A gravitational field is the region around any mass where another mass feels a pull. The strength of that field at a point tells you how much force acts on each kilogram placed there. On Earth's surface this is about 9.81 newtons per kilogram, usually written as g.
The same number appears as the free-fall acceleration, and that is not a coincidence: a force of g newtons on each kilogram produces an acceleration of g. This is why weight is mass times g, and why a 2 kg bag weighs about 20 N here.
Field strength is not the same everywhere. It is weaker on a mountain top and much weaker on the Moon, about one sixth of Earth's, which is why an astronaut can leap higher there.
In SPM you should treat g as both the field strength and the free-fall acceleration, and relate weight to mass through it.
Common misconceptions
- Gravitational field strength and mass are the same idea -> Field strength is force per kilogram; mass is the amount of matter, which does not change with location.
- The value of g is exactly 10 everywhere on Earth -> It is about 9.81 N/kg and varies slightly with location and altitude; 10 is a rounded value.
- There is no gravitational field on the Moon -> The Moon has its own field, about one sixth of Earth's, so objects still have weight there.
The physics behind it
Gravitational field strength, written g, is defined as the gravitational force acting on each kilogram of mass. As an equation it is g = W/m, where W is weight in newtons (N) and m is mass in kilograms (kg), so the unit of g is the newton per kilogram (N kg⁻¹).
Near the Earth's surface g is about 9.81 N kg⁻¹. To find the weight of a 50 kg student we rearrange to W = mg = 50 kg × 9.81 N kg⁻¹ = 490.5 N. Every kilogram of that student is pulled with 9.81 N, and those pulls simply add up.
The same number is also the free-fall acceleration, 9.81 m s⁻², because a force of g newtons on each kilogram produces an acceleration of g. The two units N kg⁻¹ and m s⁻² describe the same physical quantity.
Mass stays the same everywhere, but the field strength depends on where you are, so weight can change while mass does not.
A real Malaysian example
At a wet market a trader hangs a bag of fish on a spring balance (neraca spring). What the spring actually feels is the weight, the gravitational force pulling the bag down, and the scale is marked so that this force is shown as a mass in kilograms.
It works only because g at that place has a known, steady value of about 9.81 N kg⁻¹.
Suppose the fish weighs 29.4 N on the balance. The mass read off is m = W/g = 29.4 N ÷ 9.81 N kg⁻¹ = 3.0 kg.
If you carried the very same fish somewhere the field strength were weaker, the spring would stretch less and show a smaller reading, even though the amount of fish, its mass, has not changed at all.
This is why a spring balance measures force directly, and why the number of kilograms it displays is really a weight converted using g. The field strength quietly does the conversion every time something is weighed.
How this comes up in SPM
In Paper 2 this idea is examined with command words such as define, state, explain and relate. You may be asked to define gravitational field strength, to state its unit, or to relate weight, mass and g in a calculation.
Within the same Gravitation chapter it sits beside Newton's universal law of gravitation, where g = GM/r² shows that field strength falls off with distance from a planet's centre. It also connects to the motion of satellites and to Kepler's laws, since the same gravitational pull that gives you weight is what curves a satellite's path.
A common task is to explain why an object's mass is unchanged when it is moved to a place with different g, while its weight changes. Keep the two ideas separate: mass is the quantity of matter measured in kg, and field strength is force per kilogram measured in N kg⁻¹.
Show every unit in your working so the examiner can follow your reasoning.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)