Gravitational Field Strength & Weight

1. Definition

A. Gravitational field

A gravitational field is a region in which a mass experiences a force due to gravitational attraction.

B. Gravitational field strength, g

The gravitational field strength at a point is the gravitational force per unit mass at that point:

g = F/m

where F is the gravitational force on mass m.

C. Weight, W

Weight is the gravitational force acting on an object:

W = mg

Near Earth’s surface, g ≈ 9.8 N kg⁻¹ (often taken as 10 N kg⁻¹ in calculations).

2. Key Ideas

• Gravitational force is a non-contact force (see What Is A Force?).
• Mass m is measured in kg; weight W is measured in N.
• If g changes (different planet), mass stays the same but weight changes.
• Unit of g is N kg⁻¹ (equivalently m s⁻²).
• Weight acts towards the centre of the Earth (downwards).

3. Detailed Explanations

A. Why we use the idea of a “field”

With gravity, you do not need contact for a force to act. The Earth attracts nearby masses, so we say the space around the Earth is a gravitational field.

B. Using W = mg (exam workflow)

1. Convert mass to kg.
2. Use the value of g given in the question (or take g = 10 N kg⁻¹ if not stated).
3. Calculate weight using:
   • W = mg
4. State the unit N and (if needed) the direction: downwards.

Mini-check: if m = 2.0 kg and g = 10 N kg⁻¹, then W = 20 N.

Weight vs mass (near Earth)

A straight-line graph of weight against mass near Earth. The gradient is the gravitational field strength g.

Scroll across the graph to read all labels.

Open full-size graph

View figure data

Values for Weight vs mass (near Earth)

Mass (kg)	W = mg (g ≈ 10 N kg⁻¹)
0	0
1	10
2	20
3	30
4	40
5	50

Values for Weight vs mass (near Earth)

Mass (kg)	W = mg (g ≈ 10 N kg⁻¹)
0	0
1	10
2	20
3	30
4	40
5	50

C. Mass vs weight (common exam distinction)

D. Why g can be written as N kg⁻¹ or m s⁻²

From the definition of a newton:

1 N = 1 kg m s⁻²

So:

1 N kg⁻¹ = (1 kg m s⁻²)/(1 kg) = 1 m s⁻²

This is why the same symbol g is used for:

• gravitational field strength (N kg⁻¹)
• acceleration of free fall (m s⁻²) when air resistance is negligible

4. Common Mistakes

• Writing mass in newtons or weight in kilograms.
• Using g = 10 but forgetting the unit (N kg⁻¹ or m s⁻²).
• Using grams in calculations without converting to kg.
• Writing “weight = mass” (weight is a force; mass is not).

5. Exam Tips

• If asked to define g, say: “gravitational force per unit mass at that point”.
• If asked to find weight, use W = mg and give the unit N.
• If asked to find mass, rearrange: m = W/g.
• If asked to find g, rearrange: g = W/m.
• If direction matters, state: “weight acts downwards”.

6. Worked Examples

7. Mind Stretchers