To solve this problem, we need to calculate the astronaut's weight on Earth and on the Moon. Weight is a force that depends on both the mass of an object and the gravitational acceleration it experiences. The formula to calculate weight is:
[tex]\[ \text{Weight} = \text{mass} \times \text{gravitational acceleration} \][/tex]
1. Calculate the weight on Earth:
- The gravitational acceleration on Earth is approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
- Given the astronaut's mass is [tex]\( 100 \, \text{kg} \)[/tex].
Using the formula:
[tex]\[ \text{Weight on Earth} = 100 \, \text{kg} \times 9.8 \, \text{m/s}^2 \][/tex]
[tex]\[ \text{Weight on Earth} = 980 \, \text{N} \][/tex]
2. Calculate the weight on the Moon:
- The gravitational acceleration on the Moon is [tex]\( 1.6 \, \text{m/s}^2 \)[/tex].
- The astronaut's mass remains the same at [tex]\( 100 \, \text{kg} \)[/tex].
Using the formula:
[tex]\[ \text{Weight on the Moon} = 100 \, \text{kg} \times 1.6 \, \text{m/s}^2 \][/tex]
[tex]\[ \text{Weight on the Moon} = 160 \, \text{N} \][/tex]
Therefore, the astronaut's weight is:
- [tex]\( 980.0 \, \text{N} \)[/tex] on Earth
- [tex]\( 160.0 \, \text{N} \)[/tex] on the Moon
These calculations give us the weight an astronaut with a mass of 100 kg would experience on both Earth and the Moon.
