To determine on which body a 30 kg bowling ball would have the least gravitational potential energy when lifted to a height of 1 meter, we need to calculate the gravitational potential energy for each body. The formula for gravitational potential energy ([tex]\(E_p\)[/tex]) is:
[tex]\[ E_p = m \cdot g \cdot h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (30 kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height (1 meter).
Given the acceleration of gravity for each body:
- Earth: [tex]\( g = 9.8 \, m/s^2 \)[/tex]
- Mercury: [tex]\( g = 3.59 \, m/s^2 \)[/tex]
- Mars: [tex]\( g = 3.7 \, m/s^2 \)[/tex]
- Neptune: [tex]\( g = 14.07 \, m/s^2 \)[/tex]
- Uranus: [tex]\( g = 9.0 \, m/s^2 \)[/tex]
- Pluto: [tex]\( g = 0.42 \, m/s^2 \)[/tex]
Now, let’s calculate the gravitational potential energy for each body.
1. Earth:
[tex]\[
E_p = 30 \, kg \times 9.8 \, m/s^2 \times 1 \, m = 294.0 \, J
\][/tex]
2. Mercury:
[tex]\[
E_p = 30 \, kg \times 3.59 \, m/s^2 \times 1 \, m = 107.7 \, J
\][/tex]
3. Mars:
[tex]\[
E_p = 30 \, kg \times 3.7 \, m/s^2 \times 1 \, m = 111.0 \, J
\][/tex]
4. Neptune:
[tex]\[
E_p = 30 \, kg \times 14.07 \, m/s^2 \times 1 \, m = 422.1 \, J
\][/tex]
5. Uranus:
[tex]\[
E_p = 30 \, kg \times 9.0 \, m/s^2 \times 1 \, m = 270.0 \, J
\][/tex]
6. Pluto:
[tex]\[
E_p = 30 \, kg \times 0.42 \, m/s^2 \times 1 \, m = 12.6 \, J
\][/tex]
Now we compare the gravitational potential energies:
- Earth: 294.0 J
- Mercury: 107.7 J
- Mars: 111.0 J
- Neptune: 422.1 J
- Uranus: 270.0 J
- Pluto: 12.6 J
From these calculations, we see that the least gravitational potential energy is on Pluto with [tex]\( 12.6 \, J \)[/tex]. Therefore, the 30 kg bowling ball would have the least gravitational potential energy on Pluto when lifted to a height of 1 meter.
The correct answer is:
- Pluto
