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Jot down your answers and check them against the worked out answers at the end of the page

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2.2a What are mass and weight - how do you calculate weight?

This page will answer questions such as ... What is weight and how do we calculate it?  What is the difference between mass and weight?

Mass is the amount of matter in an object

That is all the atoms added together and is constant unless you change the object in someway to remove atoms or add atoms.

The standard unit of mass is the kilogram (kg), in chemistry or physics laboratory you often weigh things out as grams (1 g = 1 kg/1000). In chemistry calculations you tend to work in g, in physics calculations is often kg.

Mass is NOT the same as weight.

Mass is NOT a force, but the mass of an object is constant no matter where it is in the whole universe e.g.

you may be 40 kg here on Earth, in outer space, up in a satellite space station, on planet Mars or frozen on Pluto!

BUT your weight might be anything from 400 N on the Earth's surface, to zero in outer space - all will be explained!

 

One consequence of gravity is that you experience weight, which is always acts as a downward force due to a gravitational field effect and is always an attractive force.

Note :

Mass is a scalar measurement (just has size or magnitude).

Weight (or any force) is a vector measurement (it has both size and direction - always downwards for gravity).

You should appreciate immediately that your mass is constant at a given instance in time wherever you are in the universe, but the same cannot be said for weight.

 

So what is weight? Why can it vary for a given mass?

Quite simply, weight is the force of gravity acting on an object of given mass.

Weight is in effect the 'pulling' force an object experiences in a gravitational field e.g. you experience the Earth's gravitational field as your weight even if it says kg on your bathroom scales!

weight = a force in newtons

Weight varies with the mass of the object and the strength of the gravitational field at the point where the object is.

Weight is directly proportional to mass AND directly proportional to the gravitational field strength (gravitational acceleration) the object experiences too.

 

The formula to calculate this force, that is to calculate the weight of an object, is quite simple.

weight in newtons = mass of object in kilograms x gravitational field strength

W (N) = m (kg) x g (N/kg)

OR you may need to think in terms of:

force in newtons = mass of object in kilograms x gravitational acceleration

This expression is equivalent to F = ma, the equation of Newton's 2nd Law of Motion.

The general equation is easily rearranged:

W = m x g,    m = W ÷ g,    g = W ÷ m

(learn to rearrange, its better than using the triangle)

Note:

(i) There are three are variables, W, m and g.

(ii) Weight is proportional to mass for a give g.

(iii) The gravitational field strength constant (g) varies from planet to planet because the mass of the planets varies.

On a massive planet like Jupiter, the gravitational field strength is much greater than that on Earth.

On a smaller planet or our Moon, with far less mass, the gravitational field strength is much less.

Examples of surface gravitational field strength constants:

which can be units of weight in N/kg, but also units of acceleration in m/s²

Our Moon 1.62, planets: Mercury 3.70, Earth 9.81, Jupiter 24.79. To put these objects in perspective, an extremely dense neutron star may have a gravitational acceleration of 7 x 10¹² m/s² and its even greater for a black hole. kapow !!!!

(iv) g also varies with the distance you are from the centre of a large body like a planet e.g. it decreases the further up you are from the Earth's surface e.g. on the top of a mountain.

 

On the surface of planet Earth the force of gravity on objects is 9.8 N/kg (the Earth's 'g' value').

So a mass of 1 kilogram experiences an attractive force of about 10 newtons.

However, on the surface of the moon, the gravitational field force is only 1.6 N/kg (the moon's 'g' value'), so 1 kg on the moon only experiences a force of 1.6 N.

On the moon you would feel much lighter and could leap around with your Earth designed muscles to much greater heights - you may have seen how the astronauts on the moon had to be careful to not overdo things!

 

Although you would seem 'lighter' on the moon, your mass will be still the same!

Weighing machines like bathroom scales are calibrated to the strength of the Earth's gravitational field so the spring action scale can be read in kg.

Bathroom scales, or any other scales, would give a very false reading on the moon!

In travelling from the Earth to the Moon, you would seem to have lost a lot of weight!

Unless of course, you take Moon calibrated weighing scales!

You can measure weight using a calibrated spring balance, effectively a force meter or Newton meter.

Along side the spring is a scale calibrated in newtons, the unit of force.

You can use a balance that is calibrated in g/kg and multiply by 9.8 to get the weight of the object on the Earth's surface.

 

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2.2b Some simple example weight calculations

Note that it is better to be able to rearrange a formula than use a formula triangle

Q1 What is the weight of 70 kg adult on (a) the Earth, (b) the moon.

Using the gravitational field constants quoted above

On Earth the force of gravity on objects is 9.8 N/kg and  on the surface of the moon, the gravitational field force is only 1.6 N/kg

ANSWERS

 

Q2 An astronaut on Mars found an object of mass 5.50 kg gave a reading on an electronic balance meter of 20.41 N. Calculate the strength of gravity on the surface of Mars.

ANSWERS

 

 

Q3 The force of gravity on the dwarf (minor) planet Pluto is 0.710 N/kg.

What would be the mass of an object on Pluto that would experience a weight of 10.0 N?

ANSWERS

 

Q4 Imagine an astronaut in a space station experiencing 'weightlessness'.

Suppose the astronaut pushes against the wall with a force of 30 N and moves backwards with an acceleration of 0.40 m/s². What is the mass of the astronaut?

This is quite a trick problem to solve!

ANSWERS

 

INDEX physics notes FORCES section 2 on mass, weight and gravity

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Key points about mass, weight and gravity - all about mass, weight and gravity

Information sources for Doc Brown's key points: IGCSE-GCSE physics are based on textbooks & syllabus-specifications for students taking the UK AQA, Edexcel, OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE physics 9-1 level science examinations

Here's a comprehensive set of summary revision notes on mass and weight, tailored to the GCSE/IGCSE Physics specifications across major UK exam boards (AQA, Edexcel, OCR, WJEC, CCEA, CIE):

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Mass versus Weight: Core Concepts

Definitions of mass, weight and gravity

Concept	Description
Mass	The amount of matter in an object. A scalar quantity measured in kg
Weight	The force due to gravity acting on a mass. A vector quantity in N
g	Gravitational field strength (≈ 9.8 N/kg on Earth)

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Key Equation for mass, weight and gravity

Weight (W) = Mass (m) × Gravitational Field Strength (g)

W = m × g

• Mass stays constant regardless of location.
• Weight changes depending on the gravitational field strength.

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Gravitational Field Strength on Different Celestial Bodies

Location	g (N/kg)	Effect on Weight
Earth	9.8	Normal weight
Moon	1.6	Much lighter
Jupiter	24.8	Much heavier

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Required Practical for most boards

Finding the Centre of Mass of an Irregular Object:

1. Suspend the object from a point.
2. Hang a plumb line and draw a vertical line.
3. Repeat from another point.
4. The intersection = centre of mass.

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Student Tips for Exams about mass, weight and gravity

Conceptual Clarity

• Mass ≠ Weight: Mass is intrinsic; weight depends on gravity.
• Weight is a force: It has direction (towards the centre of the planet).
• Mass is scalar: It has magnitude only.

Calculation Practice

• Use W = m × g confidently.
• Be ready to rearrange the formula to find m or g.

Graph Skills

• Understand weight versus mass graphs:
  • Straight line through origin.
  • Shows direct proportionality.

Common Misconceptions about mass, weight and gravity

• Mass and weight are the same → They are fundamentally different.
• Weight is constant →  It varies with location, mass is constant.
• Weightlessness means no mass → Mass remains; only weight is zero.

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Keywords, phrases and learning objectives for forces

Know and be able to describe and explain the difference between mass and weight.

Know that mass is scalar quantity and weight is a vector quantity.

Know how to calculate weight and solve problems using the formula weight = mass x gravitational field constant g and use the correct units of newtons, kilograms and value of g

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INDEX physics notes FORCES section 2 on mass, weight and gravity