Question

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

Answer 1

Hint: The law of conservation of energy is a universal law, so the chances of it being violated are very low, close to none actually. Now if potential energy is decreasing progressively, there must be some other form of energy it is being converted into. And in turn that form of energy is maintaining the balance of the total mechanical energy of the free falling body.

Complete step-by-step answer:
The law of conservation of energy states that energy can neither be created nor destroyed, but only changed from one form into another or transferred from one object to another. In others the total mechanical energy of a system remains constant if the internal forces are conservative and the external forces do not work.
Potential energy, P.E., is the energy held by an object due to its position relative to other objects, stresses within itself, its electric charge, or other factors. An object tends to possess gravitational potential energy if it is positioned at a height above the ground. Similarly, an object tends to possess elastic potential energy if it is at any position on an elastic medium other than the equilibrium position.
For a body of mass, m at a certain height, h above the ground the potential energy, P.E. is given mathematically as:
$P.E. = mgh{\text{ }} \cdots \cdots \cdots \cdots \cdots \left( 1 \right)$
Kinetic energy is the energy possessed by a moving object due to its motion. In order words it can be defined as the work needed to accelerate a body of given mass from rest to its stated velocity.
For a body of mass, m moving with velocity, v the kinetic energy, K.E. is given mathematically as:
$K.E = \dfrac{1}{2}m{v^2}{\text{ }} \cdots \cdots \cdots \cdots \cdots \left( 2 \right)$
Total energy of an object is the sum of its potential energy and kinetic energy, given that no external force is acting on it.
 $\eqalign{
  & {\text{Total energy = Potential energy + Kinetic energy}} \cr
  & T.E.{\text{ }} = P.E. + K.E. \cr} $
$T.E. = mgh + \dfrac{1}{2}m{v^2}$
Now when a body free falls under gravitational force its height from the ground decreases progressively. Therefore potential energy keeps decreasing progressively too.
$h \downarrow {\text{ P}}.E. \downarrow $

But as potential energy decreases, kinetic energy, K.E. increases because the velocity of the free falling body keeps increasing progressively until it reaches the terminal velocity.
$v \uparrow {\text{ }}K.E. \uparrow $
The progressive decrease in the potential energy is equal to the progressive increase in the kinetic energy of the body. In other words the potential energy of the body changes into the kinetic energy of the same progressively. Hence throughout the process, the total mechanical energy of the body remains conserved. Therefore, the law of conservation of energy is not violated.

Note: To answer this question correctly, students must make sure to use the theoretical explanation as well as the mathematical equations and expression to support their answers. Do not represent the kinetic and potential energy as K and P respectively, as K represents Kelvin and P represents pressure. Each symbol in physics has its defined scope. Make sure to use proper notations in your answer.