Step-by-step explanation:
The Law of Conservation of Energy states that in a closed system, the total energy remains constant over time. In other words, energy cannot be created or destroyed but can only change from one form to another. The forms of energy commonly considered are kinetic energy, potential energy, and various other forms like thermal, chemical, and so on.
For a body of mass \(m\) falling from a height \(h\) above the ground, we can express this law in terms of kinetic energy (\(KE\)) and potential energy (\(PE\)) as follows:
(a) At point A (initial position):
The body has potential energy (\(PE_A\)) due to its height above the ground, and its kinetic energy (\(KE_A\)) is initially zero because it's at rest.
\[PE_A = m \cdot g \cdot h\]
\[KE_A = 0\]
(b) At point B (some height above the ground):
As the body falls, it loses potential energy and gains kinetic energy.
\[PE_B = m \cdot g \cdot (h - h_B)\] (where \(h_B\) is the height of point B above the ground)
\[KE_B = \frac{1}{2} \cdot m \cdot v_B^2\] (where \(v_B\) is the velocity at point B)
(c) At point C (when it reaches the ground):
All potential energy is converted into kinetic energy.
\[PE_C = 0\]
\[KE_C = \frac{1}{2} \cdot m \cdot v_C^2\] (where \(v_C\) is the velocity at point C)
The Law of Conservation of Energy states that the total mechanical energy (\(ME\)), which is the sum of potential and kinetic energies, remains constant throughout the motion:
\[ME_A = PE_A + KE_A\]
\[ME_B = PE_B + KE_B\]
\[ME_C = PE_C + KE_C\]
So, for a body falling from point A to B to C:
\[ME_A = ME_B = ME_C\]
This law asserts that the total mechanical energy at any point during the fall (A, B, or C) is constant, assuming no external forces like air resistance or friction are acting on the body.