A student has six textbooks, each with a thickness of 3.6 cm and a weight of 38 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?
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To find the minimum work the student needs to do, we need to determine the total displacement of the textbooks and then calculate the work done against gravity.
First, let's calculate the total displacement. Since the books are stacked vertically, the total displacement would be the sum of the thicknesses of all the textbooks.
Total displacement = 6 textbooks × 3.6 cm = 21.6 cm = 0.216 m
Next, we can calculate the work done against gravity using the formula:
Work = Force × Distance × Cosine(angle)
In this case, the force is the weight of the textbooks (38 N), the distance is the total displacement (0.216 m), and the angle is the angle between the force vector and the direction of motion (which is 0 degrees because the force is acting vertically downwards).
Work = 38 N × 0.216 m × Cos(0°)
Since Cos(0°) = 1, we can simplify the equation to:
Work = 38 N × 0.216 m × 1
Finally, we can calculate the work:
Work = 8.208 J (rounded to three decimal places)
Therefore, the minimum work the student would have to do to place all the books in a single vertical stack is approximately 8.208 J.