### Video Transcript

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.