Potential energy.
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no, but the POTENTIAL energy may equal the work done to life the book to the shelf
There is no direct relationship because the potential energy of the book on the shelf is defined relative to an arbitrary base line at which the potential energy would be zero. The work done in raising the book is the increase in the potential energy of book from however much PE it had in its previous location - for example, on a lower shelf.
YES!
Potential Energy If it falls, it will then be subject of gravity, so it has the potential of becoming energetic. -------------------- The bookshelf could also catch fire and the book would release energy as heat.
Yes it is. Because it has the POTENTIAL of falling off. Very simple physics, learned that in 6th grade.