Question

In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the previous one. If the average book has a mass of 1.40 kg with a height of 22.0 cm, and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?

Answer 1

Answer:

1747.9 J

Step-by-step explanation:

The work done to lift a book by a certain height $\Delta h$ is

$W=mg\Delta h$

where

m = 1.40 kg is the mass of one book

$g=9.8 m/s^2$ is the acceleration due to gravity

The first shelf is 15.0 cm (0.15 m) from the ground, and it can be filled with 28 books. So, the work done to fill the first shelf is

$W_1=28mg\Delta h=28(1.40)(9.8)(0.15)=57.6 J$

The 2nd shelf is 38.0 cm above the first one, so its height from the ground is

$\Delta h =15.0+38.0 =53.0 cm=0.53 m$

It can also contain 28 books, so the work done to fill this shelf is

$W_2=28 mg\Delta h=28(1.40)(9.8)(0.53)=203.6 J$

The height of the third shelf is

$\Delta h =15.0+38.0 +38.0=91.0 cm=0.91 m$

It can also contain 28 books, so the work done to fill this shelf is

$W_3=28 mg\Delta h=28(1.40)(9.8)(0.91)=349.6 J$

The height of the 4th shelf is

$\Delta h =15.0+38.0 +38.0+38.0=129.0 cm=1.29 m$

It can also contain 28 books, so the work done to fill this shelf is

$W_4=28 mg\Delta h=28(1.40)(9.8)(1.29)=495.6 J$

The height of the 5th shelf is

$\Delta h =15.0+38.0 +38.0+38.0+38.0=167.0 cm=1.67 m$

It can also contain 28 books, so the work done to fill this shelf is

$W_5=28 mg\Delta h=28(1.40)(9.8)(1.67)=641.5 J$

Therefore, the total work done is:

$W=W_1+W_2+W_3+W_4+W_5=57.6+203.6+349.6+495.6+641.5=1747.9 J$