Gravitational Potential Energy

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A librarian lifts a 5 kg stack of books from the floor and places it on a shelf 1.8 m above the ground at constant speed. By how much does the gravitational potential energy of the stack increase?

RankGuru · Accepted Answer

Gravitational potential energy near the Earth's surface is measured relative to a chosen reference level and changes by $\Delta \cup = mgh$ when a body is raised through a vertical height $h$. Because the books are lifted slowly at constant speed, all the work done by the librarian against gravity is stored as potential energy with no change in kinetic energy. With $m = 5	ext{ kg}$, $g = 10	ext{ m/s}^2$, and $h = 1.8	ext{ m}$, the increase is $\Delta \cup = 5 	imes 10 	imes 1.8 = 90	ext{ J}$. The option 9 J drops a factor of ten through a height misreading. The option 45 J uses half the height for no reason. The option 180 J doubles the height, perhaps confusing diameter with radius-like reasoning. This matches the NCERT treatment of potential energy as path-independent work done against gravity. As a sanity check, the units $	ext{kg}	imes	ext{m/s}^2	imes	ext{m}$ reduce to joules, and a modest shelf lift storing about 90 J is reasonable.

Gravitational Potential Energy

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