Eight books, each 8.5 cm thick with mass 1.3 kg, lie flat on a table.How much work is required to stack them one on top of another?
The average height before is 4.25cm
The average height after is 4*8.25cm
work=7(1.3)*(4*.0825 - .0425)*9.8 joules
work = massmoved*change height*g
Make certain you know why seven masses are in the calculation.
To calculate the work required to stack the books one on top of another, we need to consider the gravitational potential energy involved in lifting each book.
The work done on an object is equal to the force applied to it multiplied by the distance over which the force is applied. In this case, the force exerted is equal to the weight of the book, which can be calculated using Newton's second law: Weight = mass * gravity, where gravity is approximately 9.8 m/s^2.
Given:
Number of books = 8
Thickness of each book = 8.5 cm = 0.085 m
Mass of each book = 1.3 kg
To calculate the work required, we need to find the total height the books are lifted. This can be calculated by multiplying the number of books by the thickness of each book:
Total height = 8 books * 0.085 m/book = 0.68 m
Now, let's calculate the work required to lift each book to the respective height. The work done on each book is given by the formula: Work = Force * Distance.
The distance here is the thickness of each book, and the force exerted on each book is its weight. So, for each book:
Work = Weight * Thickness
Now, let's calculate the work done for each book:
Weight = mass * gravity = 1.3 kg * 9.8 m/s^2 ≈ 12.74 N (approximately)
Work for each book = 12.74 N * 0.085 m ≈ 1.08 J (approximately)
Finally, to find the total work required to stack all eight books, we multiply the work done for each book by the number of books:
Total work = Work per book * Number of books
Total work = 1.08 J/book * 8 books ≈ 8.64 J (approximately)
Therefore, approximately 8.64 Joules of work is required to stack the eight books one on top of another.