Lesson Notes By Weeks and Term v3 - Senior Secondary 1
Units of Measurement
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Units of Measurement
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Subject: Physics
Class: Senior Secondary 1
Term: 3rd Term
Week: 3
Theme: Physics In Technology
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This topic, "Units of Measurement," is foundational in Physics, providing students with the essential skill of quantifying physical quantities accurately and consistently. While the SI (Système International d'Unités) system is the globally accepted standard, various industries, both locally and internationally, still extensively use other systems of units, often referred to as industrial units or customary units. Understanding these units is crucial for Nigerian learners as they will encounter them in various professional fields such as engineering, construction, oil and gas, manufacturing, and agriculture, which are vital sectors of the Nigerian economy.
Calculation: Pressure in Pa = 32 psi × (6894.76 Pa / 1 psi) Pressure in Pa = 32 × 6894.76 Pa Pressure in Pa = 220632.32 Pa Pressure in Pa = 2.21 × 105 Pa (to 3 significant figures)
Explanation: The "psi" unit cancels, leaving Pascals.
Example 5: Temperature Conversion (Refrigeration) An old imported freezer specifies an operating temperature of 0°
F. Convert this to Celsius (°C) and then to Kelvin (K).
Given: 0°F Target: °C and K Conversion Formula (°F to °C): °C = (°F - 32) × 5/9 Conversion Formula (°C to K): K = °C + 273.15 Calculation (°F to °C): °C = (0 - 32) × 5/9 °C = -32 × 5/9 °C = -160 / 9 °C ≈ -17.78 °C Calculation (°C to K): K = -17.78 + 273.15 K = 255.37 K * Explanation: First, apply the Fahrenheit to Celsius formula. Then, add 273.15 to the Celsius value to get Kelvin. | | (Short) Ton (US) | ton (US) | 907.185 kg (approx. 0.907 metric ton)| 1 US ton = 2000 lb = 907.185 kg | | | (Long) Ton (UK) | ton (UK) | 1016.05 kg (approx. 1.016 metric ton)| 1 UK ton = 2240 lb = 1016.05 kg | | | Metric Tonne | t | 1000 kg (This is an SI-accepted non-SI unit)| 1 t = 1000 kg | | Volume | Fluid Ounce (US) | fl oz (US) | 0.02957 L | 1 fl oz (US) = 29.5735 mL | | | Pint (US) | pt (US) | 0.473 L | 1 pt (US) = 16 fl oz (US) = 0.473176 L | | | Gallon (US) | gal (US) | 3.785 L (0.003785 m3) | 1 gal (US) = 4 quarts = 8 pints = 3.78541 L | | | Gallon (Imperial/UK)| gal (Imp) | 4.546 L (0.004546 m3) | 1 gal (Imp) = 4 quarts (Imp) = 4.54609 L | | | Barrel (Oil) | bbl | 158.987 L (0.158987 m3) | 1 bbl = 42 gal (US) = 158.987 L | | Pressure | Pounds per sq inch | psi | 6894.76 Pa | 1 psi = 6894.757 Pa (approx 6.89 kPa) | | | Bar | bar | 100,000 Pa (100 kPa) | 1 bar = 100,000 Pa = 100 kPa (This is an SI-accepted non-SI unit)| | Temp. | Fahrenheit | °F | °C / K | To convert °F to °C: °C = (°F - 32) × 5/
9. To convert °C to K: K = °C + 273.15 | | Power | Horsepower (mech) | hp | 745.7 W | 1 hp = 745.69987 W | | Energy | British Thermal Unit| BTU | 1055.06 J | 1 BTU = 1055.05585 J | Worked Examples (for teacher demonstration): Example 1: Length Conversion (Construction) A Nigerian civil engineer specifies a building's height as 45 feet. Convert this height to metres (m).
Given: 45 ft Target: metres (m)
Conversion Factor: 1 ft = 0.3048 m Calculation: Height in metres = 45 ft × (0.3048 m / 1 ft) Height in metres = 45 × 0.3048 m Height in metres = 13.716 m Explanation: The "ft" unit in the numerator and denominator cancels out, leaving only "m".
Example 2: Volume Conversion (Oil Industry) Nigeria exports 1.8 million barrels of crude oil per day. Convert this volume to litres.
Given: 1.8 × 106 bbl Target: Litres (L)
Conversion Factor: 1 bbl = 158.987 L Calculation: Volume in litres = (1.8 × 106 bbl) × (158.987 L / 1 bbl) Volume in litres = 1.8 × 106 × 158.987 L Volume in litres = 286,176,600 L Volume in litres = 2.86 × 108 L (approximately)
Explanation: The "bbl" unit cancels, resulting in litres.
Example 3: Mass Conversion (Agriculture) A farmer harvests 5.5 US tons of maize. Convert this mass to kilograms (kg).
Given: 5.5 US tons Target: Kilograms (kg)
Conversion Factor: 1 US ton = 907.185 kg Calculation: Mass in kg = 5.5 US tons × (907.185 kg / 1 US ton) Mass in kg = 5.5 × 907.185 kg Mass in kg = 4989.5175 kg Mass in kg = 4990 kg (to 3 significant figures)
Explanation: The "US tons" unit cancels, leaving kilograms.
Example 4: Pressure Conversion (Automotive/Industrial) The recommended tire pressure for a car is 32 psi. Convert this pressure to Pascals (Pa).
Given: 32 psi Target: Pascals (Pa)
Conversion Factor: 1 psi = 6894.76 Pa Calculation: Pressure in Pa = 32 psi × (6894.76 Pa / 1 psi) Pressure in Pa = 32 × 6894.76 Pa Pressure in Pa = 220632.32 Pa Pressure in Pa = 2.21 × 105 Pa (to 3 significant figures)
Explanation: The "psi" unit cancels, leaving Pascals.
Example 5: Temperature Conversion (Refrigeration) An old imported freezer specifies an operating temperature of 0°
F. Convert this to Celsius (°C) and then to Kelvin (K).
Given: 0°F Target: °C and K * Conversion Formula (°F to °C): °C = (°F - 32) This section provides the essential knowledge base for the teacher to deliver the lesson comprehensively. 2.
1. Recap: The International System of Units (SI) The SI system is the modern form of the metric system and is the most widely used system of measurement. It comprises seven base units from which all other derived units are formed.
Length: Metre (m)
Mass: Kilogram (kg)
Time: Second (s)
Electric Current: Ampere (A)
Temperature: Kelvin (K)
Amount of Substance: Mole (mol)
Luminous Intensity: Candela (cd) 2.
2. What are Industrial Units of Measurement? Industrial units, also known as customary units or imperial units (especially for those derived from the British Imperial System), are non-SI units commonly used in specific industries or countries due to historical reasons, established practices, or convenience in certain applications. While the world largely operates on the SI system, many industries, particularly those with long histories or strong ties to countries like the United States (which primarily uses US customary units), still use these units. This often leads to a need for conversion to SI units for international consistency, scientific accuracy, or modern engineering practices. 2.
3. Why are Industrial Units Still Used in Industry (Nigerian Context)?
Legacy Equipment and Infrastructure: Many older machines, tools, and infrastructure (e.g., pipelines, construction designs) were manufactured or designed using imperial units. Replacing or redesigning everything to SI units can be prohibitively expensive and complex.
International Trade and Specifications: Nigeria's trade partners and suppliers, particularly from countries like the USA, may provide goods, machinery, or specifications in non-SI units.
Sector-Specific Conventions: Certain industries have long-established conventions. For example, crude oil is universally traded in "barrels," and shipping often measures capacity in "tons." * Familiarity and Practicality: For some practitioners, older units might feel more intuitive or practical in specific, routine tasks (e.g., using feet and inches in carpentry). 2.
4. Common Industrial Units and Their Conversion to SI Units The ability to convert between industrial units and SI units is critical. The general principle for conversion involves using conversion factors. A conversion factor is a ratio that relates two different units of measurement, and its value is always equal to
1. General Conversion Method: To convert a quantity from one unit to another:
1. Identify the given quantity and its unit.
2. Identify the target unit.
3. Find the appropriate conversion factor(s) that link the given unit to the target unit. The conversion factor should be written as a fraction, with the unit to be cancelled in the denominator and the desired unit in the numerator.
4. Multiply the given quantity by the conversion factor(s). Ensure units cancel out correctly to leave the desired unit. Examples of Common Industrial Units and Conversion Factors: | Quantity | Industrial Unit | Abbreviation | SI Equivalent (Approximate) | Conversion Factor (Exact/Commonly Used) | | :------------ | :------------------ | :----------- | :---------------------------------- | :----------------------------------------------------------- | | Length | Inch | in | 0.0254 m | 1 in = 0.0254 m (exact) | | | Foot | ft | 0.3048 m | 1 ft = 12 in = 0.3048 m (exact) | | | Yard | yd | 0.9144 m | 1 yd = 3 ft = 0.9144 m (exact) | | | Mile | mi | 1609.34 m (1.609 km) | 1 mi = 1760 yd = 5280 ft = 1609.344 m | | Mass | Pound | lb | 0.4536 kg | 1 lb = 0.453592 kg | | | Ounce | oz | 0.02835 kg | 1 lb = 16 oz; 1 oz = 28.3495 g = 0.02835 kg | | | (Short) Ton (US) | ton (US) | 907.185 kg (approx. 0.907 metric ton)| 1 US ton = 2000 lb = 907.185 kg | | | (Long) Ton (UK) | ton (UK) | 1016.05 kg (approx. 1.016 metric ton)| 1 UK ton = 2240 lb = 1016.05 kg | | | Metric Tonne | t | 1000 kg (This is an SI-accepted non-SI unit)| 1 t = 1000 kg | | Volume | Fluid Ounce (US) | fl oz (US) | 0.02957 L | 1 fl oz (US) = 29.5735 mL 3.
1. Teacher Activities Introduction (10 minutes): Initiate a brief discussion by asking students to name common quantities they measure (length, mass, time, temperature). Ask them to state the units they use for these measurements. Introduce the concept of different unit systems, specifically highlighting SI units and mentioning that other units exist in various industries. Display pictures or examples of items from various Nigerian industries (e.g., crude oil barrel, bag of cement, car tire, building plan) and ask students to identify units that might be associated with them. Explanation of Industrial Units and Their Context (15 minutes): Explain clearly why industries use non-SI units (historical reasons, international trade, legacy equipment). Present the table of common industrial units for length, mass, volume, pressure, temperature, power, and energy, explicitly stating their abbreviations and typical SI equivalents. Discuss the specific industries in Nigeria where each unit is commonly encountered, using the examples outlined in Section
1. Demonstration of Conversion Methodology (15 minutes): Introduce the concept of conversion factors as ratios equal to
1. Work through 2-3 detailed examples from Section 2.4 on the board, demonstrating step-by-step how to convert industrial units to SI units. Emphasize the cancellation of units to ensure the final answer is in the desired unit. Encourage students to ask questions during the demonstration.
Guided Practice (10 minutes): Present 1-2 additional conversion problems for students to solve in pairs or small groups while the teacher circulates to provide support and clarification. Select questions that allow students to practice different types of conversions (e.g., volume, mass).
Review and Summarization (5 minutes): Recap the key industrial units discussed and the importance of converting them to SI units. Address any lingering questions or misconceptions. 3.
2. Student Activities Introductory Brainstorm: Students identify measurements and units in daily life and industrial contexts based on teacher prompts and displayed images.
Note Taking: Students take detailed notes on the definitions, examples of industrial units, their contexts, and the conversion factors provided by the teacher. Group Discussion/Research (Optional, if time permits): In small groups, students discuss specific Nigerian industries (e.g., oil, agriculture, construction) and identify other non-SI units they might encounter, and research their SI equivalents.
Problem Solving: Students actively participate in guided practice by attempting conversion problems individually or in pairs.
Questioning: Students ask clarifying questions during explanations and demonstrations.
Oil and Gas Production and Export: Nigeria is a major oil producer. Oil quantities are almost always discussed globally in "barrels." Converting barrels to litres or cubic metres is vital for understanding national production figures, revenue calculations, and comparing with global standards. For instance, knowing how many litres are in a barrel allows citizens to contextualize oil prices and production outputs. Construction and Infrastructure Development: In Nigeria, many construction projects still reference dimensions in feet and inches, particularly older blueprints or imported equipment specifications.
However, modern engineering standards and material procurement are often in metres and kilograms. Civil engineers, architects, and artisans must accurately convert between these units to avoid costly errors, ensure structural integrity, and procure correct quantities of materials (e.g., concrete volume, steel length).
Agriculture and Commodity Trading: The measurement of agricultural produce, especially in large quantities for export or industrial processing (e.g., maize, rice, palm oil), often uses "tons" (short or long). Converting these to metric tonnes or kilograms is critical for international trade, accurate inventory management, and calculating yields for national food security assessments. Farmers need to understand these conversions to relate their harvest to market prices.