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) 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)

Notes:

(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/s**^{2}

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 10^{12} m/s^{2}
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.

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/s^{2}. What is the mass of the astronaut?

This is quite a trick problem to solve!

ANSWERS