Step-by-Step Solution:
1. Understanding Mass vs. Weight
- Mass is a measure of the amount of matter in an object, and it remains constant regardless of location. It is measured in kilograms (kg).
- Weight is the force exerted on a mass due to gravity. It is dependent on the local gravitational acceleration and is measured in newtons (N).
2. Given Data:
- Mass of the man: 70 kg
- Gravitational acceleration on Earth ([tex]\( g_{\text{earth}} \)[/tex]): 9.81 m/s²
- Gravitational acceleration on the Moon ([tex]\( g_{\text{moon}} \)[/tex]): 1.625 m/s²
3. Calculating Weight on the Moon:
- Weight is calculated using the formula:
[tex]\[
\text{Weight} = \text{Mass} \times \text{Gravitational acceleration}
\][/tex]
- Substituting the given values for the Moon:
[tex]\[
\text{Weight on the Moon} = 70 \, \text{kg} \times 1.625 \, \text{m/s}^2
\][/tex]
- Performing the multiplication:
[tex]\[
\text{Weight on the Moon} = 113.75 \, \text{N}
\][/tex]
4. Mass on Earth and Mass on the Moon:
- Since mass remains constant regardless of the location:
[tex]\[
\text{Mass on Earth} = 70 \, \text{kg}
\][/tex]
[tex]\[
\text{Mass on the Moon} = 70 \, \text{kg}
\][/tex]
Answer:
- A 70 kg man would weigh 113.75 N on the Moon.
- His mass on both Earth and the Moon would be 70 kg.
