The law of conservation of energy states that the total energy of a closed system remains constant over time. In the case of an object falling vertically under the influence of gravity, the potential energy is converted into kinetic energy as the object descends. However, it's important to note that the formulas you mentioned, namely potential energy (MGH) and kinetic energy (1/2mv^2), have different reference points and are calculated differently. This is why they may not be equal in a specific scenario.
Potential energy (PE = MGH) is the energy an object possesses due to its position in a gravitational field. It is calculated relative to a chosen reference point, typically the ground level. The potential energy is maximum at the highest point and decreases as the object falls.
Kinetic energy (KE = 1/2mv^2) is the energy associated with an object's motion. It depends on the mass of the object (m) and its velocity (v). Kinetic energy increases as the object accelerates during its fall.
The law of conservation of energy still holds in this scenario. As the object falls, potential energy is converted into kinetic energy. The total mechanical energy (the sum of potential and kinetic energy) of the system remains constant, neglecting other factors like air resistance or energy losses due to friction. Therefore, while the potential energy and kinetic energy values may differ at any given point during the object's fall, their sum remains constant.
At the highest point of the fall, the object has maximum potential energy and zero kinetic energy. As it descends, potential energy decreases, and kinetic energy increases accordingly. At the lowest point of the fall, potential energy is zero (since it's relative to the reference point), and kinetic energy is at its maximum.
In summary, the difference in values between potential energy and kinetic energy is due to the different nature of the quantities being calculated and their respective reference points. The law of conservation of energy is upheld, ensuring that the total energy of the system remains constant.