You are walking from your math class to your science class carrying a book weighing 112N. You walk 45 meters down the hall, climb 4.5 meters up the stairs and then walk another 40 meters to your science class. What is the total work performed on your books.

To find the total work performed on the book, we need to calculate the work done during each segment of the journey and then add them together.

First, let's calculate the work done while walking down the hall. The formula for calculating work is:

Work = Force × Distance × Cosθ

Since you are walking horizontally down the hall, the angle between the force and the direction of motion (θ) is 0 degrees. The weight of the book (force) is given as 112N, and the distance traveled is 45 meters. Plugging in these values, we have:

Work = 112N × 45m × Cos(0)

Since Cos(0) = 1, the work done while walking down the hall is:

Work = 112N × 45m × 1 = 5040 N·m

Next, let's calculate the work done while climbing the stairs. The formula for calculating work remains the same, but this time we need to account for the angle at which you are walking up the stairs. Let's assume that the angle of inclination of the stairs is 30 degrees (you can adjust this value if it's different).

The distance traveled while climbing the stairs is 4.5 meters, and we need to calculate the component of the force acting in the direction of motion, which is given by:

Force × Cosθ = Force × Cos(30)

Since the weight of the book is the force acting in the vertical direction, which is perpendicular to the stairs, we have:

Force = 112N

Plugging in these values, we find:

Work = 112N × 4.5m × Cos(30)

Using Cos(30) = √3/2, we can simplify the equation:

Work = 112N × 4.5m × √3/2 ≈ 340.78 N·m

Lastly, let's calculate the work done while walking the final 40 meters to your science class. The angle between the force of the book's weight and the direction of motion is again 0 degrees. The distance traveled is 40 meters, and the force is still 112N. Applying the work formula, we have:

Work = 112N × 40m × Cos(0) = 112N × 40m × 1 = 4480 N·m

Now, we add up the work done in each segment: 5040 N·m + 340.78 N·m + 4480 N·m = 9860.78 N·m

Therefore, the total work performed on the book is approximately 9860.78 N·m.

W = Fd = 112 * 4.5 = 504J.