Pulling Books

Classical Mechanics Level 2

Bob sees a stack of 8 identical books at a bookstore. Bob likes the books at the bottom, and wants to take them out slowly, by applying a horizontal force.

What would require more energy: pulling out only the last book or the last two books together?

Equal in both cases Only the last book The last two books

Pranshu Gaba by Pranshu Gaba , 22, India

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1 solution

Anuj Shikarkhane
Aug 2, 2017

When you pulling only the last book, you have to bear the weight of 7 other books on top. But when you are pulling last two books together, you just need to bear the weight of 6 other books on top. Hence, pulling out only the last book requires more energy.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Stretching that analogy to the extreme, does this mean that "When you pull all 8 books, you have to bear the weight of 0 other books on top, hence it will require the least energy"?

Calvin Lin Staff - 3 years, 10 months ago

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No, it does not mean like that. When you are pulling all the 8 books together, you have to bear the individual weight of all the 8 books in order to pull them. So it will actually require the greatest energy. This solution can not be generalized. What do you think?

Anuj Shikarkhane - 3 years, 10 months ago

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In that case, you have to explain carefully why "removing the second book reduced the amount of energy, but removing all books would then increase the amount of energy". What are the forces / actions that are in play? When does the "minimum energy" occur, and why?

Calvin Lin Staff - 3 years, 10 months ago

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@Calvin Lin – There are two kinds of force acting. One vertically and other horizontally. And we have to consider both of them to find the energy required.

Kaushik Chandra - 3 years, 9 months ago

I do not think so , when all books are bulled the energy required is at its minimum because there is no frictional force is need to be overcoming that acts at the top of the 8 books pile , you have only to counteract the force of friction between the roof and the pile of books which is the same when you bull any number of books less than 8 started from the base .

Ahmed Aljayashi - 2 years, 2 months ago

Shear force required shall b same in both cases n hence equal energy shall be used........please clarify

Pranjal Saxena - 3 years, 10 months ago

@Pranjal Saxena that's what i got.

Rohan Joshi - 4 months, 4 weeks ago

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