To determine the weight of a rock on Earth and Jupiter, given the mass and the gravitational acceleration on each of these planets, follow these steps:
1. Weight Calculation on Earth:
- The formula to calculate weight is [tex]\( \text{Weight} = \text{Mass} \times \text{Gravitational \,Acceleration} \)[/tex].
- Given:
- Mass of the rock [tex]\( m = 70 \)[/tex] kg
- Gravity on Earth [tex]\( g_{\text{Earth}} = 9.8 \)[/tex] m/s²
- Substitute the given values into the formula:
[tex]\[
\text{Weight on Earth} = 70\, \text{kg} \times 9.8\, \text{m/s}²
\][/tex]
- This results in:
[tex]\[
\text{Weight on Earth} = 686.0 \, \text{newtons}
\][/tex]
2. Weight Calculation on Jupiter:
- The same formula is used to calculate weight on Jupiter:
[tex]\[
\text{Weight} = \text{Mass} \times \text{Gravitational \,Acceleration}
\][/tex]
- Given:
- Mass of the rock [tex]\( m = 70 \)[/tex] kg
- Gravity on Jupiter [tex]\( g_{\text{Jupiter}} = 23.1 \)[/tex] m/s²
- Substitute the given values into the formula:
[tex]\[
\text{Weight on Jupiter} = 70\, \text{kg} \times 23.1\, \text{m/s}²
\][/tex]
- This results in:
[tex]\[
\text{Weight on Jupiter} = 1617.0 \, \text{newtons}
\][/tex]
So, the weight of a rock with a mass of 70 kilograms is:
- 686.0 newtons on Earth
- 1617.0 newtons on Jupiter
