Question

an acorn rolls off a roof and falls to the ground. which statement best describes the change in energy? (1 point)
the acorns potential energy and kinetic energy increase and decrease together.
the acorns potential energy is change to mechanical energy.
the acorns kinetic energy increases until it hits the ground.
the acorns potential energy decreases as its kinetic energy increases.

Explanation:

• Potential energy ($PE = mgh$, where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height) depends on the height of the acorn. As the acorn falls, its height $h$ decreases. So, its potential energy decreases.
• Kinetic energy ($KE=\frac{1}{2}mv^{2}$, where $m$ is mass and $v$ is velocity). As the acorn falls, it accelerates (due to gravity, $v = v_0+gt$, assuming initial vertical velocity $v_0 = 0$ near the Earth's surface). So, its velocity $v$ increases, and thus its kinetic energy increases.
• Mechanical energy ($ME=PE + KE$) is conserved in the absence of non - conservative forces (neglecting air resistance). So, as $PE$ decreases, $KE$ increases.

• For the first option: Potential energy decreases and kinetic energy increases (not increasing and decreasing together).
• For the second option: Potential energy is converted to kinetic energy (mechanical energy is the sum of $PE$ and $KE$, not a conversion to it in this context).
• For the third option: Kinetic energy increases until it hits the ground, but it does not mention the decrease in potential energy which is also an important part of the energy transformation.

Answer:

The acorn’s potential energy decreases as its kinetic energy increases.