What is the Work Required to Stack Books?

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In summary, the problem is to find the work required to stack eight books with a thickness of 9.5 cm and mass of 1.3 kg on top of each other when they are initially lying flat on a table. The first method used was W = F(height), but it was found to be incorrect. A second method was suggested to find the work by considering the change in potential energy of the books when they are stacked up, using the center of mass. However, the student was not familiar with this concept and used the first method instead. After further guidance, the student was able to find the correct answer of 23 J by using the second method.
  • #1
newtophysics
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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!
 
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  • #2
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.
 
  • #3
Okay, I got it, thanks so much!
 
  • #4
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.)
 
  • #5
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?
 
  • #6
IoWn3rU said:
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.
 
  • #7
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.
 
  • #8
IoWn3rU said:
I got 29 and some, while the answer is 23.

Welcome to PF :smile:! 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?
 
  • #9
It's resting on top of a table. Would the first book not take any energy?
 
  • #10
IoWn3rU said:
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.
 
  • #11
Thanks for the help

EDIT: Didn't help, I got an answer around 10, the answer is 23 J.
 
  • #12
IoWn3rU said:
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.
 
  • #13
IoWn3rU said:
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.)
 
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  • #14
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.
 
  • #15
IoWn3rU said:
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.
 
Last edited:

1. What is the purpose of calculating the work required to stack books?

The purpose of calculating the work required to stack books is to determine the amount of energy or effort needed to lift and arrange a stack of books in a specific way. This calculation can help determine the efficiency of a stacking method or the physical demands of a particular task.

2. What factors affect the work required to stack books?

The work required to stack books is affected by factors such as the weight and size of the books, the height and stability of the stack, and the strength and technique of the person stacking the books.

3. How is the work required to stack books calculated?

The work required to stack books is calculated by multiplying the force needed to lift each book by the distance over which the force is applied. This can be represented by the equation W = F x d, where W is the work, F is the force, and d is the distance.

4. Does the type of book affect the work required to stack?

Yes, the type of book can affect the work required to stack. For example, larger and heavier books will require more force to lift, while smaller and lighter books will require less force. Additionally, books with irregular shapes or sizes may be more difficult to stack and require more work.

5. How can the work required to stack books be minimized?

The work required to stack books can be minimized by using proper lifting and stacking techniques, such as keeping the stack close to the body and using the legs to lift instead of the back. Additionally, using lighter or smaller books, organizing the stack to distribute weight evenly, and taking breaks can also help reduce the overall work required.

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