Making measurements
History:
🔹 Ancient Measurements
•People once used body parts (like the forearm) for measuring.
•Ancient Egyptians created the royal cubit to standardize measurement.
🔹 Engineering Skills
•Egyptians used simple tools like cubit rods.
•Achieved high precision in building pyramids.
🔹 Eratosthenes' Discovery
•Lived around 300 BCE.
•Calculated Earth's circumference (~40,000 km) using shadows and geometry.
Modern Mistakes
•Example: Hubble Telescope had blurry images due to tiny measurement errors.
•Shows that even advanced tools can fail without precision.
🔹 Trusting Our Senses
•Eyes can be deceiving (e.g., optical illusions).
•Importance of using tools like rulers for accuracy.
🔹 Stride-Length Problem
•Eratosthenes may have used a person to pace distances.
•Solutions:
Calibrate stride first.
Use averages from multiple people.
Use wheels or mechanical counters.
🔹 Conclusion
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Our ancestors were very clever with limited tools.
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Intelligence is problem-solving, not just having
modern technology.
1. Measuring Length
Used to measure wires, heights, distances, or
diameters.
Common tool: Ruler or meter scale.
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✅ Correct Technique:
Wire must be straight and aligned with the ruler.
Start from the zero mark, not the ruler’s edge.
Watch out for ragged ends(uneven) or thick markings.
Ensure the ruler is properly calibrated means that the ruler
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must be accurate—its markings (like centimeters and millimeters) must be at the
correct distance apart as per standard measurement.
📌 Tip for Small Lengths:
Measure the total thickness of many
items (like 500 sheets).
Then divide to get the thickness of
one.
Measuring Curved Lengths:
Use a thread to follow the curve.
Then place the thread on a ruler.
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2. Measuring Volume
📏 For Regular Shapes:
•Cube/Cuboid: Use formula
Volume = length × width × height
•Cylinder or Sphere:
For Liquids:
•Use a measuring cylinder.
•Read the bottom of the meniscus at eye level.
•Choose the right size cylinder for better accuracy
•(e.g., 10 cm³ for small amounts).
Two types of meniscus:
1.Concave meniscus (curves downward):
1.Common with water and most liquids.
2.The liquid sticks to the container walls.
3.Read the bottom of the curve at eye level.
2. Convex meniscus (curves upward):
•Seen with mercury.
•The liquid does not stick to the container.
•Read the top of the curve.
. Measuring Volume by Displacement
Use for irregular objects.
Fill a cylinder with water.
Drop the object in and note the increase in
water level.
The rise = object’s volume.
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4. SI Units (International System)
📏 Length Units:
1 m = 100 cm = 1000 mm
1 km = 1000 m
1 µm = 0.000001 m
Volume Units:
1 m³ = 1000 dm³ = 1,000,000 cm³
1 dm³ = 1000 cm³
Note:
1 dm³ = 1 litre
1 cm³ = 1 millilitre (not SI units, but commonly used)
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Worksheet on SI unit conversions
🔹 Understanding Density
•Density is the mass per unit volume of a substance.
•Formula:
•SI unit of density: kg/m³
•Other commonly used units:
•g/cm³
•kg/dm³
Mass vs Density
•Mass is the quantity of matter in an object (measured in kilograms).
•Density tells how concentrated the mass is within a certain volume.
•You can estimate an object’s volume by looking, but mass must be
measured using a balance.
Density Examples
•Lead is denser than wood (same volume → more mass).
•Gold is denser than silver.
•Ice floats in water because it is less dense than water.
•Materials can float or sink based on whether their
Key Density Values
•Density of water:
•1000 kg/m³
•1.0 kg/dm³
•1.0 g/cm³
Measuring Density
•For solids with regular shape:
• Measure volume (e.g., using length × width × height).
• Measure mass (e.g., with a balance).
• Use the formula to find density.
•For liquids:
• Use a measuring cylinder on a balance.
• Tare (zero) the balance.
• Measure volume and mass → calculate density.
Density and Floating
•Objects float if they are less dense than water.
•Immiscible liquids form layers based on density (e.g.,
oil floats on water).
•Denser liquids settle at the bottom, lighter ones rise
to the top.
•Liquids like squash and water mix (miscible) because
one dissolves in the other.
Applications
•Used in material identification (e.g., checking gold
purity).
•Helps explain natural phenomena like convection
currents in oceans and atmosphere:
• Colder and saltier water sinks, causing circulation
currents.
• This process plays a role in global climate systems.
Match the terms with their correct definitions:
Term
Definition
a) Mass
i) The amount of space an
object takes up
b) Volume
ii) The quantity of matter
in an object
c) Density
iii) The mass per unit
volume of a substance
What happens when two immiscible liquids with
different densities are poured into a container? Give an
example.
When two immiscible liquids with different densities are poured
into the same container, they do not mix. Instead, they form
separate layers. The denser liquid settles at the bottom, and the
less dense liquid stays on top.
Example:
When oil and water are poured into a container, oil floats on top
of water because oil is less dense and the two liquids are
immiscible.
Thermohaline circulation refers to the movement of ocean
water caused by differences in temperature (thermo-) and
salinity (haline).
•Colder and saltier water is denser and sinks to the bottom.
•Warmer or less salty water is less dense and rises.
•This creates global ocean currents that help regulate Earth's
climate.
Salinity means the amount of salt dissolved in water,
usually measured in grams of salt per kilogram of water
(g/kg) or parts per thousand (ppt).
•Higher salinity → more salt → denser water
•Lower salinity → less salt → less dense water
Include a data table (fill in):
Object
Length (cm)
Width (cm)
Height (cm)
Volume (cm³)
Mass (g)
Density
(g/cm³)
C. Irregular Solid
•Equipment: Thread, measuring cylinder, eureka can.
•Steps:
• Measure mass with balance.
• Fill eureka can with water until it overflows.
• Tie object with thread and submerge fully.
• Collect and measure displaced water = volume.
• Calculate density.
•Extension: Discuss how to measure volume if the object
floats:
• Push it down with a sinker (known volume).
• Subtract the sinker's volume.
Flowchart Logic
Start
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|__ Is the object a liquid?
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|__ YES --> Measure mass and volume directly using
measuring cylinder and balance
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|__ NO --> Is it a regular solid?
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|__ YES --> Use ruler to measure dimensions -->
Calculate volume
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|__ NO --> Use displacement method (Eureka can or
measuring cylinder)
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|__ Does it float?
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|__ YES --> Use sinker method to find
volume
|
|__ NO --> Submerge and measure
displaced water
|
--> Use Density Formula: Density = Mass / Volume
Quick Quiz: Match Object and Likely Density
Object
Likely Density (g/cm³)
Explanation
Wood
~0.6–0.9
Less dense than water → floats
Iron
~7.8
Very dense → sinks in water
Oil
~0.9
Less dense than water → floats
Water
1.0
Reference value
Explain Why Icebergs Float
Answer:
Ice is less dense than water. Its molecules are
more spread out in solid form, so it displaces a
volume of water greater than its own mass.
That’s why about one-tenth of an iceberg stays
above the surface, and the rest floats below.