Constant
Explanation
The Law of Conservation of Mechanical Energy. This principle states that the total mechanical energy of a system remains constant if the only forces doing work are conservative forces, such as gravity.
Detailed Analysis:
- Mechanical Energy is defined as the sum of Potential Energy (PE) and Kinetic Energy (KE).
- During free fall, an object moves downwards under the influence of gravity. As the height of the object decreases, its Gravitational Potential Energy ($mgh$) decreases.
- Simultaneously, the object accelerates, causing its velocity to increase. This results in a corresponding increase in Kinetic Energy ($\frac{1}{2}mv^2$).
- Since air resistance is ignored, there are no dissipative forces to remove energy from the system. Consequently, the decrease in Potential Energy is exactly equal to the increase in Kinetic Energy.
- Therefore, at every point during the fall, the sum of Potential Energy and Kinetic Energy remains constant.
Key Takeaway:
In the absence of non-conservative forces like air resistance or friction, the total mechanical energy (PE + KE) of a freely falling body is conserved throughout its motion.