Cambridge CIE IGCSE Physics PDF

Head to www.savemyexams.com for more awesome resources Cambridge (CIE) IGCSE Physics Your notes Physical Quantities & Measurement Techniques Contents Measurement Scalars & Vectors Calculating with Vectors...

Head to www.savemyexams.com for more awesome resources Cambridge (CIE) IGCSE Physics Your notes Physical Quantities & Measurement Techniques Contents Measurement Scalars & Vectors Calculating with Vectors Page 1 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Measurement Your notes Measuring length & volume When making measurements in physics, different instruments are used for different measurements Measuring length Rulers can be used to measure small distances of a few centimetres (cm). They are able to measure to the nearest millimetre (mm) A ruler can measure lengths in cm or mm A tape measure is used to measure lengths of tens of centimetres A trundle wheel is used to measure lengths of tens of metres Page 2 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Trundle wheels can be used to measure larger distances Measuring volume Measuring cylinder are used to measure the volume of liquids By measuring the change in volume, a measuring cylinder can also be used to determine the volume of an irregular shape Page 3 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Measuring cylinders can be used to determine the volume of a liquid or an irregular shaped solid WORKED EXAMPLE The diagram shows four identical ball-bearings placed between two blocks on a steel ruler. Page 4 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Calculate the diameter of one ball-bearing. Answer: Step 1: Measure the length of all four ball-bearings The blocks mark the edges of the first and last ball bearings The blocks make it easier to measure the length of all four ball-bearings total length = 12 − 4 total length = 8 cm Step 2: Find the diameter by dividing the total length by the number of ball-bearings total length diameter = number of ball bearings 8 diameter = 4 diameter = 2 cm Measuring time In physics, stop-clocks and stopwatches are usually used to measure time intervals An important factor when measuring time intervals is human reaction time The standard human reaction time for an alert person is 0.25 s Page 5 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources This can have a significant impact upon measurements when the measurements involved are very short Your notes WORKED EXAMPLE A stopwatch is used to measure the time taken for a runner to complete a lap of a 400 m track. The images below give the readings on the stopwatch at the start and the end of the lap. Calculate how long it took the runner to complete the lap. Give your answer in seconds. Answer: Step 1: Identify the start time for the lap The stopwatch was already at 0:55:10 when the runner started the lap Start time = 55.10 seconds (s) Step 2: Identify the finish time for the lap The stopwatch reads 1:45:10 at the end of the lap Finish time = 1 minute and 45.10 s Step 3: Convert the finish time into seconds 1 minute = 60 seconds finish time = 60 s + 45. 10 s finish time = 105. 10 s Step 4: Calculate the total time taken to complete the lap total time = finish time − start time Page 6 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources total time = 105. 10 s − 55. 10 s total time = 50 s Your notes EXAM TIP You will sometimes find that information is given in the question that is not actually needed in the calculation. In this worked example, you were told that the track the runner is running on is 400 m. This had nothing to do with the calculation the question asked you to perform. This is a common method for making a question seem more difficult. Don't let it catch you out. Multiple readings In physics, multiple readings of measurements are often taken to reduce the impact of measurement errors Taking multiple measurements in physics The measurement of the thickness of a single sheet of paper is so small that it would be very difficult to get an accurate answer However, measuring the thickness of 100 sheets of paper can be done much more accurately Page 7 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Dividing the answer by 100 then gives an accurate figure for the average thickness of one sheet Measuring the time period of a simple pendulum would incur a human reaction time error at the start of the measurement and at the end of the measurement Your notes If the measurement is small, the uncertainty in the measurement is huge Therefore, multiple readings can be taken to reduce the uncertainty of the measurement The time taken for 10 swings of the pendulum can be measured Dividing the answer by 10 gives a more accurate figure for the average time taken for one swing Page 8 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Scalars & Vectors Your notes Scalar & vector quantities Extended tier only All quantities can be one of two types: A scalar A vector Scalars Scalar quantities have only a magnitude Mass is an example of a scalar quantity because it has magnitude without direction Energy and volume are also examples of scalar quantities Vectors Vector quantities have both magnitude and direction Weight is an example of a vector quantity because it is a force and therefore has both magnitude and direction Acceleration and momentum are also examples of vector quantities Distance and displacement Distance is a measure of how far an object has travelled, regardless of direction Distance is the total length of the path taken Distance, therefore, has a magnitude but no direction So, distance is a scalar quantity Displacement is a measure of how far it is between two points in space, including the direction Displacement is the length and direction of a straight line drawn from the starting point to the finishing point Displacement, therefore, has a magnitude and a direction So, displacement is a vector quantity What is the difference between distance and displacement? Page 9 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Displacement is a vector quantity, while distance is a scalar quantity When a student travels to school, there will probably be a difference between the distance they travel and their displacement The overall distance they travel includes the total lengths of all the roads, including any twists and turns The overall displacement of the student would be a straight line between their home and school, regardless of any obstacles, such as buildings, lakes or motorways, along the way Speed and velocity Speed is a measure of the distance travelled by an object per unit time, regardless of the direction The speed of an object describes how fast it is moving, but not the direction it is travelling in Speed, therefore, has magnitude but no direction So, speed is a scalar quantity Velocity is a measure of the displacement of an object per unit time, including the direction The velocity of an object describes how fast it is moving and which direction it is travelling in Page 10 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources An object can have a constant speed but a changing velocity if the object is changing direction Velocity, therefore, has magnitude and direction Your notes So, velocity is a vector quantity Examples of scalars & vectors Extended tier only The table below lists some common examples of scalar and vector quantities Corresponding scalars and their vector counterparts are aligned in the table where applicable Table of scalars and vectors Scalar Vector distance displacement speed velocity mass weight force acceleration momentum electric field strength energy volume density temperature power Page 11 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources WORKED EXAMPLE Your notes An instructor is in charge of training junior astronauts. For one of their sessions, they would like to explain the difference between mass and weight. Suggest how the instructor should explain the difference between mass and weight, using definitions of scalars and vectors in your answer. Answer: Step 1: Recall the definitions of a scalar and vector quantity Scalars are quantities that have only a magnitude Vectors are quantities that have both magnitude and direction Step 2: Identify which quantity has magnitude only Mass is a quantity with magnitude only So mass is a scalar quantity The instructor might explain to their junior astronauts that their mass will not change as their location in the Universe changes Step 3: Identify which quantity has magnitude and direction Weight is a quantity with magnitude and direction (it is a force) So weight is a vector quantity The instructor might explain that their weight, the force on them due to gravitational field strength, will vary depending on their location. For example, the force of weight acting on them would be less on the Moon than it is on Earth EXAM TIP Make sure you are comfortable with the differences between similar scalars and vectors. The most commonly confused pairings tend to be: distance and displacement speed and velocity weight and mass Page 12 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Calculating with Vectors Your notes Calculations with vectors Extended tier only Vectors can be drawn using vector diagrams Vector diagrams Vectors are represented by an arrow The length of the arrow represents the magnitude The direction of the arrow indicates the direction the scale of the arrows should be proportional to the relative magnitudes of the forces an arrow for a 4 N force should be twice as long as an arrow for a 2 N force Vector diagram of two forces acting on an object The length of the arrows are proportional to the magnitude of the forces, and show the direction that forces act in Calculating vectors graphically Vector diagrams can be used to combine vectors Vectors at right angles to one another can be combined into one resultant vector The resultant vector will have the combined effect of the two original vectors For example, a resultant force vector will have the combined effect of two component forces Page 13 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Component vectors are sometimes drawn with a dotted line and a subscript indicating horizontal or vertical Your notes A force F , for example, may have two components: FV is the vertical component of the force F FH is the horizontal component of force F To calculate vectors graphically means carefully producing a scale drawing with all lengths and angles correct This should be done using a sharp pencil, ruler and protractor Follow these steps to carry out calculations with vectors on graphs 1. Choose a scale which fits the page For example, use 1 cm = 10 m or 1 cm = 1 N, so that the diagram is around 10 cm high 2. Draw the vectors at right angles to one another 3. Complete the rectangle 4. Draw the resultant vector diagonally from the origin 5. Carefully measure the length of the resultant vector 6. Use the scale factor to calculate the magnitude 7. Use the protractor to measure the angle Page 14 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Vectors can be measured or calculated graphically using scaled vector diagrams Combining vectors by calculation In this method, a vector diagram is still essential but it does not need to be exactly to scale The vector diagram can take the form of a sketch, as long as the resultant side, component sides are clearly labelled Page 15 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Using a vector diagram to resolve two force vectors F1 and F2 into a resultant force vector FR When the magnitude of only one vector is known, and the angle is known, then trigonometry can be used to find the magnitude of the missing vector The mnemonic 'soh-cah-toa' can used to remember the trigonometric functions Page 16 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Trigonometry can be used when the magnitude of one vector and the angle is known When the magnitudes of two of the vectors are known, then Pythagoras' theorem can be used to find the magnitude of the missing vector Page 17 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Pythagoras's theorem can be used when the magnitudes of two of the three vectors are known WORKED EXAMPLE A force acts on an object with 60 N to the left. A second force of 100 N acts on the same object in the upward direction. Calculate the resultant force acting on the object. Answer: Step 1: Draw a vector diagram Page 18 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes Step 2: Calculate the magnitude of the resultant force using Pythagoras' theorem F= 60 2 + 100 2 F= 13 600 F = 117 N Step 3: Calculate the direction of the resultant vector using trigonometry Page 19 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources Your notes opposite tanθ = adjacent 100 tanθ = 60 ⎛ 100 ⎞⎟ θ = tan−1 ⎜⎜ ⎟ = 59° ⎝ 60 ⎠ Step 4: State the final answer, complete with magnitude and direction F = 117 N at 59° from the horizontal EXAM TIP If the question specifically asks you to use the calculation or graphical method, you must solve the problem as asked. However, if the choice is left up to you then any correct method will lead to the correct answer. Page 20 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  Head to www.savemyexams.com for more awesome resources The graphical method sometimes feels easier than calculating, but once you are confident with trigonometry and Pythagoras you will find calculating quicker and more accurate. Your notes Page 21 of 21 © 2015-2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers