pphysics work problem

[joonkimdds]

In a certain library the first shelf is 10.0 cm off the ground, and the remaining four shelves are each spaced 30.0 cm above the previous one. If the average book has a mass of 1.20 kg with a height of 21.0 cm, and an average shelf holds 23 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?

the answer on the book is 1.5 x 10^3 J , and that is 1500J
but I don't know how to solve this problem.
what i could think of was using potential energy equation= mgh
so what i tried was
1.2kg x 9.8 x (0.1+0.21) x 25
1.2kg x 9.8 x (0.4+0.21) x 25
1.2kg x 9.8 x (0.7+0.21) x 25
1.2kg x 9.8 x (1.0+0.21) x 25
1.2kg x 9.8 x (1.3+0.21) x 25
then add them together but it seems i get the wrong answer.
could someone tell me how to solve this problem?

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[Sicilian]

In a certain library the first shelf is 10.0 cm off the ground, and the remaining four shelves are each spaced 30.0 cm above the previous one. If the average book has a mass of 1.20 kg with a height of 21.0 cm, and an average shelf holds 23 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?

the answer on the book is 1.5 x 10^3 J , and that is 1500J
but I don't know how to solve this problem.
what i could think of was using potential energy equation= mgh
so what i tried was
1.2kg x 9.8 x (0.1+0.21) x 25
1.2kg x 9.8 x (0.4+0.21) x 25
1.2kg x 9.8 x (0.7+0.21) x 25
1.2kg x 9.8 x (1.0+0.21) x 25
1.2kg x 9.8 x (1.3+0.21) x 25
then add them together but it seems i get the wrong answer.
could someone tell me how to solve this problem?

Are you sure 1500 J is correct?

 

[osli]

My first thoughts are that mgh should work, as that is equivalent to W = FD where F = ma, but that you should use half the height of the book (.105m) instead of the full height (.21m) added to the shelf height, because that is how high you have lifted the CG of the book for the bottom edge to clear the shelf.

But that doesn't give 1500J.

 

[DrBowtie]

Your problem says 23 books but the solution is 25 books. Which is it?

 

[osli]

neither seems to work.

 

[DrBowtie]

What about taking the book height as 10.5 since the mass is centered? Also what about taking the book height as negligible since you lift from the bottom of the book to the bottom of the shelf?

Try both.

 

[osli]

What about taking the book height as 10.5 since the mass is centered? Also what about taking the book height as negligible since you lift from the bottom of the book to the bottom of the shelf?

Try both.

I suggested using half the book height but the problem is that the calculated answers come up less than his 1500J "correct" answer, not more. Taking the book height as negligible wouldn't make sense because they are lying flat to begin with and you have to raise the CG before you ever lift the bottom edge off the floor.

Unless they are counting some work somewhere else, I just think 1500J is wrong.