A stack of books rests on a table. Each book has a different weight. the topmost book has weight W, the second book from the top has weight 2W, the third book from the top has weight 3W, and so on. In addition, someone pushes on the topmost book from above with force W. Let's say W=2.5 Newtons. What is the net force on the fourth book, which has weight 4W?

Let's break down the forces acting on the fourth book from the top, which has weight \( 4W \), where \( W = 2.5 \, \text{Newtons} \).

### Forces Acting on the Fourth Book:

1. **Weight of the Fourth Book:**
   - The fourth book itself has a weight of \( 4W = 4 \times 2.5 = 10 \, \text{Newtons} \).

2. **Weights of the Books Above:**
   - The books above the fourth book also exert forces due to their weight.
     - The first book weighs \( W = 2.5 \, \text{Newtons} \),
     - The second book weighs \( 2W = 5 \, \text{Newtons} \),
     - The third book weighs \( 3W = 7.5 \, \text{Newtons} \).
   
   Therefore, the total weight of the books above the fourth book is:
   \[
   W + 2W + 3W = 2.5 + 5 + 7.5 = 15 \, \text{Newtons}.
   \]

3. **Additional Force from the Push:**
   - Someone is applying a force of \( W = 2.5 \, \text{Newtons} \) on the topmost book.
   - This force gets transmitted down through the stack, so it will also act on the fourth book.

### Total Force on the Fourth Book:

The net force acting on the fourth book is the sum of:
- The weight of the books above it (\( 15 \, \text{Newtons} \)),
- The additional downward force from the push (\( 2.5 \, \text{Newtons} \)),
- Plus its own weight (\( 10 \, \text{Newtons} \)).

Thus, the total net force on the fourth book is:
\[
15 \, \text{Newtons} + 2.5 \, \text{Newtons} + 10 \, \text{Newtons} = 27.5 \, \text{Newtons}.
\]

### Final Answer:
The net force acting on the fourth book is \( \boxed{27.5} \, \text{Newtons} \).

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What would be the net force on the third book?
2. How would the net force change if the applied force on the top book was doubled?
3. What is the net force on the bottom book if there are 5 books in total?
4. How would the net force on the fourth book change if gravity was weaker?
5. What would happen to the forces if the books had the same weight instead of increasing?

**Tip:** When dealing with stacked objects, the force on each lower object accumulates from all the objects above it plus any additional external forces applied.

A stack of books rests on a table. Each book has a different weight. The topmost book has weight W, the second book from the top has weight 2W, the third book from the top has weight 3W, and so on. In addition, someone pushes on the topmost book from above with force W. Let's say W=2.5 Newtons. What is the net force on the fourth book, which has weight 4W?

Learn how to calculate the net force acting on the fourth book in a stack of books with different weights. The problem involves understanding Newton's Laws of Motion, specifically the concept of net force. Suitable for students in Grades 9-12.

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