist and his cycle have a mass of 70kg. They descend a slope from the 2100m point to the 1600m point. Assuming that 75% is lost to friction, what is the velocity of the cyclist as he travels down? 27 ALTERNATIVE & RENEWABLE ENERGY SOURCES Fossil fuels are formed from the remains of decayed microscopic organisms, animals and plants from millions of years ago that have been pressed and subjected to hot temperatures over long periods of time. They mainly come in the forms of coal, crude oil or natural gas. Fossil fuels are finite resources that cannot be replaced and are said to be NON-RENEWABLE. In addition, the combustion of fossil fuels has, however, had negative effects on the environment, such as the GREENHOUSE EFFECT (due to the release of carbon dioxide by combustion) and ACID RAIN (due to the release of sulphur dioxide into the atmosphere). Energy sources that are infinite and can be replaced are termed RENEWABLE and can be used as viable alternatives to fossil fuels. Note that the Sun is the main source of energy for all of these, except GEOTHERMAL and NUCLEAR. Some examples of alternative energy sources include: Source Explanation SOLAR Energy obtained from the Sun are stored in photovoltaic cells in solar panels and converted to electricity. WIND Winds turn the blades that spin a shaft that powers a generator. HYDROELECTRIC The gravitational potential and kinetic energy of water flowing down a conduit helps power a generator. TIDAL The kinetic energy from the moving tides helps generate a current. GEOTHERMAL Heat generated by converting hot water from deep beneath the earth’s surface can be used as a source of power. NUCLEAR The fission (splitting) of Uranium atoms release energy from their nuclei, which can be harnessed. This is non-renewable but very efficient. BIOFUELS On a smaller scale, some farmers use the remainder of their harvest to produce ethanol that would act as fuel for their machinery. 28 Other things can be done to help conserve fossil fuels or reduce our usage of them, such as carpooling, switching off appliances when not in use, using fuel-based transport less often (bicycles for short distances, for e.g.) and switching to more energy-efficient fluorescent lights in the household. PRESSURE Pressure is simply defined as FORCE ACTING PER UNIT AREA. Note the formula and unit: Both blocks are the same mass (60kg). Block B is the same as A, but put to stand at a different position. Even though the force (weight) of both blocks would be the same, the pressure will be different because that force is acting down on two different surface areas. Calculate the pressure that blocks A and B exert. w = mg = 60 x 10 = 600N P (block A) = F / A = 600 / (5 x 2) = 60 Pa P (block B) = F / A = 600 / (3 x 2) = 100 Pa PRESSURE IN LIQUIDS AT DIFFERENT DEPTHS Pressure in a fluid increases as DEPTH increases. This occurs because as the position gets deeper, the more molecules lie above that point and thus, they will exert a greater force or weight downwards. Note the formula for pressure in a fluid: 29 30 Example question: An aquarium is filled with saltwater of density 1020kg/m3. It is 10m deep. The bottom of the aquarium is to be fitted with a glass window of measurements 2m x 1.5m. The atmosphere above the water surface is 101kPa. Calculate (i) the pressure of the water acting against the base of the glass (ii) the TOTAL pressure, in kPa, acting against the base of the glass (iii) the maximum force, in kN, the glass should be able to withstand. (i) P = ρgh = 1020 x 10 x 10 = 102 000 Pa (ii) P (total) = 102,000 + 101,000 (atm) = 203 000 Pa (iii) P=F/A F=PxA = 203,000 x (2 x 1.5) = 609 000 N = 609 kN 31 GAS PRESSURE MEASUREMENT [g = 10 ms-2] [ρ of mercury = 13,600 kg/m3] 1. BAROMETER Mercury is used instead of water because of its high density. Mercury is 13.6x denser than water. This means that if water was used instead, the column would be 13.6x taller. The atmospheric pressure acts on the mercury (Hg) in the reservoir container, applying a downward force to it. The mercury is pushed up the bore in the middle and forms a column. The higher the column has, the higher the pressure. Atmospheric pressure is given as 760 mmHg, but what is this value in Pascals? (iv) P = ρgh = 13600 x 10 x 0.76m = 103,360 Pa 2. MANOMETER Manometers are used to find pressures of fluids of interest. It does this by making a comparison to atmospheric pressure (which is already known). Atmospheric pressure is given as either 760mmHg or 101kPa. The difference in height (Δh) of the column is used to calculate the pressure of the gas. (i) If the difference in height of both columns is 30mm, what is the unknown pressure in mmHg? Pressure = 760 + 30 = 790 mmHg (ii) What is the unknown pressure of the gas, in Pascals? 32 P = ρgh = 13600 x 10 x 0.79 = 107 440 Pa 33 HYDRAULIC LIFTS The diagram above illustrates a hydraulic press model demonstrating the relationship between the pressures of a plunger/piston, liquid and ram. When the plunger is pushed down with a pressure at P1, it exerts the SAME PRESSURE in P2. This is denoted by Pascal’s Law, which states: THE PRESSURE APPLIED TO A POINT IN AN INCOMPRESSIBLE FLUID IS EVENLY DISTRIBUTED TO ALL POINTS IN THAT FLUID. Devices following this model act as force multipliers and can be used for lifting heavy objects by applying small amounts of force. This also explains why a force as small as a foot on a pedal could stop a moving car. Example Question: If a 20N force is applied to the piston: (i) (ii) (iii) Calculate the pressure exerted on the liquid by the small piston. Determine the pressure on the large piston. Calculate the force exerted by the large piston on the load: (i) P=F/A = 20 / 2 = 10 Pa (ii) 10 Pa (due to Pascal’s Law) (iii) P=F/A F = P x A = 10 x 10 = 100 N 34 HYDRAULIC BRAKES: 1. A force is applied on the brake pedal. This acts as a lever to exert a force against the master cylinder. 2. The master cylinder has a small surface area, so its pressure is large. Pascal’s Law ensures this large pressure is distributed to the brake oil and to the four wheel cylinders. 3. The four wheel cylinders fill with brake oil and expand evenly. 4. The wheel cylinders push against the brake shoes, which press against the brake drum. The friction from this eventually decelerates or stops the automobile. 35 PHYSICS, SECTION B (1/2) – STUDY AND NATURE OF HEAT Heat is a form of energy that is transferred from areas of higher temperature to lower temperature until the objects and their surroundings are at equilibrium, the same temperature. CALORIC THEORY Heat was once believed to be a weightless fluid called “caloric” that could flow from hotter to colder bodies. If a gas was compressed, the concentration of caloric would increase in the gas and the gas would become hotter. This theory is now obsolete. HOW WAS THIS DISPROVED? Count Rumford, during his cannon-boring experiments, was able to generate large amounts of heat to boil water. This occurred due to kinetic energy being converted to heat energy by friction, as later proved by James Joule. This showed that heat could be developed due to the application of mechanical energy and that it was indeed a form of energy, not a fluid. KINETIC THEORY The theory used today is called the Kinetic Theory of Matter, which states that molecules in a gas move freely and rapidly along straight lines. This random molecular bombardment can be observed with light reflecting off dust or smoke particles (BROWNIAN MOTION). Application of heat to molecules is able to add KINETIC energy, allowing the molecules to move and collide more often. Heat is also able to break their intermolecular bonds and change state of matter, e.g. adding heat to a solid weakens its bonds and turns it into liquid. Quantity Bond Strength Density Volume Other Notes Solid Highest Highest Lowest Molecules vibrate in place. Fixed shape. Liquid Takes shape of container, just like gases. Lowest Lowest Highest 36 Gas Most KE. Molecules in haphazard motion. TEMPERATURE AND THE KELVIN UNIT Heat represents the total amount of energy (due to molecular vibrations) in a substance, the temperature represents the average energy per molecule. A ‘cold’ substance such as an iceberg contains more heat energy in it compared to a lit match, though the lit match’s temperature would be higher. The S.I. unit for temperature is given as KELVIN (K) To find the temperature in Kelvin, we simply add 273 to the Celsius value. Calculate these: Temperature Kelvin (K) Celsius (oC) Equivalent to the temperature of… Lower Fixed Point 273 0 Pure melting ice at 1 atm Upper Fixed Point 373 100 Pure dry steam at 1 atm Absolute Zero 0 -273 Having no internal energy in system It should be noted that absolute zero is the temperature at which there is no internal or thermal energy in a state of matter. Put simply, it is the coldest possible temperature. Therefore, since absolute zero is 0K, there are no negative Kelvin values. THERMOMETERS AND TEMPERATURE MEASUREMENT The main idea of constructing a thermometer is to find a physical property that changes steadily with temperature and accurately link the fixed changes, e.g. when mercury is heated, it expands proportionately and moves along the bore of the thermometer. 37 COMPARING THE THREE THERMOMETERS Thermometer Response Factor Range Structural adaptation or advantages Liquid-in-glass Expansion of mercury -10 – 110 oC Long stem for wide range of readings. Clinical Expansion of mercury 35 – 45 oC Large, thin bulb conducts heat quickly. Small range. Constriction prevents mercury from returning to bulb quickly. Thermocouple Voltage -200 – 1250 oC Quick, accurate readings. Can measure from junctions of small masses. FACTORS THAT AFFECT LIQUID-IN-GLASS THERMOMETER’S PERFORMANCE Increase range Increase sensitivity Increase responsiveness Longer stem. Narrow bore. More conductive fluid. Less expansive liquid. Larger bulb. Thinner glass around bulb. THERMAL EXPANSION In a solid, the molecules are held closely together. When they are heated, kinetic energy is added to the molecules, making them vibrate faster. This causes the molecules to move apart and increase their volume. This is known as THERMAL EXPANSION. This phenomenon can be observed in several everyday situations, such as creaking roofs, power lines sagging on hot days (due to expansion), running warm water over a jar lid that is too hard to open and even in carbonated beverages. When beverages get warm, the CO2 bubbles expand and escape, leaving it with a ‘flat’ taste. In the cold, the bubbles contract and stay within the 38 drink. 39 BIMETALLIC STRIPS The bimetallic strip consists of 2 strips of different metals which expand at different rates as they are heated, usually steel/iron and copper/brass. The different expansions force the flat strip to bend one way if heated & in the opposite direction if cooled below its normal temperature. In the circuit, the bimetallic strip (when heated) would bend towards the contact to allow electricity to flow. This effect is used in a range of mechanical & electrical devices, such as thermostats and fire alarms THE GREENHOUSE EFFECT Whether or not radiated heat can penetrate glass depends on wavelength. Heat is mostly carried by infra-red waves (and some UV). Short wavelengths have higher frequencies and higher amounts of energy, and therefore more penetrative ability than longer wavelengths. Waves lose energy as they reflect off surfaces. Therefore, the short wavelengths that were able to penetrate the glass cannot escape once they convert to long wavelengths when they are reflected inside. 40 EVAPORATION Evaporation requires heat and is a cooling process. If you come out of a pool in a dry sunny day, the water on your skin will use the heat energy from your body to evaporate. This produces the "cooling effect". At any temperature, the molecules of a liquid are in continuous random motion with different speeds. Heat is absorbed by the liquid from the surroundings and thus gain KE and move FASTER. At the surface, the more energetic molecules are able to escape into the atmosphere. Since the molecules with the most heat energy escape, this cools the liquid. It should be noted that evaporation only occurs on the SURFACE of a liquid, so DEPTH has no effect on rate of evaporation. In what order would the vessels evaporate? Other factors that affect evaporation include: HUMIDITY, AIR MOVEMENT, PRESSURE, TEMPERATURE HOW IS EVAPORATION DIFFERENT FROM BOILING? Feature Evaporation Boiling Temperature it occurs Any temperature. At boiling point. Temperature change Decreases. Remains constant. Location At surface. Throughout liquid. Physical observation Bubbles absent. Bubbles present. PERSPIRATION atmosphere. This shows that evaporation is a cooling process. When you perspire, heat is conducted into your sweat and then moves out of the body via the sweat gland and duct. The sweat, with the heat, is then evaporated into the 41 42 THERMAL TRANSFER PROCESSES Heat can be transferred from one place to the next. When two objects of varying temperatures are placed together, a transfer of thermal energy occurs from HIGHER to LOWER temperature in an attempt to get both objects at the same temperature. e.g. cold water left in a 30oC room will gain heat from the room and eventually have a temp. of 30oC. The room loses a little heat. This transfer occurs via three processes: Method Definition Example CONDUCTION The transfer of heat through the vibrations of molecules to adjacent molecules. Heat moving along the metallic frame of a frying pan. CONVECTION The transfer of heat through the movement of the medium itself. Smoke particles rising from a fire. Water particles rising in a boiling pot. Losing body heat through sweating. RADIATION The transfer of heat through the flow of electromagnetic waves. (can occur in a vacuum) Heat from the Sun reaching the Earth. Heat leaving the body after vigorous exercise. THERMAL CONDUCTORS AND INSULATORS ● Simply put, thermal conductors are materials that allow heat to pass easily. Conductors are materials with free electrons (such as metals), which allow the efficient transfer of heat. ● Insulators do not have many free electrons and may have structural gaps or air spaces that do not efficiently transfer heat, such as cloth or polystyrene. Air is a POOR CONDUCTOR of heat.. 43 VACUUM FLASKS A vacuum flask is a container that is designed to retain the heat in a liquid. ABSORPTION AND REFLECTION OF THERMAL RADIATION Materials of various textures and colour, absorb, emit and reflect different amounts of heat. Note that good absorbers are also good emitters of heat. Would a Caribbean house roof be a good reflector or emitter? What about a car radiator? Or a car windscreen shade? Good absorbers Good reflectors Black colour White colour Dull / Matt Shiny / Glossy Rough texture Smooth texture Small surface area Large surface area SOLAR WATER HEATER 44 The purpose of a solar water heater is convert solar energy into useable heat energy. It consists of a solar panel, water tank and an insulated frame. 45 CONVECTION CURRENTS 1. How do the heated water molecules move? They rise as they spread out and become less dense. 2. When these molecules reach the surface, what happens? The more energetic molecules leave the surface. 3. What happens to the temperature of the The diagram above shows a metal pan surface after? As heat is lost, the placed on a hot plate. The objective is to temperature of the surface decreases. illustrate the movement of water molecules inside the pan. 4. How can one prevent heat from escaping from the pan? Place a lid, which will To determine this, we must answer the prevent heat from escaping to the room. following questions: ACTION OF SEA BREEZES Sea breezes are another example of convection currents. Note the diagram below and compare it to the heated metal pan above. 46 PHYSICS, SECTION B PT. (2/2) – RELATIONSHIPS OF HEAT SPECIFIC HEAT CAPACITY Observe the diagrams above. The same mass, 1kg, of two different liquid samples are placed in beakers A and B. Both samples had the same initial temperature (30 oC). Both beakers are heated for the same time (60s) with the burners set at the same power (70W). However, at the end, the final temperatures differed. Sample A required more heat to change its temperature. Sample A was thus said to be have a HIGHER SPECIFIC HEAT CAPACITY. The Specific Heat Capacity is defined as THE AMOUNT OF HEAT REQUIRED TO CHANGE THE TEMPERATURE OF 1KG OF A SUBSTANCE BY 1K. NOTE: The specific heat capacity of water is given as 4200J/(kg K). What this means is that 1kg of water would require 4200J of heat to increase its temperature by 1K. Similarly, it would have to lose 4200J of heat to decrease its temperature by 1K. 47 HEAT CAPACITY is defined as: THE AMOUNT OF HEAT REQUIRED TO CHANGE THE TEMPERATURE OF A BODY BY 1K. While SPECIFIC HEAT CAPACITY is used for materials and is a constant that only accounts per kg, HEAT CAPACITY is used for bodies and is dependent on the mass of that body. For example, while the specific heat capacity of pure water is 4200 J/(kg K), the heat capacity of a 10kg body of pure water is 42000 J/K (using C = mc). What this means is that 42000J of heat is required to raise the temperature of that 10kg body of water by 1K. TESTING FOR SPECIFIC HEAT CAPACITY, METHOD ONE (CALORIMETER) The setup is called a CALORIMETER, an apparatus used to measure specific heat capacity. The following must be known to calculate specific heat capacity. - Mass of material - Voltage and current (P = IV) - Time (E = IVt) The metal aluminum block is heated for 3 minutes with a 5A, 10V supply. If the initial and final temperatures of the 2kg block are 30oC and 35oC respectively, calculate its specific heat capacity. E = IVt = 5 x 10 x (3 x 60) = 9000 J E = mcΔT c = E ÷ (mΔT) = 9000 ÷ (2 x 5) = 900 J/kg oC 48 METHOD TWO (METHOD OF MIXTURES) Since the specific heat capacity of pure water is already known (4200J/(kg K) or 4.2 J/(g K)), this value could be used to determine the SHC of another material. The principle to remember is: By measuring the initial and final temperatures of both the water and metal, the following formula can be used: mcΔT (water) = mcΔT (substance) 49 Example question: A 50g block is placed in 200g of water. The block was heated to 100 oC. The temperature of the block dropped to 30oC and the water rose from 30oC to 35oC. Using 4.2J/(g K) as the SHC of water, calculate the SHC of the block, in J/(g K). mcΔT (water) = mcΔT (block) 200 x 4.2 x 5 = 50 x c x (100 – 30) 4200 c = 3500 c = 4200 ÷ 3500 = 1.2 J/g K Example question 2: A piece of iron of mass 21.5g at a temperature of 100.0oC is dropped into an insulated container of water. The mass of the water is 132g and its temperature rose from 20.0oC to 21.4oC. The iron’s final temperature is 19.6oC. Using 4.2J/(g K) as the specific heat capacity of water, calculate the specific heat capacity of iron. mcΔT (water) = mcΔT (iron) 132 x 4.2 x 1.4 = 21.5 x c x (100 – 19.6) 776.16 = 1728.6 c c = 776.16 ÷ 1728.6 = 0.45 J/g K 50 SPECIFIC LATENT HEAT Graph showing cooling curve of naphthalene Observe the sections of the graph where there are no temperature changes. Heat is still being lost at these points, but without temp. change. This type is heat is known as LATENT HEAT. Latent heat is thermal energy being used to either reform intermolecular bonds or break them. This type of heat is lost or gained only during changes in state of matter, i.e. freezing, melting, condensation, boiling. Quantity Definition Formula Specific Latent Heat of THE AMOUNT OF HEAT ENERGY REQUIRED TO CHANGE 1KG OF A SOLID TO A LIQUID WITHOUT A TEMPERATURE CHANGE. E = mLf FUSION E = Energy (J) m = mass (kg) L = Latent heat (J/kg) Specific Latent Heat of VAPOURIZATION THE AMOUNT OF HEAT ENERGY REQUIRED TO CHANGE 1KG OF A LIQUID TO A GAS WITHOUT A TEMPERATURE CHANGE. 51 E = mLv EXAMPLE QUESTION A student heats 200g of ice at 0 oC until it turns to steam at 100oC. How much energy was needed to do this? [specific heat capacity of water = 4200 J/(kg K)] [specific latent heat of fusion of ice = 3.36 x 105 J/kg] [specific latent heat of vapourization of water = 2.25 x 106 J/kg] TESTING FOR SPECIFIC LATENT HEAT OF FUSION OF ICE Calculate, in order, the following: [SHC of water = 4.2 J/(g K)] (i) The heat energy lost by the water (iii) The heat used to melt the ice (ii) The heat energy gained by the melted ice (iv) The specific latent heat of fusion of ice 52 AIR PRESSURE AND THE THREE GAS LAWS First, it is important to understand what exactly creates air pressure. Air pressure is caused by the random motion of gas molecules (Kinetic Theory of Matter) and their collisions with the surfaces of objects (not the molecules hitting each other!) There are three quantities that are examined with each of the gas laws: Pressure, Volume and Temperature. For each law, two of these quantities vary while one is kept constant. Calculate the pressure in the 20cm and 10cm cylinders, in kPa. For 20cm3 cylinder: P1V1 = P2V2 2 x 30 = P2 x 20 P2 = 60 ÷ 20 = 3 kPa Boyle’s Law can be graphed as shown below. 53 The pressure is made constant by increasing volume. This means that as heat increases, there is more space for the molecules to move, so they don’t collide against the surfaces as often, despite moving faster and hitting with greater force. (i) A gas at 27 oC was heated, which caused the gas to expand and push the syringe upwards. Pressure remained constant. If the volume increased from 30cm3 to 50cm3, what is the final temperature? (ii) What would be the temperature to raise the volume to 60cm3? Answer = 600 K There are two graphs used to represent Charles’ Law, depending whether or not the Kelvin or Celcius scale is used as the unit for temperature. 54 Why does pressure increase with At absolute zero, there will be in the temperature? This is because as the substance. This is because at this molecules are heated, they gain more kinetic temperature, the molecules have no internal energy and collide against the walls at a or kinetic energy and do not move, thus they greater rate and with greater force. cannot collide against the walls and create pressure. Two graphs may represent the Pressure Law, depending on whether Kelvin or Celcius is used as the unit for temperature. COMBINED GAS LAW / GENERAL GAS LAW All three gas laws can be combined to form one formula called the General Gas Law. This is employed when no quantity remains constant. The formula for it is a combination of all three gas laws and is stated as: NOTE: Not to be confused with the IDEAL GAS LAW, which will be learned at A’ Level. 55 PHYSICS, SECTION C (1/1) : WAVES AND OPTICS WAVE FEATURES Waves carry energy without carrying matter. Some waves must propagate through a medium. They involve oscillations, where there can be just one oscillation (called a PULSE) or a series or succession of oscillations (called a PROGRESSING WAVE). Waves that require a medium to be transferred are termed MECHANICAL waves, while those that can travel through a vacuum are classed as ELECTROMAGNETIC. Feature of Wave Definition IN PHASE Points on successive waves that lie on the same position WAVELENGTH Distance between two successive crests, troughs or points in phase AMPLITUDE Height of a wave, indicating its maximum displacement FREQUENCY Number of waves passing a point per second (measured in Hz) PERIOD Time taken for a wave’s complete oscillation (measured in s) Question: Calculate the wavelength and velocity of the waveform above. Wavelength => 6m ÷ 3 = 2m Velocity 🡺 v = fλ = 3 x 2 = 6 m/s 56 57 Wave Phenomenon Description REFLECTION All waves can bounce off a surface. REFRACTION All waves bend or change direction when entering another medium. DIFFRACTION All waves can curve or bend through narrow openings and edges. INTERFERENCE All waves can fuse, increasing or decreasing their amplitude. DISPERSION Light can split into different colours. Note that light waves with only one frequency (MONOCHROMATIC) cannot do this. TRANSVERSE and LONGITUDINAL WAVES Transverse Longitudinal Has CRESTS and TROUGHS. Has COMPRESSIONS and RAREFACTIONS. Displacement of particles is PERPENDICULAR to propagation of wave. Displacement of particles is PARALLEL to propagation of wave. Examples: Any wave from the e.m. spectrum (radio, visible light, microwaves, gamma rays) Examples: Sound and some seismic waves. 58 SOUND WAVES Sound is transferred by LONGITUDINAL waves that are MECHANICAL in nature, meaning that they require molecules or a medium for their transfer. They are unable to travel through a vacuum such as in space. The presence of more molecules enables sound to increase its speed. This means that sound will travel faster in denser states of matter, e.g. Sounds can have different pitches or volumes. The PITCH of a sound is dependent on its FREQUENCY while its LOUDNESS is dependent on its AMPLITUDE for e.g. a mouse’s squeak has high-freq, low-amp. A loudspeaker’s bass has low-freq, high-amp. State Mediu m Approx. Speed of Sound in m/s Gas Air 330 Liqui d Water 1500 Solid Steel 5000 The human audible range is 20Hz - 20000Hz. Any wave with a frequency higher than that range is termed an ULTRASOUND wave. Ultrasound has numerous practical applications, including the observation of fetuses in their pre-natal stages, ultrasonic cleaning (dental scalers, jewelry cleaning) and probing materials for internal flaws. ECHOES AND SONAR SONAR (Sound Navigation and Ranging) is a technology that uses ultrasound pulses to determine distances. It does this by measuring the time it takes for a fired sound pulse of known speed to be emitted from a transducer, echo from a surface and be received by a detector. The formula for calculation is given as: Question: If the speed of sound in sea water is 1600 m/s and the time taken for the sound pulse to hit the sea bed and return to the detector is 400 ms, calculate the depth of the sea bed, in km. 59 THE ELECTROMAGNETIC (E.M.) SPECTRUM The electromagnetic spectrum refers to the range of wavelengths or frequencies of electromagnetic radiation. All of them are transverse and all travel at 3 x 108 m/s in a vacuum. ORDER FROM SHORTEST TO LONGEST WAVELENGTH NAME SOURCE APPLICATIONS Gamma-rays Radioactive decay - Penetrates matter. X-rays Electron bombardment against an anode Ultra-violet Ultra-heated bodies (such as the Sun) - Causes fluorescence. - Gamma-rays are useful in killing cancer cells. - Tanning beds - Fluorescent lights - Used to sterilize medical equipment. Visible light Infra-red Emission of excited electrons. - Detected by stimulating nerve endings of human retina. Incandescent bodies. - Used in optical fibres in telecommunications, as well as in medicine. Heated bodies. - Our bodies emit this type of wave. - Detection of bodies and matter. Microwaves Magnetron circuits. - Radar and telephone communication 60 Radiowaves Transmitters. - Radio broadcasting or telescopes. DIFFRACTION Diffraction occurs when a wave passes through a narrow aperture (opening) and thus spread out over a large area as it continues to progress. All waves can undergo diffraction. THEORIES OF LIGHT Many notable scientists had differing theories of lights over the eras. Scientist Isaac Newton Christiaan Huygens Thomas Young Albert Einstein Theory Light is a stream of particles called corpuscles. Light is a transverse wave, not particles. Light is a wave that can undergo interference. Light behaves as both a wave and a particle. (Quantum Theory) Einstein also came up with the photoelectric effect (for which he won the Nobel Prize). The photoelectric effect is a phenomenon that produces electrons when light is shone on a metal plate. Ideal examples of this are DIGITAL CAMERAS and SOLAR PANELS. 61 In digital cameras, the photons are of different strengths, which produces variations of brightness and colour to translate the photograph image. 62 INTERFERENCE Interference occurs when two waves superpose with each other to form a resultant wave that might either raise or lower the amplitude. There are two types of interference: 1. CONSTRUCTIVE Interference 2. DESTRUCTIVE Interference The concept of interference proved that light experienced properties of a wave. The diagram below shows Thomas Young’s double-slit experiment. SHADOWS 63 REFLECTION OF LIGHT Reflection occurs when a wave bounces off a surface. Complete the diagrams below. TWO LAWS OF REFLECTION Law States First The incident ray, normal and reflected ray all lie on the same plane. Second The angle of incidence is always equal to the angle of reflection. (ϴi = ϴr) Example of a Plane Mirror Ray Diagram The image that is formed in a mirror is called a VIRTUAL image and typically has the following characteristics: They are always LATERALLY INVERTED, UPRIGHT, THE SAME HEIGHT AS THE OBJECT and THE SAME DISTANCE FROM THE MIRROR AS THE OBJECT. 64 REFRACTION Refraction occurs when a wave passes through a MEDIUM OF DIFFERING DENSITY for example: sunlight entering a piece of glass from the air, or light exiting water. In the diagram, the light is reflected off the fish and enters the person’s eye. However, because the light has to move across a different medium (water to air), it refracts and the image of the fish seems closer than it really is. Characteristic of Wave Denser medium Less dense medium Change in direction TOWARDS NORMAL AWAY FROM NORMAL Speed DECREASES INCREASES Wavelength DECREASES INCREASES Frequency NO CHANGE NO CHANGE The diagrams below show refraction of light in two prisms. 65 WAVEFRONT DIAGRAMS 66 MIRAGES Mirages occur mostly in hot places. This is because heated air is less dense than cooler air (which is why heated air rises). The difference in density is important to note, as heated air and cooler air would be considered two separate mediums. As a result, light would refract or bend as it moves from one to the other. As a result, it is as if the ground acts a mirror, showing a reflection of the sky. GLARE Upon hitting a surface, light is said to be POLARIZED. Direct light sources are unpolarized. If both a polarized and unpolarized light source enter the eye simultaneously, this results in a blurry visual called glare. LAWS OF REFRACTION Law States First The incident ray, normal and refracted ray all lie on the same plane. Second The refractive index is equal to the ratio of the sines of the angles of incidence and refraction. (also called Snell’s Law) Represented as the formula: n = sin i sin r 67 CRITICAL ANGLE AND TOTAL INTERNAL REFLECTION We have now understood the concept that light refracts away from the normal when entering a less dense medium. However, if the angle of incidence is too LARGE, it will be unable to be refracted in such a way to escape. The point at which the angle of refraction is equal to 90o is called the CRITICAL ANGLE. The angle of refraction cannot be more than 90o. Instead, TOTAL INTERNAL REFLECTION will occur, keeping the light inside the medium. In other words, the insides behave like a mirror. APPLICATIONS OF TOTAL INTERNAL REFLECTION Optical fibres are usually held in bundles to carry data at high speeds. They may be used as ENDOSCOPE, an instrument that is put into the body to view the internal parts. Light is shot into the fibre and it is reflected back up to a detector with images. Optical fibres are made of a core of high refractive index and surrounded by cladding that is LESS DENSE than the core. Another example of total internal reflection would be in the use of road reflectors, which are usually right-angled prisms that reflect light back to a vehicle. 68 REFRACTIVE INDEX The refractive index of a material, put simply, tells how optically dense an object is. The higher the refractive index, the slower the light will travel. For example, if a glass has a refractive index of 1.5, this means light will travel 1.5x more slowly in glass than in a vacuum. In order to calculate this refractive index, we may use either of these formulas: Example question 1: (i) Calculate the refractive index of light passing from Medium A to B. (ii) If the angle of the ray in Medium A was increased to 45 o, what would be the new angle of refraction? 69 (iii) What is the speed of light through Medium B? 70 Example question 2: A manufacturer was asked to investigate the relationship between angles of incidence, θi, and refraction, θr, for a certain type of fibre glass to build an optical fibre. The results are shown below. Θi / o 30.0 40.0 50.0 60.0 70.0 80.0 Θr / o 23.6 30.5 38.0 43.7 48.5 52.0 sin i 0.50 0.64 0.77 0.87 0.94 0.98 sin r 0.40 0.51 0.62 0.69 0.75 0.79 (a) (i) Complete the table above for both sin i and sin r. (i) Plot a graph of sin i vs. sin r below. (b)(i) Calculate the gradient of the line. (ii) Calculate the critical angle of fibre glass. 71 LENSES Type Diagram Example CONVEX (converging) Magnifying glass, microscope CONCAVE (diverging) Flashlights, peepholes, lenses for shortsighted people Example question: An object of 4cm height is placed 6cm distance from the optical center of a lens. It produces a 20cm height image. Calculate: (i) The magnification of the lens (iii) The focal length of the lens (ii) The image distance 72 Object between F and 2F Object between F and optical centre Object beyond 2F Object at F Concave Lens Diagram 73 74 PHYSICS, SECTION D (1/2) – ELECTROSTATICS AND CIRCUITS STATIC ELECTRICITY AND ATTRACTION Electrostatics is the study of charges at rest. When two insulators are rubbed together, they can produce electrostatic attraction. Matter is made of atoms which have negatively charged particles called ELECTRONS orbiting around a small nucleus. In the normal state, the atom has an equal number of electrons and protons, therefore we say that it is electrically balanced or uncharged. At times, when rubbing a surface, electrons are removed from the orbit and the object becomes POSITIVELY charged. The object that the electrons rubbed off on then become NEGATIVELY charged. Note the formula for charge: Q = It Charge is measured in COULOMBS. One coulomb is equivalent to 6.25 x 1018 electrons. Devices that store charge are called CAPACITORS. and gain current as time passes. It should be noted that time plays a major factor in terms of charge. Example questions: 1. During a certain lightning strike, a current of 5 x 104 A flows for a time period of 0.15 ms. Calculate the quantity of charge of the lightning strike. Q = It = (5 x 104) x (0.15 x 10-3) = 7.5C 2. The makers of a cellphone have upgraded its battery capacity from 4320C to 9000C. If a charger delivers 0.6A, how much more time will it take to charge the new battery than the old? ΔQ = 9000 – 4320 = 4680 C Δt = ΔQ ÷ I = 4680 ÷ 0.6 = 7800 s (or 130 mins) 75 POTENTIAL DIFFERENCE kinetic energy based on differences in height (such as a river flowing downstream), p.d. refers to the energy that generates an e.m.f. (electromotive force), allowing charges to flow to a component. For e.g. the laptop has to have a lower p.d. than the solar cell for the charges to flow from the solar cell to the laptop. If the laptop had a higher p.d. than the solar cell, the laptop would charge the solar cell instead. Potential difference (or p.d.) is simply another term for voltage. Similar to how gravitational potential may convert to CHARGING BY INDUCTION Objects can also be charged by placing them next to each other and using a charged rod within proximity. This method is called charging by INDUCTION. Examples of technology that employ electrostatic forces are: PHOTOCOPYING MACHINES, ELECTROSTATIC PAINTING, ELECTROSTATIC SMOKE PRECIPITATORS. ELECTRIC FIELDS An electric field is defined as a region around a charged particle or object within which a force would be exerted on other charged particles or objects. 76 CIRCUIT COMPONENTS Component Circuit Symbol Note Dry cell / Battery Converts chemical to electrical energy. Switch Controls paths of electron flow. Fixed Resistor Decreases current, value is constant. Variable Resistor (rheostat) Decreases current, value can adjust. Bulb / Lamp Converts electricity to light + heat. Voltmeter Measures voltage. Connected in parallel. Ammeter Measures current. Connected in series. Fuse Breaks circuit path if current is too high Semiconductor diode Converts a.c. voltage to d.c. voltage. a.c. Power Source Typically a power outlet. Motor Converts electrical to mechanical energy. Transformer Alters voltage by altering current. Galvanometer Deflects needle due to small currents. Heater Generates thermal energy. Bell Releases sound energy. Thermistor Resistance reduces when temperature increases. 77 Photoresistor / LDR Resistance reduces when light intensity increases. (Light-Dependent Resistor) LED (Light-Emitting Diode) Semiconductor light source. Releases photons. Very efficient. 78 WHAT IS THE DIFFERENCE BETWEEN CURRENT AND VOLTAGE? Quantity Definition Unit Derivation of Unit Voltage The amount of energy per unit charge. Volt (V) 1V = 1 J/C Current The amount of coulombs passing a point per second. Ampere (A) 1A = 1 C/s Resistance A measure in the opposition of the flow of current. Ohm (Ω) 1Ω = 1 V/A The general formula that links each quantity above is: Measuring Voltage and Current Instrument Measures How it is hooked up Why? AMMETER Current. IN SERIES It has a very low resistance, so as to not affect the circuit. VOLTMETER Voltage. IN PARALLEL It has a high resistance, which could affect the circuit in series. 79 GALVANOMETER Direction of small amounts of current. Same as ammeter. 80 Same as ammeter. WIRES AND RESISTANCE Factor Explanation LENGTH Long wires have higher resistances than shorter ones. More power loss tends to occur along far distances. Electrical energy converts to heat. THICKNESS Wires of thick diameter have more conducting material and thus can transfer more current. The thicker the wire, the lower the resistance. CONDUCTOR Wires made of good conducting material, e.g. copper have low resistance. DIRECT AND ALTERNATING CURRENT An a.c. voltage can be converted to d.c. voltage using a SEMICONDUCTOR DIODE or RECTIFIER. Alternating current is specific type of electric current in which the direction of the current's flow is REVERSED on a regular basis. The magnitude of the voltage produced FLUCTUATES a.c. voltages are found in: Power lines, transformers, power outlets Direct current is simply when it flows in ONE DIRECTION at all times. It has a FIXED magnitude. d.c. voltages are found in: Cell phone battery, laptop battery, simple electromagnet, hybrid vehicles 81 PRIMARY AND SECONDARY BATTERY CELLS Batteries can be divided in two categories: primary cells and secondary cells. Characteristic Primary cell (Dry Cell) Secondary cell (Wet Cell) Rechargeability Absent. Present. Portability High (small size) Low (usually larger size) Terminal Voltage Lower (e.g. AA = 1.5V) Higher (e.g. Car = 12V) Internal Resistance Higher Lower Structure Zinc anode, carbon cathode, contains a powder or paste of MnO2. Sulphuric acid electrolyte with lead plates. Or lithium-ion batteries. Liquid electrolyte. RECHARGING A BATTERY CELL Secondary batteries (which are d.c.) are recharged when they are connected to a.c. supplies (such as outlets). A TRANSFORMER steps down the voltage from the outlet and a RECTIFIER converts the a.c. voltage to d.c to flow into the battery and be stored. VI-GRAPHS Components that obey the relationship given by Ohm’s Law are said to be OHMIC while components that don’t, such as filaments lamps and diodes are said to be NON-OHMIC. 82 DETERMINING RESISTANCE OF AN UNKNOWN RESISTOR, R The apparatus is set up as shown in both methods with the ammeter in series with the resistor and the voltmeter in parallel. However, the methods differ when it comes to obtaining different values of current. In Method 1, the length of the resistance wire ‘d’ is varied by connecting the contact at different points (recall that longer wires have higher resistance). In Method 2, a rheostat is used to vary the resistance to obtain different values. Using the setup in Method 2, a student obtained the following results. Plot a graph of V vs. I, and find the gradient. What does the gradient represent? V/V 2.00 3.00 4.00 5.00 6.00 I/A 0.42 0.60 0.84 1.02 1.18 83 84 SERIES & PARALLEL CIRCUITS Let’s analyse the simple series circuit below to state its characteristics: RESISTANCE IN A SERIES CIRCUIT – The total resistance in series is the sum of all resistors in the circuit. For example, find the total resistance of a circuit which has two resistors of 10Ω and 15Ω. FORMULA: RS = R1 + R2 ... CALCULATION: RS = 10 + 15 = 25 Ω CURRENT IN A SERIES CIRCUIT – The current flowing into each component in a series circuit is equal to the current flowing out of each component. This means that each ammeter (A1, A2 and A 3) would have the same reading. Show the calculation: I = V/R = 6/25 = 0.24 A Note: Ammeters are placed in series next to the component to be observed. They have very low resistance, so as to avoid significant alteration of the current passing through it in series. VOLTAGE IN A SERIES CIRCUIT – The sum of the voltages of the individual components in the circuit should equal the voltage of the power source. This means that the sum of voltages in R1 and R2 should be equal to 6V. What are the voltages in R1 and R2? V (R1) => V = IR V (R2) => V = IR = 0.24 x 10 = 2.4V = 0.24 x 15 = 3.6V Now recall that total voltage = 2.4 + 3.6 = 6V Note: Voltmeters are connected in parallel to the components. They have very high resistance, so only very small amounts of current pass through it, since voltmeters are on separate wire paths. 85 Now, let’s analyse a simple parallel circuit with the same components as before. RESISTANCE IN A PARALLEL CIRCUIT – The total resistance in a parallel circuit is smaller than the value of the individual resistors. FORMULA: 1/RP = 1/R1 + 1/R2 ... CALCULATION: VOLTAGE IN A PARALLEL CIRCUIT – The voltage in a parallel circuit is equal on each wire. Therefore, on this circuit, the voltage on each wire would be 6V. CURRENT IN A PARALLEL CIRCUIT – Since the wire splits at several junctions, so does the conducting path for the electrons. This causes the current to decrease through these paths. Therefore, since A 1 and A 4 are on the same pathway, their current will be equal. However, A 2 and A 3 will have different currents. The sum of A 2 and A 3 = A 1. Calculate the currents through A 2, A 3 and then use those to find the current in A 1. For A 1 🡪 I = V/R = 6/10 = 0.6A For A 2 🡪 I = V/R = 6/15 = 0.4A Therefore, the total voltage 🡪 0.6 + 0.4 = 1.0A 86 COMBINING SERIES AND PARALLEL CIRCUITS In the diagram, each resistor is 6Ω. A and B are in series with each other. C is parallel to both A and B. And resistor D is series to A, B and C combined. To simplify the circuit, we need to reduce the number of resistors by ‘fusing’ their values. (a)(i) Calculate the total resistance of A and B. RS = 6 + 6 = 12 Ω (ii) Calculate the total resistance of A, B and C. (iii) Calculate the total resistance of A, B, C and D. RT = 4 + 6 = 10 Ω (b) Calculate the total current in the circuit. I = V/R = 12/10 = 1.2A (c) Calculate the voltage through C. (Keep in mind that resistor D draws voltage) Finding voltage through D V = IR = 1.2 x 6 = 7.2V Therefore Voltage through A, B and C would be: V = 12 – 7.2 = 4.8V 87 POTENTIAL DIVIDERS From the diagram, calculate the value of Vout. Potential dividers (or potentiometers) operate simply by splitting the voltage at various points in a circuit. They usually involve some type of variable resistor or sensor-operated resistor. They are widely used for adjusting voltages in appliance circuits. For e.g. a radio may only need 6V from a 9V battery. The divider splits the voltage and allows 6V to flow as a V out value. ELECTRICAL HAZARDS, WIRING AND FUSES Some metals melt easily at much lower temperatures than normal. These metals can be used to make a SAFETY FUSE. If too much electricity flows through the fuse wire, it will get so heated that it will melt. This will BREAK THE CIRCUIT and no more CURRENT can pass. If no fuse is present and too much current passes, there can be a risk of an electrical fire. Circuit breakers have the same purpose of a fuse. One main difference is that fuses must be replaced, while circuit breakers don’t have to be. Fuses act faster than breakers, however. If an 8A current is being delivered through the live wire, which fuse will be best? 2A, 5A or 10A? There are three types of wires: Type of Wire Purpose Colour LIVE Delivers electrical energy and high a.c. voltages to appliances. Connects all switches and fuses. BROWN (or red) NEUTRAL Carries current back to the supply. Has roughly zero volts. GREY (or blue) EARTH or GROUND Deposits excess electrons from the circuit into the ground. It is connected to the appliance frame or casing, not mains. GREEN-YELLO W Three main electrical hazards are: 1. Damp wires 2. Broken insulation in wires 3. Short circuits 88 Fuses and switches are always connected to the live wire. There is a potential danger of the live wire becoming loose and touching the metal case of appliances. Touching the metal casing can then result in electrocution. However, the ground wire will carry those excess electrons into the ground, so the earth wire is always connected to a case or frame. ELECTRICITY GENERATION & CONSERVATION Since we are dependent on non-renewable fossil fuels, we can do a number of things to conserve them: 1. 2. 3. 4. Switch off electrical appliances and lights when not in use. Convert from incandescent to LED light bulbs. Find alternative methods of transport (e.g. public transport, bicycles). Employ alternative sources of energy (e.g. solar, wind, biofuels). 89 PHYSICS, SECTION D (2/2) – ELECTROMAGNETIC COMPONENTS MAGNETS A magnet is a material that has a north and south pole that could either attract or repel other magnets or magnetic materials. Magnetic materials, however, have no poles and cannot attract others but can be attracted by a magnet. Nature Material Application Temporary Magnet Permanent Magnet Can be magnetized easily. Retains its magnetism for a long time. Iron, mu-metal Steel, alnico Electromagnets, transformers Compass needles, décor magnets, metal detectors Magnets create fields around them, as illustrated below. 90 MAGNETIC INDUCTION When a piece of unmagnetised magnetic material (such as IRON) touches or is brought near to the pole of a permanent magnet, it is attracted to the magnet and becomes a magnet itself. In other words, the material is said to have been magnetically induced. It should be noted that only 3 metals can be magnetized: By wrapping a cylindrical coil or SOLENOID around an iron core and passing d.c. through it, the iron core will become magnetized. DEMAGNETISING A MAGNET 91 Method Explanation HEATING Molecules begin to vibrate so quickly that domains are rearranged and the charges at the poles disappear. HAMMERING Physical force rearranges domains and polar charges disappear. A.C. VOLTAGE The a.c. causes some domains at the magnetic poles to switch directions. If done long enough, the polar charges will be nullified. RELAY CIRCUITS (ELECTRIC BELL) A typical relay circuit contains a switch that is electromagnetically operated. 1. When the current passes through the electromagnets, they generate a magnetic field. 2. The soft iron armature is then attracted to the electromagnet. It is pulled towards it, and the hammer hits the gong. 3. At the same time, the contacts are broken in the circuit, causing current flow to cease and the magnetic field to be lost. This restarts the circuit, causing the bell to ring in rapid successions. FLOW OF CHARGES & CONVENTIONAL CURRENT Flow of charges is different from a metal conductor and electrolyte. In an electrolyte (a liquid conducting material), both positive and negative ions can flow. It can also occur in both directions. However, in a metal conductor, only negative charges flow (electron flow) and only in one direction (-ve to +ve terminals). There is one thing to note, however. While electrons indeed do move from –ve to +ve, tradition in the field of Physics is to work the opposite way. Due to past limitations, we must assume that flow is +ve to –ve instead. This system is called CONVENTIONAL CURRENT. 92 FORCES ON CURRENT-CARRYING WIRES In the figure above, the thumb pointing straight out represents the CURRENT while the other four curved fingers represent the MAGNETIC FIELD. With this rule, the magnetic effect of a current can be predicted. 93 Fleming’s Left-Hand Rule is used to predict the force (or thrust), magnetic field and direction caused by a passing current. In order for this interaction to occur, all three must be perpendicular to each other. Force, magnetic field and current are linked this way. If two are at a right angle, the third can be produced. ● ● Predict the direction of the wire in Fig 1. (downwards) In Fig 2, the wire is being thrusted out of the page. Draw an arrow indicating the conventional current direction, as well as the +ve and –ve terminals. (downwards) APPLICATION OF LEFT HAND RULE TO A TURNING COIL Predict whether the coil ABCD will have a clockwise or anticlockwise moment by determining the forces on AB and CD. Why would there be no force on BC? 94 In order to produce a thrust, the magnetic flux must be PERPENDICULAR to the current. At BC, they are not perpendicular to each other, but parallel. There is no force as a result. 95 D.C. MOTORS AND A.C. GENERATORS Characteristics d.c. motor a.c. generator Power source Battery External turning force Energy conversion Electrical 🡪 Mechanical Mechanical 🡪 Electrical Components Split ring commutator Slip rings How to make the motor spin faster or make the generator create more power Increase battery voltage. Increase turning force velocity. Increase number of turns. Increase number of turns. Use stronger magnets. Use stronger magnets. d.c. Motor: The purpose of the d.c. motor is to create a MOMENT on both sides of the wire loops to create a turning force. This is due to Fleming’s Left Hand Rule, which says that in order to create a force, a current must be PERPENDICULAR to the magnetic flux. When the loop is turning, there is a chance the direction can reverse every half-rotation. A SPLIT RING COMMUTATOR is used to BREAK THE CIRCUIT every half-turn to keep the motor spinning in one constant direction. The direction of the turning force depends on the orientation of the magnets and direction of conventional current. a.c. Generator: It is noted that instead of a commutator, that SLIP RINGS are placed at the end of the wire loop. The purpose of these is to allow the transfer of the alternating e.m.f. induced by 96 the rotating wire to the external circuit. Each one is connected to a contact brush, where it rotates about the inner diameter. The faster the external rotator, more electrical energy can be converted. 97 ELECTROMAGNETIC INDUCTION Passing a magnet along a solenoid can allow electron flow and thus produce a VOLTAGE. This is denoted by FARADAY’S LAW, which states that: What this simply means is that the faster the magnet moves in and out of the coil, the more voltage is obtained. If the magnetic field does not move, no voltage is induced. Similarly, an alternating current constantly switches directions and by doing that, it inherently has a changing magnetic field. An a.c. is therefore able to induce voltage across an adjacent coil. 98 99 TRANSFORMERS A transformer uses the concept of a constantly changing magnetic field to induce a voltage from a primary to secondary coil. The more coils, the greater the electron flow and the higher the voltage. However, if voltage is raised (step-up transformer), it trades by lowering the current. Similarly, if voltage is lowered (step-down transformer), current is raised. The following formulas are used in transformers: Calculate the number of secondary coils and the secondary current in the primary coil. Due to the principle of conservation of energy, the power and energy output can never be more than the input. In an IDEAL transformer, power input and output are said to be equal. However, power loss does occur in transformers in real-world. To minimize power loss across a wire, electrical energy is transferred with HIGH VOLTAGES and low currents. There are numerous ways in which power loss can occur in a transformer, stated below: Cause of Power Loss Prevention Method Line loss (heating) Using wires of greater diameter. Eddy currents Laminating the soft iron core. Hysteresis (delay during magnetization) Using a perm-alloy core. 100 LOGIC GATES GATE SYMBOL NOT AND OR GATE NAND NOR SYMBOL TRUTH TABLE EXAMPLE USE Input Output 1 0 0 1 Input 1 Input 2 Output 0 0 0 0 1 0 1 0 0 1 1 1 Input 1 Input 2 Output 0 0 0 0 1 1 1 0 1 1 1 1 TRUTH TABLE Also called an inverter. It may be used in circuits that regulate factors, e.g. turning on flash in cameras when the environment is dark. An ATM will only allow a user to access his account if they swipe the correct card and enters the correct PIN. Doing one alone will deny access. If a machine is meant to shut off if the temperature OR pressure is too high, this gate can allow the machine to shut off if at least one exceeds a certain limit. EXPLANATION Input 1 Input 2 Output NAND = Opposite of AND 0 0 1 0 1 1 1 0 1 Also called the “universal gate”, where the only zero output is when there are two one inputs. 1 1 0 Input 1 Input 2 Output NOR = Opposite of OR 0 0 1 0 1 0 1 0 0 The only positive output occurs when there are two zero inputs. 1 1 0 101 Solve the following logic gate problems: 102 An electric kettle is connected to an alarm that sounds whenever the kettle is switched on and the lid is left open or the water level is below the heating element. The figure below shows the circuit that controls the electric kettle’s alarm. (a) Draw the appropriate logic gates in A, B and C to perform the electric kettle’s alarm function. (A = AND, B = AND, C = OR) (b) Complete the table below to show in which scenarios the alarm will go off or not. Input Output L M N X Y Z 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 103 PHYSICS, SECTION E (1/1) : ATOMIC PHYSICS & RADIOACTIVITY HISTORY OF THE ATOM J.J. Thomson theorised and discovered the electron. However, he believed the atom to be a cluster of positive and negative charges that he termed the “plum pudding model”. However, scientists named Ernest Rutherford and Niels Bohr later theorised (and proved) that the atom had to have a centre of positive charge. James Chadwick discovered the neutron. Two scientists named Hans Geiger and Ernest Marsden assisted Rutherford in developing the structure of the atom that we know today. They performed an experiment known today as the Geiger-Marsden experiment or “gold foil” experiment. The experiment involved setting up a radioactive source that emitted alpha-particles across a thin piece of gold foil. A ring-like detector was placed around the foil. It was observed that the majority of particles went straight through. However, a few were deflected. The ones that were deflected had to have hit the nucleus, or were repelled by its positive charge. This proved that the atom several things about the atom: The atom has a small central positive mass at its nucleus. Most of the atom is empty space. 104 SUBATOMIC PARTICLES In the atom, there are THREE types of particles: Particle Atomic mass Charge Founder Proton 1 +1 Ernest Rutherford Neutron 1 0 James Chadwick Electron 0 -1 J.J. Thompson Definitions: ATOMIC NUMBER - The number of PROTONS in an atom. MASS NUMBER / ATOMIC MASS - The number of PROTONS and NEUTRONS in an atom. For example, if a carbon atom has 6 protons and 6 neutrons, its atomic number will be 6 and its mass number (or atomic mass) will be 12. The electrons are arranged in SHELLS rotating around the atomic nucleus. When the number of protons and electrons are equal, the atom is said to be ELECTRICALLY NEUTRAL. ISOTOPES An isotope is defined as FORMS OF THE SAME ELEMENT THAT CONTAIN THE SAME NUMBERS OF PROTONS BUT DIFFERENT NUMBERS OF NEUTRONS. An atom has a nucleon number and an atomic number. Using an example of Uranium (U), which has 92 protons and 143 neutrons, we represent it as: 105 Each atom is assigned its own atomic number. An atomic number of 7 is always nitrogen, for example, while an atomic number of 8 is always oxygen. So if one proton was added to nitrogen, the element will change to oxygen. However, the number of NEUTRONS can differ. For example, Uranium (U) could have various numbers of neutrons and thus have various isotopes. 106 THE THREE TYPES OF RADIATION For an atom to be stable, it must have A NUCLEAR RATIO OF 1 PROTON: 1 NEUTRON. Unstable atoms are far removed from that ratio and lose energy by continuously emit differing forms of energy known as radiation. This overall process is called radioactive decay. These three types of radiation are represented as: Type of radiation α particles β particles γ rays Nature A helium nucleus. A fast-moving electron. A high-frequency e.m. wave. Ionising effect Strongest Intermediate Weakest Penetration strength Weakest (stopped by paper) Intermediate (stopped by aluminium) Strongest (stopped by thick lead) Range Shortest (2-10cm) Intermediate (~1m) Longest ( > 1m) Deflection in magnetic fields Attracted to negative. Attracted to positive. Undeflected. An instrument known as a G-M TUBE OR GEIGER COUNTER is used to test for the presence of radioactive emissions. There is a margin of error in using this instrument, as sometimes the number will exceed slightly. This occurs due to BACKGROUND RADIATION, which is due to radiation already present in the room or contamination of the detector tube itself. This value is simply subtracted from the total. The G-M tube may also be used to gauge the penetrating power of the three different types of radiation. 107 108 CLOUD CHAMBERS A cloud chamber can be created by setting up a petri-dish filled with dry ice and isopropyl alcohol. When a radioactive source is placed on the alcohol and dry ice, lines can be seen as particles are emitted. These lines represent the ionic trails of the particles. The density and shape of these lines determine the type of radiation being emitted. DEFLECTION OF RADIATION ALONG ELECTRIC AND MAGNETIC FIELDS Alpha particles are described as positive while beta particles are described as negative. Gamma rays do not have a charge and are thus unaffected by any magnetic fields. In the diagram below, draw how the three different types of radiation will interact. SAFETY Radioactivity was founded by MARIE CURIE. who studied elements such as Uranium and Thorium. Unfortunately, she died of radiation-induced anaemia. Awareness increased by scientists who have to work with ionising radiation, since it can break apart molecules in the body, kill cells and cause cancer. They have since been taking the following precautions: 109 RADIOACTIVE DECAY Alpha-Decay: When an element loses an alpha particle, it loses E.g. Beta-Decay: When an element loses a beta particle, the nucleon number is unchanged while the atomic number increases by 1, .e.g. Gamma-Decay: During alpha and beta-decay, the nucleus gathers spare energy. This energy is released as gamma-rays This does not affect the atomic or nucleon numbers. Decay Chains and Formulas Isotope Atomic No. Nucleon No. U-238 92 238 Th-234 90 234 Pa-234 91 234 Pb-210 (unstable) 82 210 Pb-206 (stable) 82 206 Bismuth (Bi) 83 210 Polonium (Po) 84 210 Using the table above, write the decay equations that (i) Show the process to turn U-238 into Pa-234. [2 equations] (ii) Show the process of unstable lead turning into stable lead. [3 equations] 110 HALF-LIFE Radioactive decay, explained before, represents the emission of particles due to unstable nuclei. The decay process is independent of conditions external to the nucleus. Since radioactive decay is a random process, half-life is only an estimate (though a very good one). Calculating half-life of a substance after plotting a curve: 111 Half-life Example Questions 1. The half-life of C-14 is 5700 years. A plant, upon death, experiences 8 disintegrations per minute. Calculate how much time has passed since its death if the plant now experiences 1 disintegration per minute. 8 🡪 4 🡪 2 🡪 1 (each arrow represents one half life, t½) 1 half-life = 5700 years ∴ 3 half-lives = 5700 x 3 = 17100 years 2. A 800mg sample of radon decays over a period of 20 days until only 25mg remains. What is the half-life of radon, in days? 800 🡪 400 🡪 200 🡪 100 🡪 50 🡪 25 5 half-lives = 20 days (800mg decaying to 25mg) ∴ 1 half-life = 20/5 = 4 days Background radiation and determining half-life Remember that background radiation is radiation that is recorded despite not being placed close to the radioactive source or after the source has completely decayed. It must be subtracted in order to determine accurate radiation readings. Example question 1: A Geiger counter is used to measure the radiation counts of a substance, X. At the start of the experiment, the reading is 520 counts/s. After one hour, the reading is 70 counts/s. The background radiation was found to be 40 counts/s. Calculate the half-life of X. Actual readings = 480 (520 – 40) and 30 (70 – 40) 480 🡪 240 🡪 120 🡪 60 🡪 30 4 half-lives = 1 hour = 60 mins ∴ 1 half-life = 60/4 = 15 mins Example question 2: A radioactive source is tested over a number of hours with a radiation detector. The readings are shown in the table. Use the readings to: (i) (ii) suggest a value for the background count rate during the test (Ans = 20 /s) determine the half-life of the sample. (Ans = 30 mins) 112 USES OF RADIOACTIVE ISOTOPES Field Isotope(s) Use Medical Cobalt-60 and gamma rays Killing cancer cells Nitrogen-13, Oxygen-15, Iodine-123 Used as radioactive tracers to detect tumours and abnormalities Archaelogical and Scientific Research Carbon-14 Carbon-dating fossils and older materials Power Generation Uranium-235, Thorium-232 Nuclear fission plants Industrial and Commercial Bromine-82, Iodine-125 Detecting leaks in pipes Americium-242 Smoke alarms Strontium-90 Used in thickness gauges. NUCLEAR ENERGY Albert Einstein suggested the relation between energy (E) and mass (m) in his famous formula ΔE = Δmc2, where c = speed of light (3 x 108 m/s) c2 = (9 x 1016) Reaction Description Example NUCLEAR FISSION One nucleus splits to form smaller nuclei, releasing massive amounts of energy as gamma rays. Splitting of Uranium in nuclear power plants NUCLEAR FUSION Two smaller nuclei combine to form a larger nucleus, giving off energy as it does. Two H isotopes forming helium (He) in the Sun. Nuclear energy is efficient and does not contribute to air pollution. However, nuclear waste is difficult to dispose of. Also, there is a risk of MELTDOWN. (e.g. Chernobyl and Fukushima). Example question: The mass of the sun is lost at the rate of 2.0 x 109 kg every second. If the speed of light in a vacuum is 3.0 x 108 ms-1, calculate the energy output of the sun in 1 second. Convert to kilojoules. 113 Calculating energy released in a nuclear reaction The equation below represents nuclear fusion in the Sun. When calculating the masses before and after the reaction, it will be noticed that there is a small difference. This small difference in mass was converted to energy, according to Einstein. To calculate the energy, observe the table. 1. First, calculate the mass on the left side of the equation: LHS = H-2 + H-3 = 2.014 + 3.016 = 5.03 u 2. Then the right side of the equation: RHS = He + n = 4.003 + 1.009 = 5.012 u 3. Find the difference in masses, in u. Δm = 5.03 – 5.012 = 0.018 u 4. Convert the ‘u’ value to kg by multiplying by 1.66 x 10 -27. This will be the value of Δm. Δm (to kg) = 0.018 x (1.66 x 10-27) = 2.988 x 10-29 kg 5. Lastly, apply Einstein’s formula (ΔE=Δmc2) to calculate how much energy, ΔE, was released. ΔE = Δmc2 = (2.988 x 10-29) x (9 x 1016) = 2.6892 x 10-12 J 114 Nuclide Mass / kg Uranium-238 (U) 398.350 x 10-27 Krypton (Kr) 152.620 x 10-27 Barium-139 (Ba) 232.560 x 10-27 Neutron (n) 1.670 x 10-27 In the above case, the masses aren’t given in the unit ‘u’, so there is no need for conversion. (i) Observe the diagram and write the equation of the fission reaction. Complete the missing numbers in the Barium and Krypton isotopes. (ii) Calculate the difference in mass of the elements formed before and after the reaction. Mass before (LHS) = U + n = (398.350 + 1.670) x 10-27 = 400.02 x 10-27 Mass after (RHS) = Ba + Kr + 3n = (232.560 + 152.620 + (3 x 1.670)) x 10-27 = 390.19 x 10-27 Difference (Δm) = LHS - RHS = 9.83 x 10-27 kg (iii) Calculate the energy released in the reaction. ΔE = Δmc2 = (9.83 x 10-27 kg) x (9 x 1016) = 8.847 x 10-10 J 115 WORKSHEET 1 – VECTORS, FORCES, DENSITY 1. Convert EACH reading below to its SI unit and determine which quantity is larger: (a) 500cm or 0.5m (d) 1 week or 600,000s (b) 6.5km or 65,000cm (e) 1800ms or 18s (c) 0.018MW or 180kW (f) 4500μm or 45mm 2. (a) The speed limit on Trinidad’s highways is 100km/h. Convert this value to m/s. (b) A driver received a ticket while going 24m/s on a 80 km/h road. Did he exceed the speed limit? 3. Convert the following to standard form scientific notation (to 3 s.f.) (a) 4,200 J (c) 300,000,000 m/s (b) 101,325 Pa (d) 0.03749 kg (e) 0.000004599 m (f) 0.009859 Hz 4. A light year is the distance it takes for light to travel in the span of one year (365 days). The speed of light is estimated as 3.0 x 108 m/s. (i) (ii) Calculate the number of seconds in a 365-day year. Using the formula distance = speed x time, calculate the distance (in m) light can travel in one year. Put your answer in standard form to 3 s.f. 5. The two figures below show a plane going north and being affected by a wind blowing in different directions at a magnitude of 30 km/h. Figure 1 shows the wind blowing at a right angle (90o) to the plane while Figure 2 has the wind blowing at 120o. Recreate both situations as vector diagrams using an appropriate scale, draw the resultants and state the magnitudes of the resultants. Use a scale of 1cm : 10km/h for both. 6. A Boeing 747 jet experiences a lift velocity of 125m/s while travelling horizontally on the runway at 175m/s. The angle between the lift and the runway is 60o. Recreate the vector diagram and calculate the resultant velocity and state the angle of the plane’s ascent to the runway. 7. 116 8. The acceleration due to gravity on the Earth’s moon is 1.6 ms-2. If a 75kg astronaut walks on its surface, determine his (i) mass (ii) weight 9. The acceleration due to gravity on Earth is 9.8 ms-2. A trailer has a mass of 3000 kg. Each wheel of the trailer is able to exert a maximum of 5000N of reaction force. Calculate the minimum number of wheels the trailer should have. 10. (a) (b) (c) Draw the following diagrams and show forces represented as arrows. Name the forces as well: A car on a bumpy road decelerating. (d) A basketball hitting the floor. A rocket taking off from Earth. (e) Clothes spinning in a washing machine. A submarine sinking deeper into the sea. (f) A parachuter falling at a constant speed 11. Relating to the concept of density, describe the mechanisms that allow a submarine to be able to both sink and float in seawater. Draw a simple diagram to back up your explanation. 12. Explain why hot air rises. Draw a simple diagram comparing the spread of molecules in hot air and in cold air. 13. A spring has an initial length of 2.5cm. When an 8N weight is attached to it, it extends by 0.25cm. [use g = 10N/kg] (a) Calculate the constant, k, of the spring. (b) Calculate the extension and total length of the spring when a 24N weight is attached. (c) Calculate the extension and total length of the spring when a 5.6kg mass is attached. 14. Complete the table below and plot the graph showing Weight vs. Extension. [use g = 10N/kg] Mass/kg 0.0 1.0 2.5 3.0 4.5 6.0 Weight/N 0.0 10.0 Length/cm 4.0 4.4 5.0 5.3 y 6.4 Extension/c 0.0 0.4 x m (a) Calculate the gradient, k. (b) Use the graph to find the value, x and thus y. (c) Use the value, k, to determine the extension and total length of the spring when a 12.5kg mass is attached. 15. (a) If 500kg of gasoline has a volume of 0.7m3, calculate the density of gasoline. (b) Calculate the relative density of gasoline if its placed in sea water, which has a density of 1050kg/m3. Using your answers, state and explain whether or not gasoline sinks in seawater. 16. The water in a pool has a density of 1000kg/m3. If the pool has a length of 24m, width of 8m and a depth of 6m, calculate the mass of water needed to fill the entire pool. 17. A block of pine wood has a volume of 40cm 3. The density of pine wood is 0.65g/cm3. (a) If its length is 2.5cm and its height is 8cm, how wide is it? (b) Calculate the mass of the block. 18. A sheet of aluminum foil that is 11cm wide and 12cm long has a mass of 8.9g. If aluminum has a density of 2.7g/cm3, what is the thickness of the foil? Convert your answer to mm. 117 WORKSHEET 2 - PRINCIPLE OF MOMENTS To achieve ____________________, the 1. In the figure below, Raj and Keon are sitting on opposite ends of a seesaw. They are currently balancing each other. Two distances are labelled. ________________________ moment created by Keon must be equal to the ____________________ moment created by Raj. If Raj has a weight of 450N, calculate Keon’s weight if the seesaw is balanced. 2. A metre ruler is suspended on a spring balance as shown. Calculate the reading of the tension on the spring balance. 3. The figure below shows a student doing a push-up. A force, F, acts upwards on his hands as he presses against the ground. A force also acts on his toes. The student has a weight of 600N. Calculate the force, F. 118 4. A uniform rod, P, is supported at its centre and held in a horizontal position. The length of PQ is 1.00m. A force of 12N acts at a distance of 0.30m from the support. A spring, S, is fixed at the lower end. Calculate the force exerted by the spring. 5. .The diagram shows several forces acting on a metre rule. If the system is in equilibrium, calculate the value of W. 6. Two students, Patrick and Patricia, demonstrate their “magical balancing act” as depicted below. The fulcrum is not located at the centre of the plank. (a) Label the point where the weight of the plank acts. (b) Using the Principle of Moments, calculate the weight of the plank. (c) If Patricia were to move and Patrick were to sit alone on the plank, how far from the fulcrum must he sit in order to balance the plank? 119 WORKSHEET 3 – DYNAMICS AND MOTION 1. A taxi drives from Chaguanas to Port-of-Spain in a half hour. The distance between both places is 25km. Calculate the average speed of the taxi driver. 2. If the distance between Piarco International Airport and Grantley Adams Airport in Barbados is 340.0km and a CAL airplane cruises at an average of 125.9m/s, what is the expected time of arrival if the flight leaves at 11:45pm? Round off to the nearest minute. 3. A truck driver steps on the brakes after seeing an emergency up ahead. The driver was going at 30m/s and decelerates until he is going at 14m/s. This occurs over a span of 4 seconds. Calculate the driver’s rate of deceleration. 4. (a) An airplane is travelling at 120.0m/s. It propels its forward using its jets and is able to accelerate at a rate of 3m/s2. If it accelerates for 5 seconds, calculate its final velocity (b) A similar airplane is travelling at 136.5m/s. Upon experiencing turbulence, the airplane experiences a constant deceleration of 0.5m/s2 for a half minute. Calculate its final velocity. 5. A rollercoaster ride comes to a complete stop at the top of a ride. It suddenly begins a dive, accelerating uniformly at the rate of gravity (10m/s2) downwards until it is travelling at a speed of 64.8km/h. (a) Calculate the time it takes to get to its final speed. (b) Sketch a velocity-time graph of the situation. Include the final speed and the time calculated in (a). (b) Calculate the distance the rollercoaster travels during its dive. 6. The diagram below shows three forces acting through the centre of mass of a 0.5kg object. Calculate the object’s acceleration and state in which direction. 7. Usain Bolt ran his record-breaking Olympic 100m dash in 9.58 seconds. During the first 60m, he ran 6.5 seconds before coasting at a constant maximum velocity towards the finish line. (a) Calculate Bolt’s average velocity for the first 60m. (b) Calculate the maximum velocity Bolt coasted at before the finish line. 8. A 4kg block is dropped from a building, 44m high. It hits the ground in 3s. If the block didn’t reach terminal velocity before it hit the ground, calculate its (i) velocity upon hitting the ground and (ii) momentum upon hitting the ground. [use g = 9.8ms-2] 9. (a) A bullet moving at 200 ms -1 hits a target, transferring all its momentum into it. As a result, the target, which has a mass of 5kg, moves backwards. The bullet has a mass of 0.1kg. Assuming the bullet does not stick to the target upon hitting it, calculate (i) the momentum of the bullet and (ii) the velocity of the bullet. (b) Calculate the velocity of the target in the same situation above, but assume the bullet was embedded into the target upon hitting it. 120 10. Two vehicles collide on the highway. A car, heading west, has a mass of 800kg and travels at 20m/s collides head-on with a truck, heading east, of mass 2400kg travelling at 12m/s. Assuming that the wreckage moves as a combined mass, calculate the velocity that wreckage will move at. Also, state its direction. 11. A Boeing-747 jet has a mass of 3.4 x 10 5 kg. It is fitted with two identical thrusters that propel it forward. It eventually travels at a velocity of 92 km/h after half of a minute. (a) Calculate its rate of acceleration in m/s2. (b) Calculate the force applied on each individual thruster. (c) If more passengers boarded the plane, how would this affect (a) and (b)? 12. Using at least ONE of Newton’s Laws of Motion for each, explain how/why: (a) seatbelts or airbags are essential (b) the haphazard movement of a quickly deflating balloon (c) wet roads are dangerous to drive fast on (d) a loaded truck burns fuel at a faster rate than an empty one 13. When a car driver sees an emergency ahead, he applies the brakes. During his reaction time, the car travels a steady speed and covers a distance known as the thinking distance. The braking distance is the distance the car travelled after brakes are applied. Calculate: (a) The thinking distance (b) The braking distance (c) The deceleration during braking (d) The force provided by the brakes 14 (a) Calculate the displacement the sprinter ran between reaching and leaving the hill. (b) Calculate the displacement the sprinter ran after leaving the hill. (c) Calculate the force that allows the sprinter to decelerate to rest after leaving the hill. The sprinter has a mass of 75 kg. 15. A crash test dummy of 70 kg travelling at 26 m/s is subjected to a collision that lasts a duration of 0.1 seconds. (a) Calculate the momentum of the dummy. (b) Calculate the force upon impact experienced by the dummy. 121 (c) In another scenario, all protective gear is removed and the dummy is subjected to a lethal decelerating force of 45,000 N. Calculate the duration of this collision. WORKSHEET 4 – ENERGY [acceleration due to gravity, g = 10ms-2] 1. A student wishes to work out how much power she uses to lift her body when climbing a flight of stairs. Her body mass is 60kg and the vertical height of the stairs is 3m. She takes 12s to walk up the stairs. Calculate: (i) (ii) the work done to raise her body mass up the stairs the power she develops while climbing the stairs 2. Calculate the energy used by a 60W light bulb in one day. 3. The fastest recorded time at the Olympics was by Usain Bolt, at 12.4m/s. If Bolt has a mass of 94kg, calculate his kinetic energy while he was running his fastest speed. 4. How many minutes does it take a 240W heater to produce 43.2kJ of thermal energy? 5. A 70kg man climbs a 15-rung ladder in 20 seconds. Each ladder rung is 30cm apart. Calculate: (a) The man’s weight (b) The total power he developed while climbing the ladder 6. An electric pulley has a power rating of 0.25kW. It lifts a 50kg concrete block a height of 20m. (a) Calculate the time taken to lift the block, assuming no loss. (b) If the pulley was at a constant speed, calculate the speed the block was lifted. (c) (i) State the main energy transformation in the block as it is lifted. (ii) State the main energy transformation in the rope as the block hangs from it. 7. A student rubs her hands together. Each hand movement takes 1.2N of force and moves a distance of 0.08m. (a) Calculate how many movements would be needed to generate 1.92J. (b) If one movement takes 0.2s to occur, how much power is generated? 8. A pole vaulter spends 6kJ to move his body upwards. If the pole vaulter had a mass of 80kg, calculate the maximum height he carried himself. 9. A coal plant’s total output 120,000kJ per hour. However, a supply input of 200MJ per hour is needed for this production rate to occur. (a) Calculate the efficiency of the coal plant. (b) Calculate the power output of the coal plant, using its total output. 10. A student has a mass of 60kg. Whenever he takes a step, he moves 0.2m in 1.2s. (a) Calculate the student’s weight, in N. (b) Calculate the work done by the student per step. (c) Calculate the power developed per step. 122 11. One workman is measured as having a power of 528W. His weight is 800N. He can develop the same power climbing a ladder, which rungs are 0.3m apart. How many rungs can he climb in 5s? 12. A cyclist rides up and then back down a hill, as shown. The cyclist and her bicycle have a combined mass of 90kg. (a) Calculate the GPE of the cyclist and her bicycle at the top of the hill. (b) Calculate the cyclist’s maximum velocity as she descends the hill, to the finishing point. (c) Explain why her actual speed would be less than (b). 13. The diagram below represents a hydroelectric power plant. In order to generate electricity, water flows from a high-level reservoir (600m above sea level) to a low-level reservoir (400m above sea level). As it does, only 15% of the energy is converted to the energy needed to spin a turbine at a station to generate electricity. 150kg of water flows through the station every second. (a) Write a paragraph describing the various energy transformations occurring in the diagram. (b) Explain how the water from the low-level reservoir eventually returns to the high-level reservoir. (c) Calculate the velocity of the turbine as the water flows through it. 14. A mass of a falling rock is 75 kg. It accelerates due to gravity at 10 m/s 2. The rock falls for 2 seconds before hitting a pool of water. (a) Calculate the kinetic energy of the rock just before it hits the water. (b) Suggest THREE things that happen to the kinetic energy as it hits the water. 15. In the cylindrical wind generator, air passes in at 10 m/s. The generator has a circular area of 1300 m2 and a length of 10 m. The density of air is given as 1.3 kg/m3. 123 (a) Calculate the volume of air passing the blades each second. (b) Calculate the mass of this air. (c) Calculate the kinetic energy of this air. WORKSHEET 5 – PRESSURE AND HEAT [Take any instance of g = 10ms-2] 1. Explain why atmospheric pressure is less at the top of a mountain than at sea level. 2. A person presses his thumb against the pointed end of a nail with a force of 40N. The point has a surface area of 2.52 x 10-5 m2. How much pressure is exerted on his thumb when he does this? 3. The diagram shows a person applying force on a brake pedal. The force applied is given as 75N. The brake pedal is connected to a hinge, H, which is then connected to a master cylinder. The master cylinder has a cross-sectional area of 0.04m2. (a) Calculate the force on the master cylinder. (b) Calculate the pressure against the master cylinder. 4. The diagram shows a water reservoir and dam with a conduit that ends with a valve. The valve is closed. The density of water is 1000kg/m3 and the acceleration of gravity is 10m/s2. The pressure at the valve is given as 200kPa. (a) Calculate the depth of the dam, h, from the water surface to the exit pipe. (b) The cross-sectional area of the exit pipe is 0.5m2. Calculate the force of the water on the valve. 5. (a) The pressure is taken along a vertical pipe of oil. If the pressure taken at a 60m depth is given as 4.8 x 105 Pa, calculate the density of oil. (b) In an oil leak, the oil shoots in an upward direction. The force on the oil is 3600N and the leak has a surface area of 0.05m2. Calculate the pressure of the oil and the maximum height of the jet of oil. 124 6. A large concrete block is depicted. Concrete has a density of 2400kg/m3. Calculate the (i)weight and (ii) pressure at the base of the concrete block.(show both methods of doing this) [specific heat capacity of water = 4200 J/kg K] [Lv of water = 2.25 x 106 J/kg] [Lf of water = 3.36 x 105 J/kg] 7. How much energy is required to heat 3kg of water from 30oC to its boiling point? 8. How much energy is required to heat 2500g of water, initially at 300K, to its boiling point and turn it to steam? 9. How much energy is required to convert 1500g of ice at 0oC to steam at 100oC? 10. An experiment is carried out with 75g of water in an insulated beaker. The temperature of the water increases from 20oC to 60oC in 210s. The heater’s power is 60W. Calculate the specific heat capacity of water. 11. A person drinks 4kg of water per day. Assuming this entire volume of water, initially at 15 oC, is eventually excreted as urine at 37oC, calculate: (a) the amount of heat removed each day. (b) the mass of perspiration that would remove the same quantity of heat as the urine when evaporated from the skin 12. A laboratory determination of the specific latent heat of vaporization of water uses a 120W heater to keep water boiling at its boiling point. Water is turned into steam at a rate of 0.050g/s. Calculate the specific latent heat of vaporization obtained from these experimental values. 13. A 1.2kW solar heater is designed to heat 0.3kg of water per minute. The initial temperature of the water is 23oC. (i) Convert 23oC to a Kelvin value. (ii) Calculate the energy produced by the heater per minute. (iii) Calculate the temperature of the water after one minute of heating. 14. The temperature of water at the top of a waterfall is 20oC, while the temperature at the base of the waterfall is 20.5oC. If the waterfall is 210m high, use this information to prove that the specific heat capacity of water is 4200J/kg oC. [g = 10N/kg] 125 15. In an experiment to determine the specific latent heat of fusion of ice using a container with negligible heat capacity, a student obtained the following data. Initial temp. of water = 30oC Initial mass of water = 100g (i) (ii) (iii) | Final temp of water + ice = 20oC | Final mass of water + melted ice = 110g Calculate the heat lost by the water. Calculate the heat gained by the melted ice. Calculate the specific latent heat of fusion of ice. [specific heat capacity of water = 4.2 J g-1 K-1] WORKSHEET 6 – GAS LAWS take all instances of atmospheric pressure as 1.0 x 105 Pa | g = 10N/kg 1. Use the Kinetic Theory of Matter to explain how a balloon may pop when (i) more air is put into it (ii) it is subjected to excess heat. 2. A contractible piston was used to pump gas into an air-bag. The volume of the piston is given as 125cm3. Before pumping, the pressure gauge attached to it read 140Pa. After pumping, the pressure gauge rose to 220Pa. Calculate the new volume of the piston. 3. A toilet flush is operated by the compression of air. The air inside the flush is at atmospheric pressure (1.0 x 105 Pa) and a volume of 150cm3. When the flush is operated, the volume is reduced to 50cm3. If the temperature remains constant, calculate the new pressure of the flush. 4. The diagram shows a diver. She descends 24m below sea level. Seawater has a density of 1050kg/m3. The diver’s helmet has a small glass window that is 0.32m long and 0.08m wide. (a) Calculate the water pressure exerted on the diver. (b) Calculate the force the glass window should be able to withstand at that level. 5. A piston is fitted against a cylinder filled with air. The volume of the piston is 860cm3 and the initial pressure is 1.05 x 105 Pa. When the weights are added, the volume decreases to 645cm3. The temperature remains constant. (a) State what happens to the pressure when the weights are added, and why. 126 (b) In the piston, draw a few air particles and show their directions. (c) Calculate the final pressure of the trapped air. (d) Calculate the increase in pressure. (e) The area of the piston is 5.0 x 10-3 m2. Calculate the weight that was added to the piston that caused the increase in pressure. 6. On a cool day, a freshwater pond is 12m deep. Water has a density of 1000kg/m3. (a) Calculate the pressure of the water at the base of the pond. (b) Atmospheric pressure is given as 1.0 x 105 Pa. Calculate the total pressure at the bottom of the pond. (c) On a hot day, some of the water evaporates from the pond. State what effect this has on the pressure at the base. 127 (d) A bubble of gas is released from the bottom of the pond and floats to the top. The initial volume of the bubble is 0.5cm3. Ignoring any temperature differences, calculate the volume of the bubble as it reaches the surface of the pond. 7. A car tyre is pumped to a pressure of 2 x 10 5 Nm-2 when the temperature is 23oC. Later in the day, the temp. rises to 34oC. Calculate the new pressure in the tyre if the volume was constant. 8. Ms. Wilson drove her car across town. When she started off, the pressure in her tyres was 120kPa above atmospheric pressure and the temperature was 30oC. At the end of the drive, the temperature rose to 70oC. If the volume of the tyre was not changed, what was the pressure inside the tyre at the end? 9. Ms. Wilson decided to get new elastic tyres for her car. The volume adjusts with changes in pressure and temperature. The pressure was the same at the start (120kPa above atm. pressure) and the initial volume of the tyre was 0.8m3. After the drive, calculate the volume of the tyre if the pressure increased by 10% and the temperature increased from 30oC to 70oC. 10. A hot air balloon must be filled with a certain amount of helium for it to float. When filled with 24m3 of helium at a temperature of 32oC, the balloon is able to float. In order for it to float higher, a rope must be tugged to light a fire beneath the balloon. The pressure and mass of helium is constant when this happens. (a) If the fire increases the temperature of the helium to 75oC, how much ADDITIONAL volume was there in the balloon? Express this answer as a percentage increase of the initial volume. (b) Explain why the balloon floats higher when the fire is lit. (c) Explain how the pressure of the balloon can remain constant despite being heated. 128 WORKSHEET 7 - WAVES [Speed of E.M. waves in air = 3 x 108 ms-1] 1. (a) Draw a series of four transverse waves. The final two waves should have approximately half the amplitude of the first two. (b) Redraw the above wavetrain but at double the frequency. 2. A wave of ultraviolet light travels through air and has a wavelength of 400 x 10 -9 m. Calculate its frequency. 3. A radio wave of 50kHz is sent from one signal tower to another. (a) Calculate the period of the wave. (b) Calculate the distance between the signal towers if only one wave oscillation was sent. 4. In an experiment to determine the speed of sound in air, two scientists stand a certain distance apart. One has a pistol and the other has a stopwatch. Explain how this setup can determine the speed of sound in air. State a suitable distance between the scientists. 5. (a) In an experiment, Ravi and Chantal are trying to determine the speed of sound in air. Ravi stands 60m away from a wall and claps two blocks together 20 times. Chantal records the time for the 20 echoes as 7.2 seconds. Calculate the speed of sound from this data. (b) In another experiment, there is a large vertical wall 50m in front of the loudspeaker. The wall reflects the sound waves. If the speed of sound in air was found to be 340 m/s, calculate the time taken for the waves to travel to the wall and return to the speaker. 6. A lightning strike occurs in the distance at 00:09:55 on a stopwatch. At 00:10:07, thunder is heard. If the speed of sound in air is 330m/s, how far away was the source of the thunder? 7. A boat uses a SONAR pulse to determine the depth of an oil spill. The pulse takes 200ms to travel to the spill and echo back up to the boat’s transmitter. If the oil spill is found to be 150m deep, what is the speed of the sound pulse? 8. Differentiate between the terms ELECTROMAGNETIC radiation and NUCLEAR radiation. 9. The wave shown has a speed of 340m/s and a frequency of 200Hz. Using this data, calculate the distance PX on the diagram. 129 10. (a) On the diagram, draw two arrows showing the displacement of particles. (b) If the speed of the wave is 3.2m/s, calculate the frequency of the wave. (c) Calculate the period of the wave. 11. A tsunami is a giant water wave. It may be caused by an earthquake below the ocean. Waves from a certain tsunami have a wavelength of 1.9 × 105 m and a speed of 240 m/s. The shockwave from the earthquake travels at 2.5 × 103 m/s. The centre of the earthquake is 60km from the coast of a country. (a) Calculate the frequency of the tsunami waves. (b) (i) Calculate the time it takes for the earthquake shockwave to reach the coast. (ii) The time between the arrival of the shockwave and the arrival of the tsunami is known as the “warning time”. Calculate how much warning time the people along the coast have. 12.The figure shows a white ray incident to a prism and a red refracted ray, PQ. (b) The angle of incidence for the white light is 40o. If the prism’s refractive index is 1.52, calculate the angle of refraction for the red light. (c) Calculate the speed of the red light in the prism. (d) Comment on changes in wavelength, speed and frequency when a light ray passes into glass. (a) On the figure, complete the red ray and draw the path for a violet ray. 13. The diagram below shows a glass block ABCD. Recreate the diagram in your book. 14. An object is placed 30cm away from a convex lens of 15cm focal length. Calculate: (a) the distance of the image from the lens (b) the magnification of the image 15. A 5cm wide object is placed 10cm from a convex lens. The image is 40cm wide. Calculate: (a) the image’s magnification (b) the image distance (c) the focal length of the lens 130 WORKSHEET 8 - CIRCUITS 1. (a) Calculate the reading on the: (i) ammeter (ii) voltmeter 2. Calculate the readings on both ammeters. 3. Calculate the readings on both ammeters. 4. The circuit below shows a 6V battery, rheostat and light bulb of rating 4.8V, 15W. Calculate: (i) the current used by the bulb. (ii) the energy used by the bulb after 1 hour (iii) the resistance of the rheostat. 131 5. Calculate the reading on the ammeter, in mA, when the switch, S, is (i) open (ii) closed 6. Calculate the reading on the voltmeter. 7. The circuit below shows three resistors. The resistor, Rx, has an unknown value. The ammeter has a reading of 3mA. Calculate the value of Rx. 132 133 WORKSHEET 9 – ELECTRICITY & ELECTRICAL COMPONENTS 1. (a) A Playstation Dualshock controller battery has a rating of 3600C. It uses a 0.5A USB charger. How long would it take to fully charge, in hours? (b) If an iPad battery has a charge capacity of 43200 C and it takes 6 hours to fully charge, what is the current rating of the charger? 2. A lamp is marked 12V, 36W. Calculate the current and resistance of the lamp. 3. A solenoid (coil of wire) is connected to a circuit with a variable resistor and battery. The variable resistor is set to 4Ω while the current across the circuit is 0.45A. (i) Calculate the potential difference across the circuit. (ii) Calculate the thermal energy released in the coil in 9 minutes. 4. A water heater has a power rating of 2.4kW. If it is connected to a 120V power supply, calculate the current supplied to the heater. Calculate the energy produced if the heater is left on for an hour. 5. In a household with 200V a.c., a 100W lamp is switched on. Calculate (i) the current in the lamp (ii) the charge passing through the lamp in one minute. 6. Three 60W filament lamps are replaced by three fluorescent lamps, which give the same light output but are rated at 15W each. Calculate: (i) the total reduction in power (ii) the energy saved when the fluorescent lamps are lit for one hour 7. A 24 V d.c. motor was used to lift a small appliance of mass 25kg from the ground to the second floor of a building. The second floor is 30m above the ground. The motor operates at 100% efficiency and works at a steady rate. It takes 5s to complete the activity. (i) (ii) (iii) (iv) Calculate the gravitational potential energy needed to lift the appliance. Calculate the power of the motor, in kW. Calculate the current drawn from the d.c. supply, in mA. If the the appliance had a greater mass, what effect would this have on the value of the current? [g = 10N/kg] 8. A lightning strike occurs and, in 2.0 × 10 –4 s, a charge of 560 C passes from the cloud to the tree.. Calculate the current of the lightning strike 9. One cathode-ray tube has 5000 V between the accelerating anode and the cathode. The beam of electrons carries a total charge of 0.0095 C in 5.0 s. (i) (ii) (iii) Calculate the current caused by the beam. Calculate the power of the beam. Calculate the energy produced every 20 seconds by the beam. 134 10. The diagram shows the current from a power outlet passing through a resistor of 0.6kΩ. (a) Calculate the peak voltage, from the diagram shown. (b) Calculate the frequency of the current. 11. A transformer “steps down” 1800V to 200V. If the primary side has 360 coils, how many coils would the secondary side have? 12. The primary side of a transformer has 120 coils and produces 500V. Calculate the secondary voltage if there are 300 coils on the secondary side. 13. Explain why an a.c. voltage must be used as the input for a transformer instead of a d.c. input. 14. The diagram shows a step-up transformer. (i) Calculate the secondary voltage. (ii) Calculate the secondary current. (iii) Assuming the transformer is 80% efficient, calculate the power on the secondary side. 15. On the primary side of a transformer, there are 6 turns and 8V A.C. (a) Calculate how many turns there must be on the secondary side to produce a 180V D.C. output. (b) If 100A is produced on the primary side, calculate how much current will be on the secondary side. (c) The transformer is said to be 82% efficient. Calculate how much power is developed on the secondary side as a result. 16. Electrical power produced by Powergen in Trinidad is stepped up from 11,000V at 8000A to 110,000V for transmission to Tobago. (a) If the number of turns in the secondary coil is 900, calculate the number of turns in the primary coil for an ideal transformer. (b) Calculate the transmission current for the ideal transformer in (a). (c) Calculate the transmission power if the transformer is only 70% efficient. 135 WORKSHEET 10 – ATOMIC PHYSICS [speed of light in a vacuum (c) = 3.0 x 108 ms-1] 1. Write the chemical symbols for the following: (a) Radium (Ra), atomic no. = 88, nucleon no. = 226 (b) Carbon (C), having 6 protons and 8 neutrons (c) Lead (Pb), having 82 protons and 127 neutrons (d) Uranium (U), having 92 protons and 146 neutrons 2. Write the chemical symbol for any possible isotope for Carbon or Uranium. 3. Calculate the number of neutrons in an isotope of Polonium, which has an atomic number of 84 and nucleon number of 209. 4. The diagram below represents three α-particles moving towards thin gold foil. Particle A is moving directly towards a gold nucleus. Particle B is moving along a line which passes close to a gold nucleus. Particle C is moving along a line which does not pass close to a gold nucleus. (a) Complete the paths of the α-particles. (b) Write a paragraph stating how observations seen in A, B and C, using large numbers of α-particles, provides information that helped scientists determine the structure of an atom. 5. State what makes an atom (i) unstable (ii) electrically neutral (iii) electrically positive. 6. Uranium (U) has a nucleon number of 233 and atomic no. of 92. It undergoes α –decay to become Thorium (Th). Write the equation. 7. Uranium is formed when Proctacinium (Pa) undergoes β –decay. Write the equation. Use the same nucleon and atomic nos. above for Uranium. 8. Fill in the missing numbers for the radioactive decay equations below. 136 9. Radium (Ra) has a nucleon number of 226 and atomic no. of 88. - Radium undergoes α -decay to become Radon (Rn) - Radon undergoes α -decay to become Polonium (Po). - Polonium undergoes α -decay to become Lead (Pb). - Lead undergoes β -decay to become Bismuth (Bi). Write a radioactive decay formula for each of the above. 10. (a) The half life of iodine-131 is 8 days. What percentage of an iodine-131 sample will remain after 40 days? (b) Os-182 has a half-life of 21.5 hours. How many grams of a 10.0 gram sample would have decayed after 64.5 hours? (c) U-238 has a half-life of 4.5 x 109 (4.5 billion) years. How many years would have to pass for a sample of U-238 to decay to 1/32 of its original amount? 11. The table below shows readings from a Geiger counter over a 1.5-hour periods. The background radiation has already been subtracted. Use the readings to determine the substance’s half life. Time/mins Radiation count (counts/s) 0.0 2400 90.0 300 180.0 37 270.0 5 12. The energy released in a reaction is 1.8 x 10-12 J. Calculate the change in mass in the reaction. 13. The equation below represents the fission of U-233: Nuclide Atomic mass / u U 233.03964 Sb 132.91525 Nb 97.91033 n 1.00867 [u = 1.66 x 10-27 kg] (i) Fill in the missing numbers in the equation. (ii) Calculate the energy released during the fission. 137 KINEMATICS & DYNAMICS QUANTITY / LAW FORMULA / WORDING UNIT Speed (s) s=d/t Velocity (v) v=x/t m/s or ms-1 Acceleration (a) a = Δv / t y-unit x-unit Displacement (inv-t graph) Area of shape under required portion of given v-t graph. m Displacement (if trapezium) ½ (a + b) x h m st Newton’s 1 Law (Law of Inertia) An object at rest remains at rest, or an object in motion remains in motion at constant velocity, unless acted upon by an unbalanced force. Newton’s 2nd Law Acceleration is directly proportional to the net force applied to an object and inversely proportional to its mass.(F = ma or a = F/m) Newton’s 3rd Law For every action force, there is an equal and opposite reaction force. Momentum (p) p = mv Impulse (Δp) Δp = Ft Law of Conservation of Linear Momentum The total momentum in a closed systemis the same before and after collision. kg m/s or Ns Ft = mΔv ENERGETICS QUANTITY / LAW FORMULA / WORDING UNIT Work done (W) W=Fxd J or Nm Power (P) P = E/t or P = W/t W or J/s Kinetic Energy (KE) KE = ½ mv J Gravitational Potential Energy (GPE) ∆GPE = mg∆h J Law of Conservation of Energy Energy can neither be created nor destroyed, but can only be converted into different forms. Efficiency Useful energy (Output) Totalenergy (Input) Velocity (during GPE🡪 KE conversion) UNIT Weight (w) w = mg N or Density (ρ) ρ=m/v kg/m3 or g/cm3 Relative density (RD) RD = ρ(substance) No unit. Archimedes’ Principle The weight of fluid displaced by an immersed objectis equal to the fluid’s buoyant force. Moment of a force (M) M = Fd Principle of Moments For a system in equilibrium, the sum of clockwise and anticlockwise moments about the same point are equal.(F1D1 = F2D2) Hooke’s Law The extension of a spring is directly proportional to the force applied to it until it reaches its limit of proportionality. F = kx (F = Force, k = spring constant, x = extension) ρ(reference) Nm PRESSURE MECHANICS (mv)before= (mv)after 2 FORMULA / WORDING kg ms-2 m/s or ms-2 y2 – y1 x2 – x1 Gradient/Slopeof a Graph QUANTITY / LAW 2 a=v–u t a = F/m STATICS & HYDROSTATICS % QUANTITY / LAW FORMULA / WORDING UNIT Pressure against a surface (P) P=F/A Pa or N/m2 Pressure in fluid (P) P =ρhg Pa or N/m2 Pascal’s Law The pressure exerted at a given point in an incompressible fluid is distributed equally through all points in the fluid. Boyle’s Law The volume of a gas is inversely proportional to the pressure, given that temperature is constant. (P1V1 = P2V2) or PV = k Charles’ Law The volume of a gas is directly proportional to its temperature, given that pressure is constant. (V1 / T1 = V2 / T2) or V/T = k Pressure Law The temperature of a gas is directly proportional to its pressure, given that volume is constant. (P1 / T1 = P2 / T2) or P/T = k Complete Gas Equation P1V1 = P2V2(if P, V or T aren’t constant) T1 T2 m/s 138 ELECTROMAGNETISM & ELECTRONICS THERMODYNAMICS UNIT QUANTITY / LAW FORMULA / WORDING The amount of heat 1kg of a substance required to change its temperature by 1K.(E = mcΔӨ) J/kg K or J kg-1 K-1 Conv. current Flow of +ve charge from +ve to –ve. Electron Flow Flow of –ve charge from -ve to +ve Derivations 1V = 1 J/C 1A = 1 C/s Heat Capacity (C) C = mc J/K V and I in Series VT = V1 + V2... I in = I out Specific Latent Heat of Fusion (Lf) The amount of heat 1kg of a substance required to convert it from a solid to liquid without changing its temperature.(E = mLf) J/kg or J kg-1 Voltage (V) V = IR V = E/Q V Power (P) P = IV P = E/t W Energy (E) E = IVt E=Pxt J Ω J/kg or J kg-1 Resistance (series) (Rs) Rs = R1 + R2... The amount of heat 1kg of a substance requiresto convert it from a liquid to gas without changing its temperature.(E = mLv) Resistance (parallel) (Rp) 1 = 1 + 1… RpR1R2 Ω Charge (Q) Q = It C Ohm’s Law The current through a conductorof constant temperature is directly proportional to itsp.d. and inversely proportional toresistance. (V = IR) Faraday’s Law The emf in a coil is proportional to the rate of change of magnetic flux. QUANTITY / LAW Specific Heat Capacity (c) Specific Latent Heat of Vapourization (Lv) Kinetic Theory of Matter FORMULA / WORDING Matter is made up of particles in random motion. Adding energy makes particles move farther apart. WAVES & OPTICS QUANTITY / LAW FORMULA / WORDING UNIT Wave velocity (v) v=fλ m/s Echo speed (s) s = 2d / t Frequency (f) f =no. waves time elapsed Period (T) T = 1/f Two Laws of Reflection 1. The incident ray, reflected ray and normal all lie on the same plane. 2. The angle of incidence is equal to the angle of reflection.(Өi = Өr) Two Laws of Refraction 1. The incident ray, refracted ray and normal all lie on the same plane. Refractive index (n) Hz or s-1 Equations for ideal transformers s 1 Ω=1VA-1 All three must be 90o to each other to generate a turning force in a motor or current in a generator. Fleming’s Left Hand Rule m/s f = 1_ T UNIT Np / Ns= Vp / Vs ...where, N = No. of Turns VpIp = VsIs or Pp = Ps …where, p = primary, s = secondary NUCLEAR PHYSICS 2. The refractive index (n) between two media is equal to the ratio of the sines of angles of incidence and refraction. (Snell’s Law) Atomic no. (Z) No. of Protons Nucleon no. (A) A = Z + N (protons + neutrons) n = Speed of lightin air (c)__ Speed of light in medium (v) n = __ λ in air____ λ in medium n = sinӨ1 / sinӨ2 Nuclear stability When N : Z = 1 : 1 (same no. of protons and neutrons) Radiation Particles Alpha =42He Beta = o-1e Isotope An element with the same atomic no. of another but different nucleon no. No unit. Өi when r = 90o Critical angle n = 1/sin c Total internal reflection When angle of incidence exceeds the critical angle. (Өi>Өcrit) Half-Life (t1/2) The time it takes for half of a substance to radioactively decay. Magnification M = hi/ ho Lens formula 1 = 1 + 1 f do di Energy gained in a nuclear reaction ΔE = Δmc2(Einstein’s formula) (m = mass, c = speed of light) M = di / do 1 = 1 + 1 f u v 139