Final answer:
The work-energy theorem explains that the work done by gravity on the falling book equals the change in kinetic energy, which enables us to calculate the book's speed before it hits the floor using the provided mass and distance.
Step-by-step explanation:
The question at hand can be explained through the work-energy theorem in physics, which states that the work done on an object results in a change in its kinetic energy. When a book falls from a shelf to the floor, the force of gravity does work on the book, which is transformed into kinetic energy as the book gains speed. The potential energy (PE) the book has on the shelf is converted to kinetic energy (KE) just before it hits the floor, allowing us to calculate the speed of the book.
Given that the work done on the book by gravity (W) is equal to the change in potential energy (ΔPE), which itself is equal to the change in kinetic energy (ΔKE), we have:
W = ΔKE = ΔPE
W = mgd = (1/2)mv²
Where m is the mass of the book, g is the acceleration due to gravity (approximately 9.8 m/s²), d is the distance fallen, and v is the final speed of the book. As the book starts from rest, its initial kinetic energy is zero, so the final kinetic energy is solely due to the fall.
Since the mass of the book is given and the distance it falls is known, we can solve for the book's final speed before impact with this equation:
(1/2)mv² = mgd
v² = 2gd
v = √(2gd)
Therefore, the correct answer would be: b) Work done is equal to the change in energy, which provides us with enough information to calculate the book's speed upon hitting the floor.