An object that weighs 120 newtons on the Earth weighs 20 newtons on the Moon. Given that the weight of an object on Earth is directly proportional to its weight on the Moon, find the weight of an object on the Moon given that its weight on Earth is 126 newtons.
Now it might feel a little bit strange that the same object would have a different weight on the Earth versus the Moon. But remember, weight and mass are different things. The mass of the object remains constant, but the weight is the downwards force that the object exerts on the surface it rests on, and it’s proportional to its acceleration due to gravity. And we know acceleration due to gravity is different on Earth than it is on the Moon.
So with that issue addressed, let’s recall what it means if the weight of the object on Earth is directly proportional to its weight on the Moon. Let’s define 𝑊 sub E to be the weight of the object on Earth and 𝑊 sub M to be the weight of the object on the Moon. This symbol tells us that the weight of the object on Earth is proportional to the weight of the object on the Moon. And we know that this means that the ratio of these variables is equal to some constant. Since when the weight on the Earth is equal to 120 newtons, the weight on the Moon is 20 newtons, we can find The value of 𝑘. That is 120 over 20 equals 𝑘, so 𝑘 is equal to six.
So we rewrite our earlier equation as 𝑊 sub E over 𝑊 sub M equals six. This value of 𝑘 is constant for all values of 𝑊 sub E and 𝑊 sub M. So to find the weight of an object on the Moon given that its weight on Earth is 126 newtons, we need to substitute 𝑊 sub E equals 126 into this equation. When we do, we get 126 over 𝑊 sub M equals six. Then we’re looking to make 𝑊 sub M the subject. So let’s multiply both sides by this variable. And we get 126 equals six times 𝑊 sub M.
Finally, we’re going to divide through by six. So 126 divided by six is 𝑊 sub M. And this is a calculation that we can perform in our head. Since 12 divided by six is two, 120 divided by six is 20. Then 126 divided by six must be equal to 21. Since the units for force in this question are newtons throughout, the units for 𝑊 sub M must also be newtons. So the weight of the object on the Moon given that its weight on Earth is 126 newtons is 21 newtons.