IB MYP 4-5 Physics- Measuring length and time- Study Notes - New Syllabus
IB MYP 4-5 Physics- Measuring length and time- Study Notes
Key Concepts
- Measuring Length and Time
Measuring Length and Time
Measuring Length
Length is the distance between two points and is one of the seven fundamental physical quantities. It is commonly measured in metres (m), and submultiples or multiples are used depending on the scale (e.g., mm, cm, km).
- SI Unit of Length: metre (m)
Common Instruments:
Ruler / Meter Rule
- Range: Up to 1 m
- Resolution: 1 mm (0.1 cm)
- Used for: Books, tables, notebooks, etc.
- Limitation: Parallax error if eye not aligned perpendicular to the scale
Vernier Calipers
- Range: Up to 15–20 cm
- Resolution: 0.1 mm (0.01 cm)
- Used for: Measuring internal/external diameters of cylinders, depth of holes
- Working: Uses main scale and vernier scale (the reading is the sum of both)
Micrometer Screw Gauge
- Range: Typically 0–25 mm
- Resolution: 0.01 mm
- Used for: Measuring thickness of wires, small rods, thin plates
- Working: Based on a calibrated screw mechanism; includes a thimble and spindle
Sources of Error and Accuracy Tips:
- Avoid parallax error by keeping the eye perpendicular to the scale.
- Use the most suitable instrument with the smallest least count.
- Repeat the measurement and take an average to reduce random errors.
- Ensure contact between object and measuring instrument is tight but not forced.
Example:
The main scale reading of a vernier caliper is \( 2.3\,\text{cm} \), and the 7th vernier mark coincides with the main scale. What is the total reading? (Each vernier division = 0.01 cm)
▶️ Answer/Explanation
Main scale reading = \( 2.3\,\text{cm} \)
Vernier scale reading = \( 7 \times 0.01 = 0.07\,\text{cm} \)
Total reading = \( 2.3 + 0.07 = 2.37\,\text{cm} \)
Final Answer: \( \boxed{2.37\,\text{cm}} \)
Example:
A micrometer screw gauge shows a main scale reading of \( 5.5\,\text{mm} \) and a thimble reading of 28 divisions. If the thimble scale has 50 divisions, what is the total measurement?
▶️ Answer/Explanation
Thimble reading = \( \dfrac{28}{100} = 0.28\,\text{mm} \)
Total reading = \( 5.5 + 0.28 = 5.78\,\text{mm} \)
Final Answer: \( \boxed{5.78\,\text{mm}} \)
Measuring Time
Time is a fundamental physical quantity representing the interval between two events. Accurate measurement of time is essential for studying motion, reaction time, oscillations, etc.
- SI Unit of Time: second (s)
Common Instruments:
Stopwatch
- Resolution: 0.01 s for digital; 0.1 s for analogue
- Used for: Sports, reaction timing, short experiments
- Limitations: Human reaction time (~0.2 s delay)
Electronic Timer / Data Logger
- High precision and automatic operation
- Used in: Free fall, speed, pendulum and acceleration experiments
- Advantage: Eliminates reaction time error
Pendulum Clock
- Based on periodic motion (simple harmonic motion)
- Period \( T = 2\pi \sqrt{\dfrac{L}{g}} \)
- Used in old clocks; mainly for demonstration today
Sources of Error and Accuracy Tips:
- Human reaction time affects starting/stopping manually operated timers.
- Repeat measurements and use average of multiple trials to improve reliability.
- Use electronic or sensor-based timing methods when high precision is needed.
- Ensure all devices are calibrated and zeroed before use.
Example:
A student starts a stopwatch manually when a ball is dropped and stops it when the ball hits the ground. The measured time is \( 0.45\,\text{s} \), but the actual free fall time is \( 0.41\,\text{s} \). What is the estimated reaction delay?
▶️ Answer/Explanation
Reaction delay = Measured time – Actual time
\( 0.45 – 0.41 = 0.04\,\text{s} \)
Final Answer: \( \boxed{0.04\,\text{s}} \)
Example:
A simple pendulum completes 20 oscillations in 34 seconds. What is the time period of one oscillation?
▶️ Answer/Explanation
Time period \( T = \dfrac{\text{Total time}}{\text{Number of oscillations}} \)
\( T = \dfrac{34}{20} = 1.7\,\text{s} \)
Final Answer: \( \boxed{1.7\,\text{s}} \)