To calculate the gain in potential energy when the books are stacked one on top of the other, we need to consider the change in height of the center of mass of the system.
Each book has a thickness of 2.50 cm, so when five books are stacked, the total height of the stack is 5 * 2.50 cm = 12.50 cm = 0.125 m.
Since the books are initially lying flat on the table, the center of mass of the system is initially at a height of zero.
When the books are stacked, the center of mass of the system is raised to a height of 0.125 m.
The gain in potential energy of the system is given by the formula:
Gain in potential energy = mass * acceleration due to gravity * change in height
Since all the books are identical with a mass of 0.85 kg each, the total mass of the system is 5 * 0.85 kg = 4.25 kg.
The acceleration due to gravity is approximately 9.8 m/s^2.
The change in height is 0.125 m.
Substituting these values into the formula, we can calculate the gain in potential energy:
Gain in potential energy = 4.25 kg * 9.8 m/s^2 * 0.125 m
Gain in potential energy ≈ 5.26 J
Therefore, the gain in potential energy of the system when the books are stacked one on top of the other is approximately 5.26 Joules.