Question Video: Understanding the Relation between Mass, Weight, and Gravitational Field Strength

An astronaut on Earth, where the gravitational field strength is 9.8 N/kg, has a mass of 65 kg and a weight of 637 N. The astronaut is sent to a space station, where the gravitational field strength is 9.5 N/kg. What is the astronaut’s mass on the space station? What is the astronaut’s weight on the space station?

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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.

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