Mass, Weight & Density
Understanding the difference between mass and weight, and how density determines floating
🎯 The Hook: Why Does Weight Change in Space?
Imagine you're standing on Earth. You step on a scale: 60 kg. Now you travel to the Moon and step on the same scale. Suddenly, you feel much lighter! But did your body actually lose matter? No. Your mass stayed the same, but your weight changed. This is because weight depends on gravity.
📚 The Deep Theory
CORE: Mass vs Weight
- Mass (m): A measure of the quantity of matter in an object at rest. Unit: kilogram (kg). Mass is constant everywhere.
- Weight (W): The gravitational force on an object that has mass. Unit: newton (N). Weight changes with location.
- Gravitational Field Strength (g): Force per unit mass. On Earth, g ≈ 10 N/kg. This is equivalent to the acceleration of free fall.
Formula Triangle:
W = m × g
Therefore: g = W/m or m = W/g
SUPPLEMENT: Weight as Gravitational Field Effect
Weight is the effect of a gravitational field on a mass. Different planets have different gravitational field strengths, which is why your weight changes but your mass doesn't.
CORE: Density
- Density (ρ): Mass per unit volume. Unit: kg/m³ or g/cm³
- Formula: ρ = m/V where m = mass (kg), V = volume (m³)
- Floating Rule: An object floats if its density is less than the density of the fluid (water = 1.0 g/cm³ or 1000 kg/m³)
🌍 Interactive: The Moon Jump Simulator
Change the location to see how weight changes while mass stays constant!
Location: 🌍 Earth
g = 10 N/kg
Mass (Constant)
60 kg
Same everywhere! ✓
Weight (Variable)
600 N
Changes with g!
W = m × g = 60 × 10 = 600 N
🔢 Interactive: Density Triangle Calculator
Choose what to calculate, input two values, and the third is calculated automatically!
Density (ρ)
5.00 kg/m³
ρ = m/V = 50/10
🌊 Interactive: Sink or Float Tank
Drag blocks into the water tank to see if they sink or float! Water density = 1.0 g/cm³
Wood
ρ = 0.6 g/cm³
Plastic
ρ = 0.9 g/cm³
Metal
ρ = 7 g/cm³
Results:
- 🟤 Wood (0.6): Floats high (60% submerged)
- 🔵 Plastic (0.9): Floats low (90% submerged)
- ⚫ Metal (7.0): Sinks completely
⚠️ Examiner's Traps
TRAP 1: Confusing Mass and Weight
Students often say "I weigh 60 kg." This is WRONG! Mass is measured in kg, weight in N. Correct: "My mass is 60 kg" or "My weight is 600 N."
TRAP 2: Forgetting g = 10 N/kg
In IGCSE, always use g = 10 N/kg unless told otherwise. Don't use 9.8 or 9.81!
TRAP 3: Density Units
Watch out! Density can be in kg/m³ OR g/cm³. Remember: 1 g/cm³ = 1000 kg/m³. Water is 1.0 g/cm³ = 1000 kg/m³.
TRAP 4: Floating Condition
Object floats when ρobject < ρfluid. Students mix up the inequality direction!
🔬 Paper 6: Lab Skills
Core Practical: Measuring Density
You must know how to determine density experimentally!
Regular Solid (e.g., cube):
- Measure dimensions with ruler (l, w, h)
- Calculate V = l × w × h
- Measure mass with balance (m)
- Calculate ρ = m/V
Irregular Solid (e.g., stone):
- Measure mass with balance (m)
- Fill measuring cylinder with water (V₁)
- Submerge object, read new level (V₂)
- Volume = V₂ - V₁ (displacement)
- Calculate ρ = m/V
✅ Mark Scheme Keywords
For full marks, use these EXACT phrases:
- ✓ "Mass is the quantity of matter"
- ✓ "Weight is a gravitational force"
- ✓ "g is force per unit mass"
- ✓ "Density is mass per unit volume"
- ✓ "Mass is constant everywhere"
- ✓ "Weight depends on location"
📋 Syllabus Checklist
CORE Coverage:
- ✓ 1.3.1 - Mass as quantity of matter
- ✓ 1.3.2 - Weight as gravitational force
- ✓ 1.3.3 - g = W/m equation
- ✓ 1.3.4 - Using a balance
- ✓ 1.4.1 - ρ = m/V equation
- ✓ 1.4.2 - Density experiments
- ✓ 1.4.3 - Floating prediction
SUPPLEMENT Coverage:
- ✓ 1.3.5 - Weight as effect of field
- ✓ 1.4.4 - Liquid on liquid floating
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