law of conservation of energy | conservation of energy during freely falling body | simple pendulum

Описание: Energy can be transformed (or changed) from one form to another.
According to the law of conservation of energy : Whenever energy changes from one form to another, the total amount of energy remains constant.
In other words, when energy changes from one form to another, there is no loss or gain of energy.
The total energy before and after transformation remains the same.
Another definition of the law of conservation of energy is that : Energy can neither be created nor destroyed.
During the conversion of energy from one form to another, some energy may be wasted.
For example, when electrical energy is converted into light energy in an electric bulb, then some electrical energy is wasted in the form of heat.
Although some energy may be wasted during conversion, but the total energy of the system remains the same.
Suppose we have a ball of mass m and we raise it to a height h above the ground.
The work done in raising the ball gives it a potential energy equal to m ×g×h.
Let us allow the ball to fall downwards.
As the ball falls, its height h above the ground decreases and thus the potential energy also decreases.
But as the ball falls, its velocity v constantly increases and, therefore, its kinetic energy 1 /2 mv2 also increases.
As the ball falls more and more, its potential energy is gradually converted into an equal amount of kinetic energy.
But the sum of potential energy and kinetic energy of the ball remains the same at every point during its fall.
When the ball just reaches the ground, its potential energy becomes zero (because h becomes zero) and its kinetic energy becomes the maximum (because v becomes the maximum).
At this stage, all the potential energy has been converted into kinetic energy.
From this we conclude that the potential energy of ball has been changed into an equal amount of kinetic energy.
There is no destruction of energy, and the total amount of energy remains constant.
This is an example of the conservation of energy during the free fall of a body.
When a falling ball hits the ground, a sound (of hitting) is produced and the ground (where the ball hits) also gets heated slightly.
This means that when a falling ball hits the ground, then some of its kinetic energy is converted into sound energy and heat energy.
But the total energy (kinetic energy + sound energy + heat energy) remains the same.
Thus, the law of conservation of energy is valid even after the ball hits the ground.
The conservation of energy during the free fall of a body will become more clear from the following data obtained in an experiment in which the potential energy (P.E.) and kinetic energy (K.E.) of a freely falling ball were calculated at different positions of its downward journey :
We can see from the data given in Figure 65 that :
(i) At position A, when the ball is at rest, it has 20 J of potential energy but zero kinetic energy. So, the total energy of the ball at position A is 20 + 0 = 20 J.
(ii) At position B when the ball is falling, it has 15 J of potential energy and 5 J of kinetic energy. So, the total energy of the ball at position B is 15 + 5 = 20 J.
(iii) At position C when the ball has fallen by half the distance, it has 10 J of potential energy and 10 J of kinetic energy. So, the total energy of the ball at position C is 10 + 10 = 20 J.
(iv) At position D when the ball has fallen by more than half the distance, it has 5 J of potential energy and 15 J of kinetic energy. So, the total energy of the ball at position D is 5 + 15 = 20 J.
(v) At position E when the ball is about to hit the ground, it has 0 J of potential energy and 20 J of kinetic energy.
So, the total energy of the ball at position E is 0 + 20 = 20 J.
It is clear from the above observations that as the ball falls downwards, its potential energy goes on decreasing but its kinetic energy goes on increasing.
The decrease in potential energy of the freely falling ball at any point in its path appears as an equal increase in its kinetic energy.
So, the total energy (potential energy + kinetic energy) of the ball remains the same (20 joules) at every point during its free fall.
Thus, the energy of a freely falling ball is conserved.
If, however, a ball is thrown upwards, then its kinetic energy goes on decreasing and its potential energy goes on increasing.
The decrease in kinetic energy of the upward going ball at any point during its flight appears as an equal increase in its potential energy.
But the total energy (kinetic energy + potential energy) of a ball thrown upwards remains constant at every stage of its flight.
In this way, the energy of a ball thrown upwards is also conserved.
We will now discuss the case of a simple pendulum