Answer:
The gravitational potential energy of the drum would have increased by [tex]450\; {\rm J}[/tex], assuming that [tex]g = 10\; {\rm N\cdot kg^{-1}}[/tex].
Step-by-step explanation:
When an object of mass [tex]m[/tex] in a gravitational field of constant strength [tex]g[/tex] moves by a distance of [tex]\Delta h[/tex] in the direction of the field lines, the gravitational potential energy ([tex]\text{GPE}[/tex]) gained would be:
[tex]\displaystyle \text{GPE} = m\, g\, \Delta h[/tex].
In this question, it is given that:
- [tex]m = 9\; {\rm kg}[/tex] is the mass of the object that was moved.
- [tex]\Delta h = 5\; {\rm m}[/tex] is the displacement of the object in the direction of the gravitational field lines (upwards.)
Assuming that [tex]g = 10\; {\rm N\cdot kg^{-1}}[/tex], the gravitational potential energy that was gained would be:
[tex]\begin{aligned}(\text{GPE}) &= m\, g\, \Delta h \\ &= (9\; {\rm kg})\, (10\; {\rm N \cdot kg^{-1}})\, (5\; {\rm m}) \\ &= 450\; {\rm J}\end{aligned}[/tex].
(Note that [tex]1\; {\rm N\cdot m^{-1}} = 1\; {\rm J}[/tex].)
