Physics (0625) | Mass and weight

1.3 Mass and Weight: Unlocking the Difference

Welcome to one of the most frequently confused topics in Physics! Almost everyone uses the words 'mass' and 'weight' interchangeably in everyday conversation ("I weigh 70 kilograms"), but in science, they mean two completely different things.

Understanding this distinction is vital for IGCSE Physics. Don't worry if it seems tricky at first—we will break down these concepts with clear definitions and helpful examples.

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Section 1: Understanding Mass (The 'Stuff' of an Object)

What is Mass? (Core 1)

Mass is a fundamental property of matter. It is defined as a measure of the quantity of matter in an object, relative to an observer at rest. Think of mass as the amount of 'stuff' (protons, neutrons, electrons) an object contains.

The more mass an object has, the harder it is to accelerate it (to make it speed up or slow down). This resistance to change in motion is called inertia.

Key Characteristics of Mass

• Unit: The standard SI unit for mass is the kilogram (kg). Other common units include grams (g).
• Scalar Quantity: Mass only has magnitude (size); it does not have a direction. (Remember this from Section 1.1: Scalars have size only).
• Constancy: The mass of an object is constant, no matter where it is located in the Universe. Your mass is the same on Earth, on the Moon, or floating in deep space.

Measuring Mass (Core 4)

In the lab, we compare masses (or weights) using a balance, such as a beam balance or an electronic balance. Even though electronic balances give a reading based on the downward force (weight), they are calibrated to measure and display the mass (in kilograms).

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Section 2: Understanding Weight (The Force of Gravity)

What is Weight? (Core 2, Supplement 5)

Weight is not a measure of matter; it is a force. Specifically, weight is the gravitational force exerted by a massive body (like a planet) on an object that has mass.

Weight is simply the force pulling the object down towards the center of the planet.

Key Characteristics of Weight

• Unit: Since weight is a force, its standard SI unit is the Newton (N).
• Vector Quantity: Weight has both magnitude and direction. The direction is always vertically downwards, towards the center of the gravitational field.
• Variability: Weight changes depending on the strength of the gravitational field. An object weighs less on the Moon than on Earth because the Moon has a weaker gravitational field.

Analogy: Imagine a magnet (Earth's gravity) pulling on a piece of iron (your mass). The strength of the pull is your weight. If you move the iron to a weaker magnet (the Moon), the amount of iron hasn't changed (mass is constant), but the force pulling it has decreased (weight decreases).

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Section 3: Gravitational Field Strength (\(g\))

The link between mass (\(m\)) and weight (\(W\)) is the gravitational field strength (\(g\)).

Definition of Gravitational Field Strength (Core 3)

Gravitational field strength, \(g\), is defined as the gravitational force per unit mass acting on an object.

In other words, it tells you exactly how many Newtons of force (weight) are acting on every kilogram of mass.

The Key Equation (Core 3)

We can express the relationship between weight, mass, and gravitational field strength mathematically:

\[ W = m \times g \]

Where:

• \(W\) is the Weight (Force, measured in Newtons, N)
• \(m\) is the Mass (measured in kilograms, kg)
• \(g\) is the Gravitational Field Strength (measured in Newtons per kilogram, N/kg)

We can rearrange this definition to find \(g\):

\[ g = \frac{W}{m} \]

Value and Equivalence of \(g\) (Core 3, Core 8)

Near the surface of the Earth, the gravitational field strength, $g$, is approximately constant:

\[ g \approx 9.8 \text{ N/kg} \]

This value is extremely important because it is equivalent to the acceleration of free fall, which has the unit \(\text{m/s}^2\).

• $g$ as Field Strength: $9.8 \text{ N/kg}$ (This is the force applied to 1 kg of mass).
• $g$ as Acceleration: $9.8 \text{ m/s}^2$ (This is the acceleration experienced by an object falling freely).

They are numerically the same, which simplifies our force calculations greatly!

Example Calculation

Question: A student has a mass of 65 kg on Earth, where \(g = 9.8 \text{ N/kg}\). Calculate their weight.

Step 1: Identify known values.
Mass (\(m\)) = 65 kg
Gravitational field strength (\(g\)) = \(9.8 \text{ N/kg}\)

Step 2: Use the formula.
\(W = m \times g\)
\(W = 65 \text{ kg} \times 9.8 \text{ N/kg}\)
\(W = 637 \text{ N}\)

The student's weight is 637 Newtons.

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Section 4: Summary of Differences and Common Mistakes

Mass vs. Weight Comparison Table

Feature	Mass (m)	Weight (W)
Definition	Measure of the quantity of matter (stuff).	Force of gravity acting on a mass.
Unit	Kilogram (kg)	Newton (N)
Quantity Type	Scalar (magnitude only)	Vector (magnitude and direction)
Consistency	Constant everywhere in the Universe.	Changes depending on gravitational field strength ($g$).
Measured by	Balance (e.g., electronic or beam balance)	Force meter or spring balance

Understanding Change in Gravitational Field

Imagine the 65 kg student goes to the Moon, where the gravitational field strength is about \(g_{\text{Moon}} = 1.6 \text{ N/kg}\).

• Mass on Moon: \(m = 65 \text{ kg}\) (Mass is unchanged!)
• Weight on Moon: \(W = m \times g_{\text{Moon}} = 65 \text{ kg} \times 1.6 \text{ N/kg} = 104 \text{ N}\)

The student's weight has dropped from 637 N to 104 N, but the amount of matter making up the student (mass) is still 65 kg.

Memory Aid: If you want to lose weight, go to the Moon. If you want to lose mass, go on a diet!

Common Pitfall: Confusing Balances and Scales

Although we use a balance (which relies on gravity) to measure mass, if you were to use a spring scale (like a simple bathroom scale or a Newton meter), you are technically measuring weight. A spring scale measures how much the gravitational force stretches a spring. If you took that spring scale to the Moon, it would show a much smaller reading (if not recalibrated).

A balance measures mass. A force meter (spring scale) measures weight.