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An astronaut who has a mass of 81.25 kilograms goes to the Moon, where the acceleration due to gravity is 1.6 metres per second squared.
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What force does the astronaut’s weight apply to the lunar surface beneath the astronaut’s feet?
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Okay, so in this question, we’ve been told that we’ve got an astronaut who is currently on the surface of the Moon.
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We know that the mass of the astronaut, which we’ll call 𝑚, is 81.25 kilograms.
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And as well as this, we know that the gravitational field strength on the Moon, or in other words the acceleration due to gravity, is 1.6 metres per second squared.
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This is obviously different to the gravitational field strength on Earth, which is about 9.8 metres per second squared.
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And therefore, to differentiate between what we normally call the gravitational field strength on Earth, which is 𝑔, and the gravitational field strength on the Moon, we’ve added the subscript 𝑚.
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This is so we know that we’re talking about the gravitational field strength on the Moon, being 1.6 metres per second squared.
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Now with these two pieces of information, the mass of the astronaut and the gravitational field strength on the Moon, we can work out the weight of the astronaut on the Moon.
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Now we know that the weight of an object is the gravitational force acting on the object.
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And when the astronaut is on the Moon, the gravitational force on the astronaut is going to be acting towards the centre of the Moon.
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In other words, towards the astronaut’s feet.
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Hence, we can draw an arrow pointing downwards, and we can say that this represents the weight of the astronaut, which we’ll call 𝑊.
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Then we can realise that the astronaut’s feet are in contact with the surface of the Moon.
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Therefore, the weight acting on the astronaut will result in a force being exerted on the surface of the Moon by the astronaut.
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This is because, like we said, the astronaut and the surface of the Moon are in contact with each other.
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And in order to stop the astronaut’s feet and the surface of the Moon going through each other, they need to be exerting forces upon each other.
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And so, the force that the astronaut exerts on the surface of the Moon is equal to their weight.
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Hence, when we work out the weight of the astronaut, we will also be working out the force applied by the astronaut’s weight to the lunar surface.
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So, let’s start by recalling that the weight of any object is given by multiplying the mass of the object by the strength of the gravitational field that the object is placed in.
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In this case, it’s the strength of the gravitational field of the Moon.
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Then, we can substitute in the values for the right-hand side of the equation, which happen to be 81.25 kilograms for the mass of the astronaut and 1.6 metres per second squared for the acceleration due to gravity on the Moon.
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And now we can notice that since we’re working in base units, that’s kilograms for mass and metres per second squared for acceleration, we will, therefore, find our weight to be in its own base unit, which is newtons.
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Because, remember, weight is a force.
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So, when we evaluate the right-hand side of the equation, we find that the weight of the astronaut is 130 newtons.
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And since we said earlier that the weight of the astronaut is the same as the force applied by the astronaut’s weight to the lunar surface, we can, therefore, say that the force that we’re trying to find in this question is 130 newtons.