In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 31.0 cm above the previous one.
If the average book has a mass of 1.4 kg with a height of 22 cm, and an average shelf holds 29 books, how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?
Part A Answer
Start by calculating the total mass of the books on a shelf. Since each shelf holds 29 books and each book is 1.4 kg, that gives a mass of 40.6 kg/shelf.
Now we can calculate the work required to fill each shelf. The work, in this case, just equals the energy done to move the books.
U = mgh
W = mgh
Now since the average book has a height of 22 cm, its center of mass is 11 cm above the base of the shelf. So 11 cm must be added to the height of each shelf. This gives the starting shelf a height of (0.11 + 0.15 = 0.26) 0.26 m. This is because the books were lying flat and have to be raised upright. To continue:
U = mgh
U = 71 * 9.8 * (0.26 + 0.57 + 0.88 + 1.19 + 1.5)
U = 71 * 9.8 * (4.4)
U = 3061.52 J