Physics Matters - GCE O Level Textbook - Chapter 1: Measurements PDF

# Chapter 1: Measurements ## 1.1: What is Physics? - Physics is the study of our natural world, from the very large (e.g., the solar system) to the very small (e.g., the atom). - It can be divided into major topics such as those shown in Figure 1.1. - These topics are related to two main ideas: ma...

# Chapter 1: Measurements ## 1.1: What is Physics? - Physics is the study of our natural world, from the very large (e.g., the solar system) to the very small (e.g., the atom). - It can be divided into major topics such as those shown in Figure 1.1. - These topics are related to two main ideas: matter and energy. - The [Disciplinary Ideas of Physics](https://www.youtube.com/watch?v=dQw4w9WgXcQ) highlight the overarching ideas of Physics that can be applied to explain real-life problems or phenomena. - Matter and energy make up the Universe. - Matter interacts through forces and fields. - Forces help us understand motion. - Waves can transfer energy without transferring matter. - Conservation laws constrain the changes in systems. - Microscopic models can explain macroscopic phenomena. - We will revisit the Disciplinary Ideas at relevant junctures of the book. **[Image of a diagram showing different fields within the study of physics]** ## 1.2: What are Physical Quantities? - A physical quantity is a quantity that can be measured. It consists of a numerical magnitude and a unit. - Altogether, there are seven basic physical quantities, or base quantities. **Table 1.1: Base quantities and their SI units** | Base Quantity | SI Unit | Symbol for SI Unit | Link | |---|---|---|---| | Length | Metre | m | | | Mass | Kilogram | kg | | | Time | Second | s | | | Electric current | Ampere | A | | | Thermodynamic temperature | Kelvin | K | | | Amount of substance | Mole | mol | That the mole is the unit of the amount of substance. One mole contains 6.02 x 10²³ particles. These particles may be electrons, atoms, ions, or molecules. The value 6.02 x 10²³ is called the Avogadro's constant. | - We use a system of standardized units called **SI units** or the **International System of Units** (abbreviated SI from French: Système International d’Unités). - SI units ensure we follow a common standard when taking measurements. - Other common physical quantities such as area, volume and speed are derived from these base quantities through an equation. For example, speed is defined as distance travelled per unit time (Speed = distance travelled / time). - Using decimal notation is not always efficient, so prefixes are used to represent quantities. **Table 1.2: Some common prefixes and their symbols** | Multiples | Factor | Prefix | Symbol | |---|---|---|---| | | 10¹² | tera- | T | | | 10⁹ | giga- | G | | | 10⁶ | mega- | M | | | 10³ | kilo- | k | |Sub-multiples| 10⁻¹ | deci- | d | | | 10⁻² | centi- | c | | | 10⁻³ | milli- | m | | | 10⁻⁶ | micro- | µ | | | 10⁻⁹ | nano- | n | ## 1.3: How do we measure physical quantities? - We should use the appropriate instruments and methods to measure different types of length. The SI unit for length is the metre (m). - There is a wide range of lengths in this world, from the radius of a hydrogen nucleus to the length of a football field. **[Image of a diagram showing the relative sizes of different objects and their corresponding measurements]** - We use a **metre rule** and a **measuring tape** to measure length. A **digital caliper** is used to measure the internal and external diameters of an object accurately. - The **digital micrometer screw gauge** is used to measure objects that are too small to be measured using the digital calipers. **[Image of a digital caliper]** **[Image of a digital micrometer screw gauge]** The smallest unit an instrument can measure is known as its **precision**. **Table 1.3: Common measuring instruments with their range, smallest division and usage** | Instrument | Measuring Range | Smallest Division | Example of Usage | |---|---|---|---| | Measuring tape | zero to several metres | 0.1 cm or 1 mm | a person's waist | | Metre rule | zero to one metre | 0.1 cm or 1 mm | height of a table | | Digital calipers | zero to 15 centimetres | 0.001 cm or 0.01 mm | diameter of a test tube | | Digital micrometer screw gauge | zero to 2.5 centimetres | 0.0001 cm or 0.001 mm | diameter of a wire | - We need to avoid **errors of measurement**. These include **parallax errors** and **zero errors**. - The **period of a simple pendulum** is the time taken for one complete oscillation. - **Atomic clocks** are the most accurate timekeeping devices. **[Image of an atomic clock]** - Time can also be measured using a **pendulum clock** or a **stopwatch**. **[Image of a pendulum clock]** ## 1.4: What are Scalars and Vectors? - **Scalar quantities** are physical quantities that have only magnitude. - **Vector quantities** are physical quantities that have both magnitude and direction. **Table 1.5: Common scalar and vector quantities** | Scalar | Vector | |---|---| | Distance | Displacement | | Speed | Velocity | | Mass | Acceleration | | Energy | Force | | Time | Weight | - **Distance** is the total length covered by a moving object regardless of the direction of motion. It is a scalar quantity. - **Displacement** is the distance measured in a straight line in a specified direction. It is a vector quantity. **[Image of a diagram showing distance and displacement]** - **Speed** is the distance moved per unit time. It is a scalar quantity. - **Velocity** is the rate of change of displacement. It is a vector quantity. **[Image of a diagram showing speed and velocity]** - Vectors can be added by the **graphical method**. The length of the arrow is proportional to the magnitude of the vector, and the direction of the arrow indicates the direction of the vector. **[Image of a diagram showing how to add two vectors graphically]** **[Image of the Mind Map summarising the content of the chapter]** # Let's Practice 1.4 1. What are the similarities and differences between scalar and vector quantities? 2. A car travels at 90 km/h due east for an hour and then travels at 60 km/h due west for another hour. Determine the resultant velocity graphically. 3. A man walks 1 km due east and then walks 1 km due north. Determine the resultant displacement graphically. # Let's Review ## Section A: Multiple-choice Questions 1. In an experiment, you are required to measure the distance between two points that are between 0.7 m and 0.8 m apart. Which of the following instruments should you use in order to obtain a reading that has a precision of 0.001 m? * A half-metre rule * B metre rule * C metre rule and digital calipers * D ten-metre measuring tape 2. The digital micrometer screw gauge can be used to measure the: * A circumference of a coin * B depth of a test tube * C thickness of a coin * D thickness of 1000 pieces of A4 paper 3. An object has a width of about 1.5 cm. The reading shown on the digital micrometer screw gauge when it is used to measure the width of the object is: * A 15 mm * B 15.1 mm * C 15.01 mm * D 15.001 mm ## Section B: Structured Questions 1. (a) List three examples of base quantities and their corresponding SI units. (b) The mass of a car is 1 300 000 g. Express the mass of the car in SI unit and standard form. 2. Fill in the blanks with the correct prefixes. The first has been done for you. (a) 1 kg = 10³ g (b) 1 µs = 10⁻⁶ s (c) 1 cm = 10⁻² m (d) 1 MW = 10⁶ W (e) 1 mA = 10⁻³ A (f) 1 cm² = 10⁻⁴ m² 3. (a) What is a scalar quantity? (b) Give two examples of scalar quantities. (c) If a car travels 10 km from point A to point B and then another 12 km to point C, what is the total distance travelled by the car? ## Section C: Free-response Questions 1. A student conducted an experiment to measure the acceleration due to gravity *g* of a simple pendulum. The data obtained were tabulated in Table 1.7. **Table 1.7** | Length of Thread *l*/m | 0.35 | 0.65 | 1.00 | 1.45 | 1.95 | |---|---|---|---|---|---| | Time for 20 Oscillations *t*/s | 24.1 | 32.4 | 40.1 | 47.5 | 56.3 | Given that the relation between the period *T*, the length *l* of the pendulum and the acceleration due to gravity *g* is *T* = 2π √(*/g*), find the value of *g* using the graphical approach. 2. Define precision of an instrument. State a suitable instrument to measure the diameter of a ten-cent coin. Explain your answer in terms of the precision of the instrument.