A student librarian picks up a 2.2 kg book from the floor to a height of 1.15 m. He carries the book 8.0 m to the stacks and places the book on a shelf that is 0.35 m above the floor. How much work does he do on the book?

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9988

7.5

To calculate the work done on an object, you need to use the formula:

Work = force × distance × cos(θ)

Here, the force is the weight of the book, the distance is the vertical distance the book is lifted, and θ is the angle between the force and the displacement. In this case, since the book is lifted vertically, θ is 0 degrees, and cos(0) = 1.

Let's break down the problem step by step to find the solution:

1. Find the force (weight) of the book:
The weight of an object is given by the formula:

Force = mass × acceleration due to gravity

In this case, the mass of the book is 2.2 kg, and the acceleration due to gravity is approximately 9.8 m/s² (standard value). Thus:

Force = 2.2 kg × 9.8 m/s² = 21.56 N

2. Calculate the work done in lifting the book to the shelf:
The vertical distance the book is lifted is 1.15 m. As mentioned earlier, the angle θ is 0 degrees, so cos(0) = 1. Using the formula for work:

Work = Force × Distance × cos(θ)
= 21.56 N × 1.15 m × 1
= 24.794 N·m or 24.794 J (joules)

3. Find the work done in carrying the book to the stacks:
The book is carried a horizontal distance of 8.0 m. Since there is no vertical displacement, θ is 90 degrees, and cos(90) = 0. Therefore, the work done in carrying the book horizontally is:

Work = Force × Distance × cos(θ)
= 21.56 N × 8.0 m × 0
= 0 J (joules)

4. Calculate the total work done:
Since the work done in carrying the book horizontally is zero, we only need to consider the work done in lifting the book to the shelf:

Total Work = Work lifting the book
= 24.794 J