What is the primary difference between mass and weight in terms of their variability?

Mass is a constant property of an object that does not change with location. Weight is a variable property that changes depending on the local gravitational field strength ($g$).

How do the SI units for mass and weight differ?

Mass is measured in kilograms (kg), which is a base SI unit for quantity of matter. Weight is measured in Newtons (N), which is the SI unit for force, defined as $1 \text{ kg} \cdot \text{m/s}^2$.

Compare the mathematical types of mass and weight.

Mass is a scalar quantity, meaning it only has magnitude and no direction. Weight is a vector quantity because it is a force that always acts in a specific direction (downward toward the center of the gravitational source).

What is a common error when using the formula $W = mg$ with mass given in grams?

The most common error is failing to convert grams to kilograms. Since the standard unit for $g$ is N/kg, the mass must be in kg (divide grams by 1,000) to get the correct weight in Newtons.

Why is it incorrect to say an astronaut on the Moon has 'less mass' than on Earth?

Mass is the amount of matter in the astronaut's body, which does not change by moving to the Moon. The astronaut has less weight because the Moon's gravitational field is weaker, but their physical substance remains the same.

What mistake is made when a student uses a spring scale to measure mass in a different gravitational field?

A spring scale measures force (weight). If it is calibrated for Earth's gravity but used on the Moon, the reading will be incorrect for mass because the spring will stretch less due to the weaker gravitational pull.

Define Gravitational Field Strength ($g$).

Gravitational field strength is the amount of gravitational force exerted per unit mass at a specific point in space. On Earth, it is approximately $9.8 \text{ N/kg}$, meaning every kilogram of mass experiences $9.8$ Newtons of force.

What is the definition of a Newton (N) in terms of mass and acceleration?

One Newton is the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared ($1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2$).

What is a 'Beam Balance' used to measure, and why?

A beam balance is used to measure mass. It works by comparing an unknown mass against known masses; since gravity acts equally on both sides, the balance remains accurate even if the local gravity changes.

Why does weight change as you move further away from the center of the Earth?

Weight depends on the gravitational field strength ($g$), which weakens as the distance between the two masses increases. Therefore, as you move to higher altitudes, the value of $g$ decreases, resulting in a slightly lower weight.

Mass & Weight | Cambridge International Examinations AS-Level Physics

Revision Notes

AS-Level

Cambridge International Examinations

Physics

3. Dynamics

Mass & Weight

Summary

Mass and weight are fundamental physical quantities that describe the properties of matter and its interaction with gravity. While mass is an intrinsic, unchanging measure of the amount of matter in an object, weight is the extrinsic force exerted on that mass by a gravitational field, varying based on location and local gravitational strength.

1. Definition & Core Concepts

Mass: This is a measure of the quantity of matter contained within an object. It is an intrinsic property, meaning it does not change regardless of where the object is located in the universe.
Weight: This is the force of gravity acting upon an object's mass. Because it is a force, it is a vector quantity that always points toward the center of the body (like a planet) creating the gravitational field.
Units of Measurement: In the International System of Units (SI), mass is measured in kilograms (kg), while weight, being a force, is measured in Newtons (N).

Comparison of an object on Earth and the Moon showing that mass remains constant while the weight vector changes in magnitude.

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

The following table summarizes the critical differences between mass and weight that are essential for problem-solving:

Feature	Mass	Weight
Definition	Amount of matter in an object	Force of gravity on an object
SI Unit	Kilogram (kg)	Newton (N)
Quantity Type	Scalar (magnitude only)	Vector (magnitude and direction)
Location	Constant everywhere	Varies with gravity
Instrument	Beam balance	Spring balance / Force meter

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions

The 'Zero Gravity' Myth: Students often think an object in space has no mass because it is 'weightless.' In reality, the object still contains the same amount of matter and requires the same force to accelerate (inertia), even if the gravitational pull is negligible.
Colloquial Confusion: In everyday life, people use 'weight' to mean mass (e.g., 'I weigh 70 kg'). In physics, this is technically incorrect; you should say 'My mass is 70 kg' or 'I weigh 700 N.'
Directionality: Forgetting that weight is a vector. In free-body diagrams, weight must always be drawn as an arrow pointing vertically downward toward the center of the planet.