NUSH PC1131 Notes

PC1131 Notes Foundations in Physics I Chapters 2 to 15 This is a compilation of questions and notes provided in PC1131. Made by LQ (uwu) Links of All LQ Notes: LQ Notes Links Document Topic Chapter 2: Mathematics and Physics I Chapter 3: Measurements Chapter 4: Measurements of Length Chapter 5: Measurements of Time Chapter 6: Mathematics and Physics II Chapter 7: Mass, Weight and Density Chapter 8: General Wave Properties I Chapter 9: General Wave Properties II: Reflection & Refraction of Waves Chapter 10: Sound Chapter 11: Electromagnetic Spectrum [No notes cuz LQ lazy sowee :(] Chapter 12: Mathematics and Physics III Chapter 13: Light I - Reflection Chapter 14: Light II - Refraction Chapter 15: Light III - Lenses Legend Yellow: Common Test 1 Orange: Midyear Exam Red: EOY Exam Purple : Practical Test

Chapter 2: Mathematics and Physics I 2.1 SI Units SI units is the designated universal classification of units. 2.1.1 SI Base Units There are 7 SI base units. Base physical quantities SI base unit Name Symbol length meter m mass kilogramme kg time second s electric current ampere A thermodynamic temperature kelvin K amount of substance mole mol luminous intensity candela cd 2.1.2 SI derived units Derived quantity SI derived unit Name Symbol area square meter m 2 volume cubic meter m 3 speed (velocity) meter per second m/s (m s -1 ) acceleration meter per second squared m/s 2 (m s -2 ) density kilogram per cubic meter kg/m 3 (kg m -3 ) 2.1.3 SI derived units with special names Derived quantity Name Symbol in SI base units force newton N m kg/s 2 (m kg s -2 )

pressure pascal Pa kg / m s 2 (kg m -1 s -2 ) energy joule J kg m 2 /s 2 (kg m 2 s -2 ) frequency (Used for calculating frequency of a wave: See 8.8 Frequency) hertz Hz s -1 2.2 Prefixes Prefixes are used to express physical quantities that are very big or small by making use of factors of 10, similar to scientific notation. The prefix is used in front of the unit (e.g. kilo meter, centi meter) Prefix Symbol Sci. Notation Femto- f 10 -15 Pico- p 10 -12 Nano- n 10 -9 Micro- μ 10 -6 Milli- m 10 -3 Centi- c 10 -2 Deci- d 10 -1 Kilo- k 10 3 Mega- M 10 6 Giga- G 10 9 Tera- T 10 12 Common Test 1 Revision Package Question 2 The following shows 3 values of length: X = 1.23 × 10 8 µm Y = 1.23 × 10 -7 Mm Z = 1.23 × 10 6 nm What is the correct order of the lengths from the longest to the shortest? [1]

A) X, Y, Z C) Y, Z, X B) Y, X, Z D) Z, X, Y Answer Firstly, it is a very common strategy to convert all the measurements into just meters. X = 1.23 × 10 8 × 10 -6 m = 1.23 × 10 2 m Y = 1.23 × 10 -7 × 10 6 m = 1.23 × 10 -1 m Z = 1.23 × 10 6 × 10 -9 m = 1.23 × 10 -3 m The orange portions is the original value given, while the green section is accounting for the prefix. (e.g. For X, 1 µm becomes 10 -6 m) (also looks like carrot lmao) From this, we can now compare the values and we see that X > Y > Z. Hence, the answer is (A). 2.3 Scientific Notation Scientific Notation is expressed as a product of two numbers. The first number is between 1 and 10, while the second is a power of 10. E.g. 6.9 × 10 2 2.4 Why SI Units? Course Pack, Chapter 2, Page 10, Example 1 In the Egyptian Middle Kingdom (1600 BC to 600 BC), the units for length used included the palm and the cubit (which is the distance from the human elbow to the end of the middle finger). Here is the conversion: 1 cubit = 6 palms = 56.3 cm a) An Egyptian Pharaoh once ordered a pyramid to be built. The pyramid has a square base with sides of length of 420 cubits each and a vertical height of 1500 palms. Given that the volume of a square-base pyramid is × base area × height , calculate the volume of the 1 3 pyramid: i) in cubic cubits, ii) in cubic meters. b) suggest 2 advantages in using the meter compared to the cubit as a unit of length. Answers a) i) …in cubic cubits. First, we convert the height of the pyramid to cubits. 1500 palms = 250 cubits

Now, volume = × base area × height. 1 3 × 420 2 square cubits × 250 cubits = 14 700 000 cubic cubits (1.47 × 10 7 cubic cubits) 1 3 ii) …in cubic meters. First, we convert 1 cubic cubit to cubic meters. Given that 1 cubit = 56.3 cm, 1 cubic cubit = (56.3 cm) 3 = (0.563 m) 3 = 0.178 m 3 (3 sf). Now, we convert 1.47 × 10 7 cubic cubits = 1.47 × 10 7 × 0.178 m 3 = 2.61 × 10 6 m 3 (3 sf). b) Suggest 2 advantages in using the meter compared to the cubit as a unit of length. The meter does not change unlike the length between the human elbow to the end of the middle finger, which varies from person to person. It is in multiples of powers of 10 .

Chapter 3: Measurements 3.1 Basic Arithmetic Precision We follow 3 rules: 1. When adding/subtracting, we round the result to the number with the lowest decimal place (dp). 2. When multiplying/dividing, we round the result to the number with the lowest significant figures (sf). 3. A constant has infinite significant figures. (E.g. while taking the average of 2 things, division by 2 has infinite sf) 3.2 Errors Error is the difference between the true value and the measured value. 3.2.1 Random Error Random Errors are random and can occur from: - quantities that change with time (e.g. BMI) - human judgement - manufacturing faults - estimation of the last significant figure - background noise or mechanical vibrations in the laboratory (e.g. sound) Random Errors can be minimised by taking a large number of readings and taking the average. Note: Random Errors can NOT be eliminated completely. Under the same conditions, it can cause errors of different sizes and signs. This is why Random Errors cannot be eliminated completely. 3.2.2 Systematic Error A Systematic Error is a constant error caused by an imperfection in the instrument being used, from mistakes the individual makes while taking the measurement, or from certain extreme conditions such as a very high or very low temperature. Repeating the measurement under the same conditions will cause errors of the same size and sign. Hence, Systematic Errors can be completely eliminated . 3.2.2.1 Zero Error Zero Error refers to instruments of length losing the zero mark or causing the instrument to be slightly deformed from prolonged use.

This can be found on instruments to measure length like Vernier Calipers and Micrometer Screw Gauges. (See Chapter 4: Measurements of Length) Since it is a systematic error, zero errors can be eliminated completely . 3.2.2.2 Parallax Error While using an instrument that measures volume, if your eye is not at water level while rea