A student has six textbooks, each with a thickness of 4.0 cm and a weight of 30 N. What is the minimum work the student would have to do to place all the books in a single vertical stack, starting with all the books on the surface of the table?
well, the second book has to be lifted 4cm, the third 8 cm, ...
you are lifting books 2,3,4,5,6,7,8 Book 5 is the average book, so
work= 30*.04*4 Nm
To calculate the minimum work required to place all the books in a single vertical stack, we need to consider two factors: lifting the books off the table and then stacking them.
Step 1: Calculate the work to lift the books off the table
Each book has a weight of 30 N, so the work required to lift one book off the table is given by the equation:
Work = Force x Distance
Since the distance is the height of the book stack, the work to lift one book is:
Work = 30 N x 4.0 cm
Note: We need to convert the thickness of the book from centimeters to meters to match the standard SI unit used for force. 1 cm = 0.01 m.
Work = 30 N x 0.04 m
Work = 1.2 Nm (Joules)
Step 2: Calculate the work to stack the books
To stack the books, the student needs to move each book vertically to the height of the previous book.
The first book doesn't require any work to move, as it is already at the desired height.
The second book needs to be moved to a height of 4.0 cm relative to the first book. The work required is:
Work = 30 N x 4.0 cm
Converting the thickness to meters:
Work = 30 N x 0.04 m
Work = 1.2 Nm (Joules)
Similarly, the third book needs to be moved to a height of 8.0 cm, the fourth book to 12.0 cm, and so on.
The total work required to stack all the books can be calculated by summing the work required for each book:
Total Work = Work(book1) + Work(book2) + Work(book3) + ... + Work(book6)
Total Work = 1.2 Nm + 1.2 Nm + 1.2 Nm + 1.2 Nm + 1.2 Nm + 1.2 Nm
Total Work = 7.2 Nm (Joules)
Therefore, the minimum work the student would have to do to place all the books in a single vertical stack starting with all the books on the surface of the table is 7.2 Joules.
To find the minimum work the student would have to do to place all the books in a single vertical stack, we need to calculate the work done for each individual book and then sum them up.
First, let's calculate the work done to lift one book from the surface of the table to a height where it is stacked on top of another book. The work done formula is given by:
Work = Force x Distance
In this case, the force is the weight of the book, which is 30 N. The distance over which the book needs to be lifted is the thickness of the book, which is 4.0 cm or 0.04 m.
So, the work done to lift one book is:
Work = 30 N x 0.04 m = 1.2 N·m
Now we can calculate the total work done to place all six books in a single vertical stack. Since we are stacking the books one on top of another, the total distance over which the books are lifted will be the sum of their individual thicknesses.
Total distance = 6 books x 0.04 m/book = 0.24 m
Therefore, the total work done to stack all the books is:
Total work = Work per book x Total distance
= 1.2 N·m x 0.24 m
= 0.288 N·m
So, the minimum work the student would have to do to place all the books in a single vertical stack is 0.288 N·m.