Weight and Gravitational Field Strength

Gravity is a non-contact force of attraction between any two objects that have mass. It is one of the four fundamental forces of nature.

Key facts about gravity:

• Every object with mass attracts every other object with mass
• The greater the mass of the objects, the greater the gravitational force
• The greater the distance between the objects, the weaker the gravitational force
• Gravity is always attractive — it only pulls, never pushes

On the surface of the Earth, gravity pulls all objects towards the centre of the Earth.

A gravitational field is the region around any object with mass where other objects experience a force due to gravity.

Gravitational field strength ($g$) tells us how strong the gravitational field is at a particular point. It is defined as:

$g = \frac{\text{force (weight)}}{\text{mass}}$

The units of $g$ are N/kg (newtons per kilogram).

Values of $g$ on Different Bodies

On Earth, we commonly use $g \approx 9.8$ N/kg (sometimes rounded to 10 N/kg in exam calculations).

Note: $g$ also represents the acceleration due to gravity, measured in m/s². Numerically, $g = 9.8$ N/kg = $9.8$ m/s².

This is one of the most important distinctions in GCSE Physics:

Everyday language trap: People often say "I weigh 70 kg" — but technically this is their mass. Their weight on Earth would be $70 \times 9.8 = 686$ N.

The relationship between weight, mass, and gravitational field strength is:

$\boxed{W = m \times g}$

Where:

• $W$ = weight (in newtons, N)
• $m$ = mass (in kilograms, kg)
• $g$ = gravitational field strength (in N/kg)

This equation can be rearranged:

$m = \frac{W}{g} \qquad g = \frac{W}{m}$

Using a Formula Triangle

Arrange W, m, and g in a triangle:

• W on top
• m and g on the bottom (multiplied)

Cover the quantity you want to find:

• Cover W → $m \times g$
• Cover m → $W \div g$
• Cover g → $W \div m$

The centre of mass (or centre of gravity) is the single point where the weight of an object appears to act.

• For a uniform, regular object (like a rectangle), the centre of mass is at the geometric centre
• For irregular objects, the centre of mass can be found experimentally by suspending the object from different points
• The centre of mass does not have to be inside the object (e.g., for a ring, it's at the centre of the hole)

Why does it matter? If the line of action of the weight (acting through the centre of mass) falls outside the base of an object, the object will topple over.

Since weight depends on gravitational field strength, your weight changes depending on where you are in the Solar System — but your mass stays the same.

Example: An astronaut has a mass of 80 kg.

The astronaut's mass is always 80 kg, but their weight varies enormously!

Weight is measured using a newtonmeter (also called a spring balance):

1. Attach the object to the hook at the bottom of the newtonmeter
2. The spring stretches due to the weight of the object
3. Read the scale — the weight is given directly in newtons

Calibrated on Earth: A newtonmeter calibrated on Earth would give incorrect readings on the Moon because $g$ is different.

Gravitational field lines show the direction of the gravitational force:

• Around the Earth, field lines point towards the centre (because gravity is attractive)
• The lines are closer together near the surface (stronger field) and further apart far from the surface (weaker field)
• At the Earth's surface, the field is approximately uniform — field lines are parallel and evenly spaced

Required Practical Method

1. Set up a newtonmeter vertically
2. Hang a 100 g (0.1 kg) mass from the newtonmeter
3. Record the weight shown on the newtonmeter
4. Repeat with 200 g, 300 g, 400 g, 500 g masses
5. Plot a graph of weight (y-axis) against mass (x-axis)

Expected Results

The graph should be a straight line through the origin, showing that weight is directly proportional to mass. The gradient of the line equals $g$ (approximately 9.8 N/kg or 10 N/kg).

• Gravity is a non-contact force that attracts objects with mass
• Gravitational field strength ($g$) is measured in N/kg
• On Earth, $g \approx 9.8$ N/kg
• Weight = mass × gravitational field strength: $W = mg$
• Mass (kg) stays constant; weight (N) depends on location
• Weight is a vector acting towards the centre of the planet
• Gravitational field lines point towards the centre of the massive body