Question

Mass is an indicator of the amount of matter that an object possesses. Scientists determine the weight of an object by multiplying its mass by the acceleration that the object experiences due to gravity. The acceleration due to gravity on the moon is approximately \(\frac{1}{6}\) the acceleration due to gravity on the earth. Based on the information above, a person would have

Short answer

A person on the moon would have \(\frac{1}{6}\) of their weight on Earth due to the difference in acceleration due to gravity between the Moon and the Earth.

Step-by-step solution

Understand the relationship between weight, mass, and gravity

The weight of an object can be calculated using the formula: Weight = Mass × Acceleration due to gravity As mentioned, the acceleration due to gravity on the moon is 1/6 of the acceleration due to gravity on Earth.

Calculate the weight on the moon relative to the weight on Earth

Let's denote the person's mass on Earth as \(m\), the acceleration due to gravity on Earth by \(g_{E}\), and the acceleration due to gravity on the moon by \(g_{M}\). According to the information, the acceleration due to gravity on the moon is approximately 1/6 of the acceleration due to gravity on Earth. Therefore, we can represent the relationship as follows: \(g_{M} = \frac{1}{6} g_{E}\) Now, we can calculate the person's weight on the Earth (\(W_{E}\)) and on the moon (\(W_{M}\)): On Earth: \(W_{E} = m \times g_{E}\) On Moon: \(W_{M} = m \times g_{M}\) To find the ratio of the weight on the moon to the weight on the Earth, we need to divide the weight on the moon by the weight of the Earth: \(\frac{W_{M}}{W_{E}} = \frac{m \times g_{M}}{m \times g_{E}}\) The mass (\(m\)) cancels out in the equation: \(\frac{W_{M}}{W_{E}} = \frac{g_{M}}{g_{E}}\) Now, we can substitute the relationship between \(g_{M}\) and \(g_{E}\) given in the problem: \(\frac{W_{M}}{W_{E}} = \frac{\frac{1}{6} g_{E}}{g_{E}}\) The acceleration due to gravity on Earth \(g_{E}\) cancels out in the equation: \(\frac{W_{M}}{W_{E}} = \frac{1}{6}\)

Interpret the result

Based on the calculations, a person's weight on the moon is 1/6 of their weight on Earth because of the difference in acceleration due to gravity between the Moon and the Earth. So, a person on the moon would have 1/6 of their weight on Earth.