If you weighed 112 N on the Moon where g = 1.6 N/kg, how much would you weigh on Earth?

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Q: 

If you weighed 112 Newtons (N) on the moon, where the force of gravity (g) = 1.6 N/kg, how much would you weigh on Earth?

A:

The key piece of knowledge for solving this problem is that weight (given here in Newtons) is in direct proportion to the force of gravity. That is, as the force of gravity increases, so too does weight. The formula that governs this relationship is `W = m*g` , where W is the weight of the object, m is the mass of the object, and g is the force of gravity.

Thus, from the question, we know that

`112 N = m*(1.6 N)/(kg)`

We can therefore solve for mass, m, by dividing both sides by `(1.6 N)/(kg)`

Newtons cancel out and we have our answer in kilograms. By this calculation, the mass of the person is 70 kg. 

Now, let's use the same formula for gravity to find the person's weight on Earth. Again, `W = m*g`. This time, however, the gravitational force is `(9.81 N)/(kg)`  

We will solve for W using this formula:

`W = 70 kg * (9.81 N)/(kg)` 

Kilograms cancel out and we are given an answer in Newtons. Rounded to 3 significant figures, this yields a weight of 687 N on Earth, the final answer.

 

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