Question

a book is falling from the top shelf of a bookcase. which statement correctly describes the change in the energy of the book? the potential energy and kinetic energy remain the same. the potential energy decreases as kinetic energy increases. the kinetic energy decreases as potential energy increases. the kinetic energy remains at zero, but potential energy increases.

Explanation:

The total mechanical energy (sum of potential and kinetic energy) of the book - Earth system is conserved in the absence of non - conservative forces (like air resistance, which is often ignored in basic cases). As the book falls, its height above the ground decreases, so its gravitational potential energy $U = mgh$ (where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height) decreases. At the same time, its speed $v$ increases, and its kinetic energy $K=\frac{1}{2}mv^{2}$ increases.

Answer:

The potential energy decreases as kinetic energy increases.