Question

The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?

Answer 1

Potential Energy of a Freely Falling Object and Conservation of Energy 

1. Observation

When an object falls freely under gravity, its potential energy (PE) decreases as it approaches the ground. The formula for potential energy is:

\( PE = m g h \)

where \( m \) = mass of the object, \( g \) = acceleration due to gravity, and \( h \) = height above the ground.

2. Does this violate the Law of Conservation of Energy?

No, it does not violate the law of conservation of energy. The law states that:

"Energy can neither be created nor destroyed, it can only change from one form to another."

In the case of the falling object:

• As height decreases, potential energy decreases.
• At the same time, the object’s kinetic energy (KE) increases because its velocity increases. The formula for kinetic energy is: 
  \( KE = \frac{1}{2} m v^2 \)
• The sum of potential energy and kinetic energy remains constant (ignoring air resistance): 
  \( PE + KE = \text{constant} \)

3. Energy Transformation

The process involves conversion of energy:

Gravitational Potential Energy → Kinetic Energy

Initially, the object has maximum potential energy at height \( h \) and zero kinetic energy. As it falls, PE decreases while KE increases, keeping total mechanical energy constant.

4. Conclusion

The decrease in potential energy of a freely falling object does not violate the law of conservation of energy because the lost potential energy is completely converted into kinetic energy.