Question

If a ball falls in vacuum from a certain height describe the total energy, the kinetic energy, and the potential energy during the fall. Describe the energy values at the initial point (highest point), at an intermediate point during the fall, and at the final point (ground level). Make sure to mention how the free fall in vacuum is different from a real life fall.

Answer 1

If a body of mass m falls freely from a height H in vacuum then its initial velocity is zero. Hence its kinetic energy is zero and its potential energy is given by mgH. Hence the total energy is mgH. At inital position the total energy equals the potential energy.

During free fall, its potential energy decreases and its speed increases due to gravity. Hence the decrease in potential energy results in increase in kinetic energy. The total energy is sum of potential energy and kinetic energy.

When the body just reaches the ground then its potential energy is zero and is converted into kinetic energy. Hence the total energy is only kinetic energy.

At any instant the total energy of the body is mgH.

As the body is falling in vacuum then the total energy remains constant during its motion. But if it falls through air like in real life then due to air resistance the total energy continuously decreases. Hence final kinetic energy is less than its initial potential energy.