A student librarian picks up a 2.2 kg book from the floor to a height of 1.05 m. He carries the book 8.3 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?
work=2.2 g*(.35)
gsh
To calculate the work done on the book, we need to use the formula:
Work = Force × Distance × cos(θ)
In this case, the force exerted on the book is equal to the weight of the book, which can be calculated using the formula:
Weight = mass × acceleration due to gravity
Given that the mass of the book is 2.2 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can find the weight of the book:
Weight = 2.2 kg × 9.8 m/s^2
Next, we need to find the vertical distance the book is lifted. The student librarian raises the book from the floor to a height of 1.05 m. Therefore, the lifting distance is 1.05 m.
Once the book is lifted, the student librarian carries it horizontally for a distance of 8.3 m.
The angle (θ) between the force vector and the displacement vector is 0 degrees because the force is acting vertically upwards and the displacement is also vertically upwards.
Using these values, we can calculate the work done on the book:
Work = Weight × Distance × cos(θ)
Work = (Mass × acceleration due to gravity) × Distance × cos(θ)
Work = (2.2 kg × 9.8 m/s^2) × (1.05 m + 0.35 m) × cos(0°)
Work = (2.2 kg × 9.8 m/s^2) × 1.4 m × 1
Now, we can calculate the work:
Work = 2.2 kg × 9.8 m/s^2 × 1.4 m
By simplifying this expression, we can find the final answer.