How many uniform, identical textbooks of width 25.0 cm can be stacked on top of each other on a level surface without the stack falling over if each successive book is displaced 3.00 cm in width relative to the book below it?
If the books are 5.00 cm thick, what will be the height of the center of mass of the stack above the level surface?
divide width by displacement and add the 1st book.
25/3 = 8.33333 + 1 = 9 books
take the number of books form the 1st answer and multiply by the thickness of the books and then divide by 2. 9*5 = 45/2 = 22.5
To find the number of textbooks that can be stacked without falling over, we need to calculate the number of textbooks needed to fill the gap between each successive book.
The width of each book is 25.0 cm, and each book is displaced 3.00 cm in width relative to the book below it. This means that the effective width of each book in the stack will be 25.0 cm + 3.00 cm = 28.0 cm.
To calculate the number of textbooks that can be stacked, we need to divide the total width available for stacking by the effective width of each book.
Let's assume the total available width for stacking is x cm. The equation will be:
x / 28.0 cm = number of textbooks
Now, let's calculate the height of the center of mass of the stack above the level surface.
The height of the stack will be the number of textbooks multiplied by the thickness of each book, which is 5.00 cm.
To find the height of the center of mass, we need to divide the height of the stack in half as all the textbooks will be stacked symmetrically.
Therefore, the height of the center of mass of the stack above the level surface will be:
(number of textbooks * 5.00 cm) / 2
To calculate the number of books that can be stacked without falling over, we need to find the maximum displacement that the stack can handle before it becomes unstable.
In this case, each book is displaced 3.00 cm in width relative to the book below it. So, the effective width of each book in the stack is 25.0 cm + 3.00 cm = 28.0 cm.
To find the number of books that can be stacked, we divide the total available width by the effective width of each book:
Number of books = Total available width / Effective width of each book
Total available width = Width of each book = 25.0 cm
Effective width of each book = 28.0 cm
Number of books = 25.0 cm / 28.0 cm = 0.8929
Since we cannot have a fraction of a book, we can stack a maximum of 0 books without the stack falling over.
As for the height of the center of mass of the stack, we can calculate it using the following formula:
Height of center of mass = (Number of books * Thickness of each book) + (Thickness of each book / 2)
Number of books = 0 (as calculated above)
Thickness of each book = 5.00 cm
Height of center of mass = (0 * 5.00 cm) + (5.00 cm / 2) = 2.50 cm
Therefore, the height of the center of mass of the stack above the level surface will be 2.50 cm.