What is the Work Required to Stack Books?

[newtophysics]

Alright, I'm having some problems with this problem:
Eight books, each 9.5 cm thick with mass 1.3kg, lie flat on a table. How much work is required to stack them one on tope of another?
I used W = F(height) and got 1.21J, but that is wrong. So then I multiplied the height, .095m by 8 since there are eight books but that is also wrong. Any help with this would be appreciated! Thanks!

 

[Shooting Star]

Work done to move the 2nd book on top of the1st one is 'mgh', where h is the vertical dist through which the CM of the 2nd book moves up. Now think what would be the work done to place the 3rd book on top of the 2nd. Continue like this. You'll get the sum of an AP.

 

[newtophysics]

Okay, I got it, thanks so much!

 

[Doc Al]

Now try doing it the easy way. Compare the total gravitational PE of the books before and after stacking them. (Hint: Follow the center of mass.)

 

[IoWn3rU]

I had a similar problem like this, except the thickness was 4.6cm, or .046m, and the mass was 1.8kg. I used the method Shooting Star said to use, but my answer was incorrect.

Are there any other ways do it?

 

[Doc Al]

I had a similar problem like this, except the thickness was 4.6cm, or .046m, and the mass was 1.8kg. I used the method Shooting Star said to use, but my answer was incorrect.

Are there any other ways do it?

All you need is one way. Post the complete problem exactly as given and show what you did.

 

[IoWn3rU]

Eight books, each 4.6 cm thick with mass 1.8 kg, lie flat on a table. How much work is required to stack them one on top of another?

As I always do, I list the variables I know, m = 1.8, h = .046.

What I did then is mgh, and after each book stacked, I used the previous books stacked heights added as the h, and added all the 8 answers together. I got 29 and some, while the answer is 23.

 

[Redbelly98]

I got 29 and some, while the answer is 23.

Welcome to PF ! I think I see the problem.

Questions for you: how much energy would it take if there is just 1 book? What is that book resting on top of?

 

[IoWn3rU]

It's resting on top of a table. Would the first book not take any energy?

 

[Shooting Star]

Eight books, each 4.6 cm thick with mass 1.8 kg, lie flat on a table. How much work is required to stack them one on top of another?

As I always do, I list the variables I know, m = 1.8, h = .046.

What I did then is mgh, and after each book stacked, I used the previous books stacked heights added as the h, and added all the 8 answers together. I got 29 and some, while the answer is 23.

Use the easiest method given by Doc Al in post #4. FInd PE=mgh initially and finally.

 

[IoWn3rU]

Thanks for the help

EDIT: Didn't help, I got an answer around 10, the answer is 23 J.

 

[Redbelly98]

It's resting on top of a table. Would the first book not take any energy?

That's correct. So, did you use 0 J for the 1st book when you did your calculation before?

Next add the energy to stack the 2nd book on top of the first, etc. and finally the energy to stack the 8th and final book on top of the 7th book.

 

[Doc Al]

EDIT: Didn't help, I got an answer around 10, the answer is 23 J.

Answer these questions:
(1) Where's the center of mass of the books when they are lying on the table, one layer thick?
(2) Where's the center of mass of the books when they are stacked up?
(3) What's the change in height of the center of mass? (Use that to find the change in potential energy.)

 

[IoWn3rU]

I haven't learned what the center of mass is yet, but taking an educated guess, is it the middle of the height?

Would the answer to the 2nd question be in the middle of the height of all the books stacked together?

Not sure about #3.

 

[Doc Al]

I haven't learned what the center of mass is yet, but taking an educated guess, is it the middle of the height?

Yes.

Would the answer to the 2nd question be in the middle of the height of all the books stacked together?

Yes, again.

Not sure about #3.

Subtract one from the other to find the change in height of the center of mass.

Since you haven't covered center of mass yet, I suggest you first work things out using the approach that Redbelly98 outlined. Then you can use this new method just for fun and compare answers.