Q.) A student has six textbooks, each 4.0 cm thick and 30 N inweight. What is the minimum work the student would have to do toplace the books in a vertical stack, starting with all the books onthe surface of the table?

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BleabyinfibiaG · Accepted Answer

Let mg be the weight of each book  let t be the thichness of each book.  The 1st book is aready on the table, so no work needs to be done.  The 2nd book has to be lifted through a height of t to beplaced on top of the 1st book.  The 3rd book has to be lifted through a height of 2t to beplaced on top of the 2nd book. etc.  The general case can be given as,  W1=mg×t  W2=mg×2t  W3=mg×3t  Wn−1=mg×(n−1)t  So, if you have n books, of thickness t, then the work done inlifting (n-1) of them on top of each other is given by,  W=m&amp;gt;(1+2+3+…+(n−1))  You have a simple summation of the 1st (n-1) integers which is 12(n−1)n so,  W=12m&amp;gt;(n−1)n  mg=30N  t=0.04m  n=6  W=12×30×0.04×5×6  W=15×0.2×6  W=18J

Q.) A student has six textbooks, each 4.0 cm thick and 30 N inweight. What is the minimum work the student would have to do toplace the books in a vertical stack, starting with all the books onthe surface of the table?

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