How to calculate the Work (Joules) of lifting a book

AI Thread Summary
To calculate the work required to lift four books stacked 20 cm high, the formula for Potential Energy (mgh) is applied, leading to an initial calculation of 8J. The user initially miscalculated the work for each book, particularly with the height unit, as they used centimeters instead of meters. A suggestion was made that the answer key might contain a typo, possibly meaning 8.0 J instead of 80J. Additionally, it was pointed out that the problem's use of mixed units could lead to confusion and incorrect results. Ensuring consistent unit usage is crucial for accurate calculations.
Alyssa Eiger
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1. I'm trying to calculate work it takes to lift 4 books, and stack them on top of each other in a 20 cm high stack. The problem reports:
- 5 books are lying on the ground. They are each: 2kg, 4cm thick.


Using the formula for Potential Energy (mgh), my calculations reflect it takes 8J:
- Book 1 is already on the ground.
- Book 2 on Book 1: (2kg)*(10m/s^2)*(.04m) = 8 J
- Book 3 on Book 2: 1.6 J
- Book 4 on Book 3: 2.4 J
- Book 5 on Book 4: 3.2 J

Thus, I get 8J - however the answer key to the problem reports it's 80J. Am I missing a critical component?

Any input is appreciated.
 
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UPDATE: this should read: "- Book 2 on Book 1: (2kg)*(10m/s^2)*(.04m) = .8 J"
 
Hi Alyssa Eiger,

Welcome to Physics Forums!

In future, please retain formatting template in your post. Don't delete or write over it. Thanks.

Your work looks good and the result fine. Perhaps the answer key has a typo and should read "8.0 J".
 
gneill said:
Hi Alyssa Eiger,

Welcome to Physics Forums!

In future, please retain formatting template in your post. Don't delete or write over it. Thanks.

Your work looks good and the result fine. Perhaps the answer key has a typo and should read "8.0 J".
Thank you GNeill. I will be sure to keep formatting in the future.
AE
 
I have not checked your arithmetic, but one potential difficulty is in the problem statement itself. It uses mixed units. Centimeters are not SI units; this data needs to be converted to meters to have any prospect of a correct result. This is a flaw in the way the problem is posed, not in the OP solution.
 
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