CIE IGCSE Physics (0625) Physical quantities and measurement techniques Study Notes - New Syllabus
CIE IGCSE Physics (0625) Physical quantities and measurement techniques Study Notes
LEARNING OBJECTIVE
- Understanding the concepts of Physical quantities and measurement techniques
Key Concepts:
- Measuring Length and Volume
Measuring Length and Volume
Measuring Length and Volume
- Length is a physical quantity representing the distance between two points. Its SI unit is the metre (m).
- Volume is the amount of space an object occupies. Its SI unit is the cubic metre (m³), but in practice smaller units like cm³ and mL are often used.
Using a Ruler to Measure Length:
- Use a metre rule or ruler marked in millimetres (mm) or centimetres (cm).
- Place the object on a flat surface and align it with the zero mark of the ruler — NOT the edge of the ruler.
- Take readings at eye level to avoid parallax error (which happens when viewed from an angle).
- For accuracy, use a ruler with smaller divisions (e.g. mm).
Example: Measuring the length of a pencil using a ruler. Align one end with the 0 cm mark and read the other end. If it ends at 12.4 cm, the length is \( 12.4~\text{cm} \).
Using a Measuring Cylinder to Find Volume:
- A measuring cylinder is used to measure the volume of liquids or irregular solids via water displacement.
- Place the measuring cylinder on a flat surface and read the bottom of the meniscus at eye level.
- To measure the volume of an irregular object, use the displacement method:
- Fill the measuring cylinder with water and record the initial volume \( V_1 \).
- Gently submerge the object and record the new volume \( V_2 \).
- Volume of object = \( V_2 – V_1 \).
Example: A stone is placed in water. Initial volume = \( 50~\text{cm}^3 \), final volume = \( 63~\text{cm}^3 \). The volume of the stone = \( 63 – 50 = 13~\text{cm}^3 \).
Example:
You are given a pencil to measure. You place it along a ruler and observe that one end is at the 0.0 cm mark and the other end is at the 13.2 cm mark. What is the length of the pencil?
▶️ Answer/Explanation
Initial position: \( 0.0~\text{cm} \)
Final position: \( 13.2~\text{cm} \)
Length of the pencil = Final – Initial = \( 13.2~\text{cm} – 0.0~\text{cm} = \boxed{13.2~\text{cm}} \)
Example:
A small stone is placed in a measuring cylinder containing water. The water level rises from 60 mL to 76 mL. What is the volume of the stone?
▶️ Answer/Explanation
Initial volume \( V_1 = 60~\text{mL} \), Final volume \( V_2 = 76~\text{mL} \)
Volume of stone = \( V_2 – V_1 = 76~\text{mL} – 60~\text{mL} = \boxed{16~\text{mL}} \)
Measuring Time Intervals Using Clocks and Digital Timers
Measuring Time Intervals Using Clocks and Digital Timers
- Time is a physical quantity used to measure the duration between two events. Its SI unit is the second (s).
- In the lab and in real life, we use devices like:
- Analogue clocks
- Stopwatches (digital or analogue)
- Electronic/digital timers (e.g., on sensors or circuit boards)
Measuring Time Using a Clock:
- Use when measuring longer durations such as minutes or hours.
- Analogue clocks show time using hands, while digital clocks use numbers (e.g., 14:32).
- Accuracy depends on how precisely you can note the start and end times.
Measuring Short Intervals with a Stopwatch or Timer:
- Used in experiments like timing pendulum swings, reaction times, or fall times.
- Digital stopwatches are more precise, typically accurate to \( 0.01~\text{s} \) or better.
- Start the timer as the event begins and stop when it ends — quick reaction time is essential.
Electronic Timers in Physics Labs:
- Often used in advanced setups like light gates or motion sensors.
- Eliminates human error by automatically starting/stopping when the object passes a sensor.
Key Tips:
- Always repeat the measurement multiple times and take the average to reduce random error.
- Minimize reaction delay (human error) in manual timing by practicing or using automated methods.
Example:
You use a stopwatch to measure the time it takes for a ball to fall from a height of 2 m. You record the time as 0.64 seconds. What kind of instrument is suitable for this experiment and what can you do to reduce error?
▶️ Answer/Explanation
A digital stopwatch is suitable because the interval is very short (under 1 second).
To reduce error, repeat the timing multiple times and take the average. Also, minimize reaction time error or use an electronic timer with sensors.
Determine an Average Value for Small Distance and Short Time
Determine an Average Value for Small Distance and Short Time
When measuring very small distances or short time intervals, it can be difficult to get accurate readings due to limitations in timing devices or human reaction time. To improve accuracy, we use the method of averaging over multiple measurements.
1. Measuring Small Distances Accurately:
- Instead of measuring a tiny length once, measure a longer section made up of many small units.
- Then divide by the number of units to get the average small distance.
Example: To measure the thickness of one sheet of paper:
- Measure the thickness of a stack of 100 sheets: e.g., \( 1.2~\text{cm} \)
- Average thickness = \( \dfrac{1.2~\text{cm}}{100} = 0.012~\text{cm} \)
2. Measuring Short Time Intervals (e.g., Period of a Pendulum):
- It is hard to measure one swing of a pendulum due to short time and reaction delay.
- Instead, time multiple oscillations (e.g., 10 or 20), then divide by the number to find the average period.
Period = time for one complete oscillation (to-and-fro motion).
If 20 oscillations take \( 32~\text{s} \), then period = \( \dfrac{32}{20} = 1.6~\text{s} \)
Why Use Averages?
- Reduces the effect of measurement errors or human reaction delay.
- Increases precision, especially when dealing with small or fast phenomena.
Example:
You measure the thickness of 50 sheets of paper as 0.9 cm. What is the average thickness of one sheet?
▶️ Answer/Explanation
Total thickness = \( 0.9~\text{cm} \), Number of sheets = 50
Average thickness = \( \dfrac{0.9}{50} = \boxed{0.018~\text{cm}} \)
Example:
A student times 25 swings of a pendulum and finds the total time is 40 seconds. What is the average time period of one swing?
▶️ Answer/Explanation
Total time = \( 40~\text{s} \), Number of oscillations = 25
Average period = \( \dfrac{40}{25} = \boxed{1.6~\text{s}} \)
Scalar and Vector Quantities
Scalar and Vector Quantities
Physical quantities are properties of objects that can be measured, such as mass, time, or force. These are broadly classified into two types:
Scalar Quantities
- Have magnitude (size) only
- No direction involved
- Fully described by a single number and a unit
- Examples: \( \text{Speed} = 25~\text{m/s} \), \( \text{Time} = 5~\text{s} \)
- Do not change depending on direction
Example Explanation: If two cars are moving at the same speed but in opposite directions, their speed (scalar) is the same. But their velocity (vector) is different because of the direction.
Vector Quantities
- Have both magnitude and direction
- Fully described by a number, unit, and a direction
- Often represented as arrows on diagrams:
- Arrow length = magnitude
- Arrowhead = direction
- Direction matters — changing direction changes the quantity
Example Explanation: A car moving north at 10 m/s has a different velocity from one moving south at 10 m/s, even though the speed is the same.
Why This Distinction Matters:
- In physics problems, vector quantities must be added/subtracted using vector rules (not simple arithmetic).
- Scalars are added algebraically (just add the numbers).
- Forces and motions often involve vector combinations, which can affect the result greatly depending on direction.
Common Scalar Quantities
| Quantity | Unit | Why Scalar? |
|---|---|---|
| Distance | metre (m) | Has only magnitude |
| Speed | m/s | Direction not needed |
| Time | second (s) | No direction |
| Mass | kilogram (kg) | Only size matters |
| Energy | joule (J) | No direction required |
| Temperature | °C or K | Purely magnitude |
Common Vector Quantities
| Quantity | Unit | Why Vector? |
|---|---|---|
| Force | newton (N) | Direction affects result |
| Weight | newton (N) | Always acts downward |
| Velocity | m/s | Speed + direction |
| Acceleration | m/s² | Direction of change matters |
| Momentum | kg·m/s | Mass × velocity (has direction) |
| Electric Field Strength | N/C | Field has direction |
| Gravitational Field Strength | N/kg | Always directed toward mass |
Example:
A car is moving at 20 m/s north. Is this quantity scalar or vector?
▶️ Answer/Explanation
The quantity includes both magnitude (20 m/s) and direction (north).
Therefore, it is a vector. This is an example of velocity, not just speed.
Example:
Classify each of the following as scalar or vector:
(a) 40 kg (b) 15 m/s south (c) 300 K (d) 50 N upward
▶️ Answer/Explanation
- (a) 40 kg → Scalar (mass)
- (b) 15 m/s south → Vector (velocity — has direction)
- (c) 300 K → Scalar (temperature)
- (d) 50 N upward → Vector (force with direction)
Concept of Resultant Vector
Concept of Resultant Vector
The resultant vector is the single vector that has the same effect as two or more vectors acting together.
- When two vectors (like forces or velocities) act at right angles (90°), the resultant is found using the Pythagorean theorem.
- This applies to both forces and velocities.
Calculation Method:
If two vectors \( A \) and \( B \) are at right angles:
Resultant \( R = \sqrt{A^2 + B^2} \)
To find the direction (angle \( \theta \)) of the resultant with respect to one of the vectors:
\( \theta = \tan^{-1} \left( \dfrac{B}{A} \right) \)
Graphical Method (Scale Diagram):
- Draw vector A to scale (e.g., 1 cm = 2 N or 1 cm = 1 m/s)
- From the head of vector A, draw vector B at a 90° angle
- Join the tail of A to the head of B — this is the resultant
- Measure the length of the resultant and convert back using the scale
Key Points:
- This method only works when the angle between the vectors is exactly 90°.
- Vectors must represent the same quantity (e.g., both are forces, or both are velocities).
Example:
Two forces act on a box: 6 N to the right and 8 N upward. Calculate the magnitude and direction of the resultant force.
▶️ Answer/Explanation
Given: Forces are at right angles.
Use Pythagoras: \( R = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = \boxed{10~\text{N}} \)
Direction: \( \theta = \tan^{-1} \left( \dfrac{8}{6} \right) = \tan^{-1} (1.333) \approx \boxed{53.1^\circ} \) above the horizontal
Example:
A boat moves 5 m/s east across a river flowing at 12 m/s south. Find the boat’s resultant velocity and its direction of motion.
▶️ Answer/Explanation
Given: Velocities at right angles.
Resultant velocity: \( R = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = \boxed{13~\text{m/s}} \)
Direction: \( \theta = \tan^{-1} \left( \dfrac{12}{5} \right) = \tan^{-1}(2.4) \approx \boxed{67.4^\circ} \) south of east