Learning Objectives
7 objectivesBy the end of this note, you should be able to:
- State that mass is a measure of the quantity of matter in an object at rest relative to the observer.
- State that weight is a gravitational force on an object that has mass.
- Define gravitational field strength as force per unit mass.
- Recall and use the equation g = W / m.
- Know that gravitational field strength equals the acceleration of free fall.
- Know that weights and masses may be compared using a balance.
- Describe, and use the concept of, weight as the effect of a gravitational field on a mass.
CORE VS EXTENDED GUIDE
- Core students study only the unlabelled sections.
- Extended students must study everything, including Extended Extended points.
- Extended = Core + Supplement.
Mass as a Measure of Quantity of Matter
Mass is a measure of the quantity of matter in an object at rest relative to the observer.
Mass is a fundamental property of an object. It does not change when the object moves to a different location, because the amount of matter inside the object stays the same. A 2 kg brick on Earth still has a mass of 2 kg on the Moon or in deep space, because no matter has been added or removed.
Mass is a scalar quantity, so it has magnitude only and no direction. The SI unit of mass is the kilogram (kg).
MisconceptionStudents sometimes say mass changes when you go to the Moon. Mass never changes with location — only weight changes, because gravitational field strength differs. Exam cue: If a question asks "what stays the same on the Moon?", the answer is mass.
Weight as a Gravitational Force
Weight is the gravitational force on an object that has mass.
Weight arises because a gravitational field pulls on the mass of an object. Unlike mass, weight depends on where the object is located, because different locations have different gravitational field strengths. An astronaut on the Moon weighs less than on Earth, because the Moon's gravitational field strength is smaller.
Weight is a vector quantity — it has both magnitude and direction. The direction of weight is always towards the centre of the massive body producing the gravitational field (e.g. towards the centre of the Earth). The SI unit of weight is the newton (N).
| Property | Mass | Weight |
|---|---|---|
| Definition | A measure of the quantity of matter in an object at rest relative to the observer | The gravitational force on an object that has mass |
| SI unit | kg | N |
| Scalar or vector | Scalar | Vector (directed towards centre of gravitational body) |
| Changes with location? | No — constant everywhere | Yes — depends on gravitational field strength |
Extended Weight is the effect of a gravitational field on a mass. Any object that has mass and sits within a gravitational field experiences a force — that force is its weight. The stronger the gravitational field, the greater the weight for the same mass.
This concept links weight directly to the field model: the field exists in the space around a massive body, and any mass placed in that field experiences a downward pull proportional to the field strength.
Exam TipAlways draw the weight arrow from the centre of the object, not from its base.
Gravitational Field Strength and g = W / m
Gravitational field strength is force per unit mass.
Gravitational field strength tells us how strong the gravitational pull is at a particular location. On the surface of the Earth, the gravitational field strength is approximately 9.8 N/kg (often rounded to 10 N/kg in calculations). This means every kilogram of mass experiences a gravitational force of about 9.8 N.
Gravitational field strength g is numerically equivalent to the acceleration of free fall. An object falling freely near the Earth's surface accelerates at approximately 9.8 m s⁻² — this is the same number as g expressed in N kg⁻¹. The two quantities share the same numerical value because the newton can be expressed as kg m s⁻², so N kg⁻¹ simplifies to m s⁻².
Reading the equation: In the formula below, the symbol g represents gravitational field strength, W represents weight (the gravitational force), and m represents mass. The equation states that gravitational field strength equals the weight of an object divided by its mass.
Key Equations
Gravitational field strength:
$$g=\frac{W}{m}$$
Variables:
- $g$ = gravitational field strength, in N kg⁻¹ (or equivalently, acceleration of free fall in m s⁻²)
- $W$ = weight, in N
- $m$ = mass, in kg
SI unit of calculated quantity: N kg⁻¹
Rearrangements:
Starting from $g=\frac{W}{m}$:
Multiply both sides by $m$:
$$W=m\times g$$
Divide both sides by $g$:
$$m=\frac{W}{g}$$
ProportionalityWeight is directly proportional to mass when gravitational field strength is constant. Doubling the mass doubles the weight. Weight is also directly proportional to gravitational field strength when mass is constant.
Worked Example
A rock has a mass of 1500 g. Calculate its weight on Earth where g = 9.8 N kg⁻¹.
Finding the weight
Equation used
$$W=m\times g$$
Given
$$m=1500\text{ g}$$
$$g=9.8{\text{ N kg}}^{-1}$$
Converting mass to SI units
$$m=\frac{1500}{1000}$$
$$m=1.5\text{ kg}$$
Substitution
$$W=1.5\times 9.8$$
$$W=14.7\text{ N}$$
Worked Example (Rearrangement)
An object weighs 45 N on a planet where g = 3.7 N kg⁻¹. Calculate the mass of the object.
Finding the mass
Equation used
$$g=\frac{W}{m}$$
Rearranging for m:
$$m=\frac{W}{g}$$
Given
$$W=45\text{ N}$$
$$g=3.7{\text{ N kg}}^{-1}$$
Substitution
$$m=\frac{45}{3.7}$$
$$m = 12.162\ldots \approx 12.2 \text{ kg (3 s.f.)}$$
Examiner InsightCIE papers frequently ask students to distinguish between the units N kg⁻¹ (gravitational field strength) and m s⁻² (acceleration of free fall) and to show they are equivalent. Remember: g = 9.8 N kg⁻¹ = 9.8 m s⁻². Exam cue: If the question says "free fall," use m s⁻²; if it says "field strength," use N kg⁻¹.
MisconceptionStudents often believe that heavier objects fall faster. In free fall (no air resistance), all objects accelerate at the same rate, g, regardless of mass. A feather and a hammer dropped in a vacuum hit the ground at the same time. Exam cue: "Acceleration of free fall is independent of mass" earns the mark.
Comparing Masses and Weights Using a Balance
Weights and masses may be compared using a balance.
A beam balance (also called a lever balance or top-pan balance) compares an unknown mass against known standard masses. When the beam is level, the downward gravitational force (weight) on each side is equal, which means the masses on each side are also equal — provided both sides are in the same gravitational field.
A key distinction exists between two types of instrument:
| Instrument | What it actually measures | Affected by changes in g? |
|---|---|---|
| Beam balance (two-pan) | Compares masses directly | No — both sides experience the same g, so the comparison remains valid |
| Spring balance (newton meter) | Measures weight (force) | Yes — reading changes if g changes |
A beam balance gives the same reading on the Moon as on Earth, because both pans experience the same reduced g. A spring balance reads a lower value on the Moon, because the weight of the object decreases while the spring's calibration does not adjust.
Exam TipLabel the pivot clearly and ensure the beam is shown horizontal when balanced.
QUICK RECAP
Key Points
- Mass is a measure of the quantity of matter in an object at rest.
- Mass is a scalar quantity measured in kg.
- Mass does not change with location.
- Weight is the gravitational force on an object that has mass.
- Weight is a vector quantity measured in N.
- Weight changes when gravitational field strength changes.
- Gravitational field strength g = force per unit mass (N kg⁻¹).
- g = W / m, rearranged: W = mg or m = W / g.
- g is numerically equal to the acceleration of free fall.
- On Earth, g ≈ 9.8 N kg⁻¹ (≈ 9.8 m s⁻²).
- Weight is directly proportional to mass (constant g).
- A beam balance compares masses; unaffected by changes in g.
- A spring balance measures weight; affected by changes in g.
- Extended Weight is the effect of a gravitational field on a mass.
CAN I…? PROGRESS CHECK
Self-Assessment
- State the definition of mass using CIE-approved phrasing?
- State the definition of weight using CIE-approved phrasing?
- Define gravitational field strength as force per unit mass?
- Use g = W / m and its rearrangements to solve problems?
- Explain why g in N kg⁻¹ equals the acceleration of free fall in m s⁻²?
- Distinguish between a beam balance and a spring balance?
- Convert grams to kilograms before substituting into equations?
- Extended Describe weight as the effect of a gravitational field on a mass?