1. Overview
Mass and weight are two terms often used interchangeably in daily life, but they have distinct meanings in physics. Understanding the relationship between the amount of matter in an object and the gravitational force acting upon it is fundamental to studying how objects move and interact across the universe.
Key Definitions
- Mass: A measure of the quantity of matter in an object at rest relative to the observer.
- Weight: A gravitational force on an object that has mass.
- Gravitational Field Strength ($g$): The force per unit mass exerted by a gravitational field.
- Gravitational Field: A region in which a mass experiences a force due to gravitational attraction.
Core Content
Understanding Mass
- Mass is a property of the object itself.
- It does not change regardless of where the object is located (e.g., your mass is the same on Earth, on the Moon, or floating in deep space).
- Mass is measured in kilograms (kg).
Understanding Weight
- Weight is a force, not a mass.
- Because it is a force, it is measured in Newtons (N).
- Weight acts vertically downwards towards the center of the planet or moon.
- The weight of an object depends on the gravitational field strength of the location.
Comparing Mass and Weight
- Weights (and therefore masses) can be compared using a balance.
- A beam balance compares an unknown mass against a known mass. Since gravity acts on both sides equally, it works anywhere.
- An electronic balance or spring balance measures the downward force (weight) and is usually calibrated to display the mass in kg based on Earth's gravity.
Calculating Weight To find the weight of an object, we use the formula: $$Weight = mass \times gravitational \ field \ strength$$ $$W = m \times g$$
Worked Example (Core): An apple has a mass of 0.1 kg. If the gravitational field strength on Earth is 9.8 N/kg, calculate its weight.
- $W = m \times g$
- $W = 0.1 \times 9.8$
- $W = 0.98\text{ N}$
Extended Content (Extended Curriculum Only)
Weight as an Effect of a Gravitational Field Weight is not an intrinsic property of an object; it is an effect caused by the presence of a gravitational field. Without a gravitational field, a mass has no weight.
- A gravitational field surrounds any object with mass (like planets).
- When a second mass enters this field, the field exerts a force on it. This force is what we call weight.
- If the field strength ($g$) increases, the weight increases, even if the mass remains constant.
Worked Example (Extended): An astronaut has a mass of 70 kg. The gravitational field strength on Earth is 9.8 N/kg, and on the Moon, it is 1.6 N/kg. Calculate the astronaut's weight on both.
- On Earth: $W = 70 \times 9.8 = 686\text{ N}$
- On the Moon: $W = 70 \times 1.6 = 112\text{ N}$ Note: The mass remains 70 kg in both locations, but the weight changes because the field strength changes.
Key Equations
| Equation | Symbols | Units |
|---|---|---|
| $W = m \times g$ | $W$ = Weight | Newtons (N) |
| $m$ = Mass | Kilograms (kg) | |
| $g$ = Gravitational field strength | Newtons per kilogram (N/kg) |
Common Mistakes to Avoid
- ❌ Wrong: Assuming mass changes when you go to another planet.
- ✓ Right: Mass is constant; only weight changes depending on the gravity of the location.
- ❌ Wrong: Thinking that changing the shape or appearance of an object (like crushing a can) changes its mass.
- ✓ Right: Mass is the "quantity of matter"—changing the shape does not change the amount of atoms present.
- ❌ Wrong: Calculating weight by dividing mass by gravity ($W = m / g$).
- ✓ Right: Weight is the product of mass and gravity ($W = m \times g$). Always check that weight (in N) is a larger value than mass (in kg) when on Earth.
- ❌ Wrong: Giving weight in kg or mass in N.
- ✓ Right: Weight is a Force (Newtons); Mass is Matter (Kilograms).
Exam Tips
- Unit Conversion: Examiners often give mass in grams (g). You must convert this to kilograms (kg) before using the $W = mg$ formula (divide by 1000).
- Check the $g$ value: Look closely at the front of your exam paper or the specific question. Sometimes IGCSE uses $g = 10\text{ N/kg}$ for simplicity, and sometimes it uses $g = 9.8\text{ N/kg}$.
- The "Mass is Constant" Rule: If a multi-part question asks for the mass of an object on Earth and then its mass on the Moon, the answer is the same for both. Do not perform any calculations for mass when location changes!