Sum of Potential and Kinetic Energies of a Free Falling Body

When a body falls freely, it experiences a change in its potential and kinetic energies. Here is an explanation of how the sum of potential and kinetic energies of the free falling body remains fixed:

Initial State:

- At the initial state, the body is at rest and has only potential energy.
- The potential energy of the body depends on its mass, height and acceleration due to gravity.
- Let us assume that the potential energy of the body is Ep.

When the Body Starts Falling:

- As the body starts falling, it loses its potential energy and gains kinetic energy.
- The kinetic energy of the body depends on its mass and velocity.
- Let us assume that the kinetic energy of the body is Ek.

During the Fall:

- As the body falls, its potential energy decreases and its kinetic energy increases.
- This happens because the body is gaining velocity as it falls towards the ground.
- At any point during the fall, the sum of potential and kinetic energies of the body is constant.
- This is because the total energy of the body is conserved, i.e., energy cannot be created or destroyed, only transformed from one form to another.

At the End of the Fall:

- When the body hits the ground, all of its potential energy is converted into kinetic energy.
- At this point, the sum of potential and kinetic energies of the body is equal to the initial potential energy, i.e., Ep.

Conclusion:

- The sum of potential and kinetic energies of a free falling body remains fixed throughout the fall.
- This is because the total energy of the body is conserved.
- The potential energy of the body is converted into kinetic energy as it falls towards the ground.
- At the end of the fall, all of the potential energy is converted into kinetic energy, and the sum of potential and kinetic energies is equal to the initial potential energy.