Video Transcript
In this video, we will be looking
at the subtle difference between mass and weight. In everyday language, we often use
them interchangeably. They are certainly very closely
linked, but they are not the same thing. So let’s take a look at the
definitions of mass and weight and understand the difference between them.
Firstly, mass is a measure of the
amount of matter or stuff that makes up an object. Now we can see that matter is a
technical term and it refers to stuff in the universe, stuff such as atoms or
protons and neutrons and electrons which happen to be the building blocks of things
with mass. So mass is a measure of the amount
of stuff that makes up an object. As well as this, the mass of an
object is also a measure of the object’s resistance to acceleration when a certain
net force is applied to it.
In other words, let’s think about a
block that we have. Let’s say it’s a wooden block with
a mass 𝑚. And on this wooden block, we exert
a net force of magnitude 𝐹 onto it. Well, in that situation, the block
is going to accelerate in the direction of the net force. So we’ll say it has an acceleration
𝑎.
And the relationship between the
net force 𝐹, the mass of the block 𝑚, and the acceleration 𝑎 is given by Newton’s
second law of motion, which tells us that the net force is equal to the mass of the
object multiplied by the acceleration it experiences.
So if we rearrange this equation,
we can see that for any particular net force exerted on an object, the acceleration
that the object experiences is inversely proportional to the mass. In other words, if the same forces
exerted on two different objects with two different masses, the object with larger
mass is going to result in a smaller acceleration. And hence, we can think of the
object’s mass as its resistance to acceleration when a particular net force is
exerted on it. As well as this, mass is measured
in kilograms. This is its base unit. So this is what we mean when we
talk about mass.
Let’s now take a look at
weight. Now weight on the other hand is the
force experienced by an object when it’s placed in a gravitational field. In other words, we can think of
weight as the gravitational force experienced by an object.
So if we come back to our wooden
block with mass 𝑚 and now also consider the fact that it’s in Earth’s gravitational
field, so let’s say here is the surface of the Earth, well in that situation the
Earth’s gravitational field is going to exert a gravitational force onto the block
with mass 𝑚. And this force is going to be an
attractive force and it’s going to be acting towards the centre of the Earth. We can label this force as 𝑊
because it’s the weight of the wooden block.
It’s important to realize by the
way that if we had considered the Earth in the first situation, then we would also
have to consider the weight of the block. But we didn’t think about the block
being in a gravitational field. So we could have basically just
assumed that in the first case it was floating around in outer space or something
like that. However, when an object is placed
in a gravitational field, it experiences a gravitational force and that force is the
weight of the object.
Now this gravitational force can be
calculated by multiplying the mass of the object — in this case our wooden block —
by what’s known as the gravitational field strength at the position of the wooden
block in this case. Now because we’re considering the
wooden block being placed in the gravitational field of the Earth, then in this
particular situation 𝑔 is referring to the gravitational field strength of the
Earth. It doesn’t necessarily have to be
the gravitational field strength of the Earth though. It’s just a gravitational field
strength of whatever gravitational field the object is in at that point in time.
And by the way, it’s worth noting
that an object doesn’t necessarily only have weight when it’s touching the surface
of the Earth for example. It will still experiencing a
gravitational force even if it is slightly raised above the surface. And it’s at this point that we can
realize that because weight is a gravitational force, it is measured in newtons. In other words, newtons is the base
unit of weight.
Now, we’ve seen what happens when
there is a net force acting on an object. The object accelerates in the
direction of the force. So we can say that if we had this
wooden block and the only force acting on it was the weight of the block, then it
would accelerate downwards towards the surface of the Earth with an acceleration 𝑎
that we could find by using this equation here, Newton’s second law of motion.
We could say that the net force on
the block which in this case was equal to the weight of the block was equal to the
mass of the block multiplied by the acceleration experienced 𝑎. But hang on a minute! Haven’t we just said that the
weight of the object is equal to the mass multiplied by the gravitational field
strength? So this is where we can spot
something really interesting: the gravitational field strength of the gravitational
field that the object is in is the same thing as the acceleration experienced by the
object if the only force acting on the object was the weight of the object.
In other words, gravitational field
strength is equivalent to an acceleration. And this is why the quantity 𝑔 is
also often known as the acceleration due to gravity. And so, an important thing to
realize is that this equation 𝑊 is equal to 𝑚𝑔 is just a special case of 𝐹 is
equal to 𝑚𝑎. This is because Newton’s second law
of motion refers to any net force acting on an object. And it shows the relationship
between the mass of that object and the acceleration experienced by the object. So if we say that the net force on
the object is just 𝐹, then it would accelerate with 𝑎 in the same direction as the
net force. And this is the relationship that
we need to use.
However, this equation 𝑊 is equal
to 𝑚𝑔 specifically refers to how the gravitational force 𝑊 — the weight of the
object — is related to its mass and the gravitational field strength or acceleration
due to gravity.
Now coming back to a distinction
between mass and weight, since we said earlier that mass is a measure of the amount
of matter or stuff that makes up an object, then this means that we could take the
exact same object — let’s say this wooden block with mass 𝑚 — into different
gravitational fields. And if this object is still exactly
the same object as before that there’s nothing has broken off from it for example,
then the mass of that object will still be the same regardless of which
gravitational field the object is in.
This is because mass is an
intrinsic measure of the amount of stuff that makes up an object. And if we take that same object to
different locations, the amount of stuff that makes it up is not going to
change. Hence, the mass is not going to
change.
However, the weight of an object is
very dependent on the gravitational field that the object is placed in. This is because the weight of an
object is equal to the mass of that object which stays constant multiplied by the
gravitational field strength which can change. In other words, Earth’s
gravitational field strength is different to the gravitational field strength of the
moon for example. And so, if we took the same object
with the same mass from Earth to the moon, it would have a different weight on the
moon. And that is one very important
distinction between mass and weight. So having seen all of this, let’s
take a look at an example question.
An astronaut on Earth, where
the gravitational field strength is 9.8 newtons per kilogram, has a mass of 65
kilograms and a weight of 637 newtons. The astronaut is sent to a
space station, where the gravitational field strength is 9.5 newtons per
kilogram. What is the astronaut’s mass on
the space station? What is the astronaut’s weight
on the space station?
Okay, so in this question,
we’ve initially got an astronaut that’s on the surface of the Earth. And then later, that astronaut
is sent to a space station. Now we’ve been told that on
Earth where the gravitational field strength is 9.8 newtons per kilogram. So we can say that the
gravitational field strength 𝑔 of the Earth subscript 𝐸 is 9.8 newtons per
kilogram.
We’ve been told that on Earth,
the astronaut has a mass which we’ll call 𝑚 of 65 kilograms and a weight which
will be a downward acting force. And we’ll call this 𝑊 and it
happens to be 637 newtons. Now based on this information,
we need to work out what happens to the astronaut when they are sent to a space
station. And we’ve been told that on
this space station, the gravitational field strength is 9.5 newtons per
kilogram. So we can say that 𝑔 sub 𝑠,
which is what we’ll call the gravitational field strength on the space station,
is 9.5 newtons per kilogram.
Now we’ve been asked to state
what the astronaut’s mass is on the space station and what their weight is on
the space station. To do this, let’s recall a
relationship between weight, mass, and gravitational field strength. We can recall that the weight
of an object 𝑊 is given by multiplying the mass of that object by the
gravitational field strength which is also known as the acceleration due to
gravity caused by the gravitational field that the object is in.
As well as this, we can recall
that mass is a measure of the amount of matter or stuff that makes up an
object. Therefore, if we take the same
object and put it in a new gravitational field, the mass of that object is not
going to change because the object is still made up of the same amount of
stuff. Therefore, if we’ve been told
that the mass of the astronaut is 65 kilograms on Earth, then the mass of the
astronaut is 65 kilograms everywhere, regardless of whether they’re on Earth or
in a space station or in some part of outer space.
If the astronaut is made up of
the same amount of stuff as earlier, then the mass is going to be exactly the
same always. So when we’re asked what the
astronaut’s mass is on the space station, we can say that their mass is still 65
kilograms. However, looking at this
equation, we can see that the weight of the astronaut will change depending on
the strength of the gravitational field that the astronaut is in. And this does change between
the Earth and the space station. We can see that the values of
𝑔 are different.
So before we find the weight of
the astronaut on the space station, let’s first confirm that this equation does
make sense based on the values we’ve been given in the question when the
astronaut was on Earth. We can, therefore, say that the
weight of the astronaut on Earth, we’ll add this subscript 𝐸 now since we’ve
realized that the weight changes based on where the astronaut is. We can say that the astronaut’s
weight 𝑊 subscript 𝐸 on Earth is equal to the mass multiplied by the
gravitational field strength on Earth 𝑔 subscript 𝐸.
And substituting in values, we
see that 637 newtons is equal to 65 kilograms multiplied by 9.8 newtons per
kilogram. And the right-hand side of the
equation does end up being 637 newtons. Therefore, this equation does
work. And we’ve just confirmed this
based on the numbers we’ve been given in the question. So now we can move on to
applying this to the space station.
We can say that the weight of
the astronaut on the space station now — which we’ll call 𝑊 subscript 𝑠, so
that’s the downward force when the astronaut is on the space station — is equal
to the mass of the astronaut which is still the same multiplied by the
gravitational field strength on the space station 𝑔 subscript 𝑠.
Then, we can plug in the values
on the right-hand side. The mass is still 65
kilograms. But this time, the
gravitational field strength is 9.5 newtons per kilogram. And when we evaluate the
right-hand side, we find that the new weight of the astronaut is 617.5
newtons. Therefore, our final answer to
this part of the question is that the astronaut’s weight on the space station is
617.5 newtons.
Okay, so now that we’ve had a look
at an example question, let’s summarize what we’ve talked about in this video. Firstly, we saw that weight and
mass are not the same thing. But they are closely related by the
equation 𝑊 is equal to 𝑚𝑔. Where 𝑊 is the weight of an
object, 𝑚 is the mass of that object and 𝑔 is the gravitational field
strength.
Secondly, we saw that the equation
𝑊 is equal to 𝑚𝑔 is a special case of Newton’s second law of motion 𝐹 is equal
to 𝑚𝑎 because Newton’s second law of motion generally refers to the net force on
an object, whereas 𝑊 is equal to 𝑚𝑔 specifically refers to the gravitational
force exerted on an object or in other words the weight of that object. And this means that 𝑔 the
gravitational field strength is also known as the acceleration due to gravity.
And finally, we saw that an object
will have the same mass everywhere, assuming of course the object doesn’t break into
pieces or anything like that. But that same object may have a
different weight in different gravitational fields. This depends specifically on the
value of 𝑔, the gravitational field strength. So this is our review on the
relationship between mass and weight.
