Law of conservation of energy is one of the most fundamental concept in all physics. This law states that energy can neither be created nor destroyed, but can only be transformed from one form to another.
For instance, when an object is at a certain height from surface of the earth, then the energy possessed by it is wholly potential energy. But, when it starts to fall on the surface of the earth, the potential energy gradually changes into the kinetic energy and when the object is just to hit the surface of the earth, then it has only kinetic energy.
When it hits the the surface, the kinetic energy gets transformed into sound, heat, and mechanical energy. But, at any instant of time, the total energy remains same in this process. Thus, the principle of conservation of energy may also be stated as “the total energy of any isolated system remains constant i.e. does not change”. An isolated system is a system that does not gain or loss energy when it contacts with another energy source.
This general law of energy conservation is true for all forces and for any kind of energy transformation between different forms of energy. It can be applied to all domains of nature, from the microscopic to macroscopic systems.
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Realtime Example of Energy Conservation
Let’s understand it with the help of real-time example. Suppose you have a bank account in a bank and contain a certain amount of money. Now suppose you have spent some money to purchase an item from another country, USA and your back account balance decreases. Your money is no longer in the form of rupees, but it has been transferred into another currency, such as dollars. Thus, your money was not lost. It only changed the forms.
Similarly, when an object is at a certain height from the ground, initially, it has only potential energy and zero kinetic energy. As soon as when it starts to fall into the ground, the potential energy gradually converts into an equal amount of the kinetic energy. After striking the ground, the kinetic energy is converted into sound, heat, and mechanical energy. In the whole process, energy never lost anywhere. It only transforms its form.
Mechanical energy is the sum of kinetic energy and gravitational potential energy of a system. If K denotes kinetic energy and U the potential energy of the system, then according to the law of conservation of mechanical energy,
K + U = constant
Hope that you will have understood basic concept of the law of energy conservation with the help of real-time example.
Now suppose the total money supply in a country is low, the government of the country can print more currency. But, in the world of physics, the total amount of energy throughout the universe remains fixed, and it is known as the law of conservation of energy. We can never truly destroy the energy. However, governments can collect and destroy the currency. Thus, the law of energy conservation tells the total energy is always conserved (i.e. can neither be created nor destroyed) in any system.
Verification of Law of Conservation of Energy
We can verify the law of conservation of energy by theoretically as well as experimentally as well. So, let’s first verify theoretically.
Theoretical Verification:
Suppose m be the mass of an object held at a position A at a height h above the ground, as shown in the below figure.
At position A:
Since the object is at rest at position A, its initial velocity is zero. Therefore,
Kinetic energy of the body (K.E.) = 0
Since the object is held at a height h, potential energy of the object (P.E.) = mgh
Thus, total mechanical energy at position A (E1) = K.E. + P.E. = 0 + mgh = mgh
Hence, E1 = mgh
Assume that the object be allowed to fall freely under the action of gravity. In the free fall, assume the object reaches the position B with a velocity v1 where AB = x.
At position B:
From the equation of motion,
v2 – u2 = 2as
v12 + 0 = 2gx (Here, acceleration is gravity)
v12 = 2gx . . . (1)
Kinetic energy of the object at position B (K.E.) = 1/2mv12 . . . (2)
Put the value of v12 from equation (1) into equation (2), we will get as:
K.E. = 1/2m(2gx) = mgx
Height of the object above the ground = CB = h – x
Thus, potential energy of the object at position B (P.E.) = mg(h – x)
Total mechanical energy at position B (E2) = K.E. + P.E. = mgx + mg(h – x)
Hence, E2 = mgx + mgh – mgx = mgh
Assume that the object be allowed to fall freely under the gravity. When it hits the ground at position C with a velocity v.
At position C:
From the equation of motion,
v2 – u2 = 2as
v2 – 0 = 2gh
v2 = 2gh . . . (3)
Kinetic energy of the object at position C (K.E.) = 1/2mv2 . . . (4)
Put the value of v2 from the equation (3) into the equation (4), we will get as:
K.E. = 1/2m(2gh) = mgh
Potential energy at the ground = mgh = mg(0) = 0 (because the object is on the ground. So, h = 0)
Total mechanical energy (E3) = mgh + 0 = mgh
Therefore, E3 = mgh
Thus, we get that
E1 = E2 = E3 = mgh (proved)
From the above equation, it is clear that the total mechanical energy (i.e. sum of kinetic energy and potential energy) always remains constant at each point of the motion of an object falling freely under the gravity. Hence, the mechanical energy is equal to mgh, which is the initial potential energy at a height h. As the object falls, its potential energy decreases and kinetic energy increases. The potential energy converts into kinetic energy.
At position A, the energy of the object is wholly potential energy. There is zero kinetic energy initially. At the position C, there is entirely kinetic energy but no potential energy. However, at the position B, energy is partly kinetic and partly potential. Hence, the total mechanical energy (i.e. mgh) is constant throughout. This proves the law of conservation of mechanical energy. The below figure shows the variation of conservation of mechanical energy for a freely falling body.
Experimental Verification:
Assume that we drop an object of mass 30 kg from a height 5 m. Let’s calculate the potential energy and kinetic energy of this freely falling object at different position of its downward moving. Assume that acceleration due to gravity g = 10 m/s2.
We will the use the following formulas for a free falling object.
- v2 – u2 = 2as
- K.E. = 1/2mv2
- P.E. = mgh
At a height 5 m, P.E. = mgh = 30 * 10 * 5 = 1500 J and K.E. = 0 because the object is at rest, zero initial velocity. It has only potential energy, but no kinetic energy. Thus, the total mechanical energy of the object = 1500 J + 0 = 1500 J.
As the object is allowed to fall freely under the action of gravity, the height of the object above the ground starts to decrease. Thus, the potential energy of the object also decreases. But, as the object falls, it gains the velocity. Therefore, its kinetic energy also increases due to the increase in its velocity.
At a height 4 m, P.E. = 30 * 10 * 4 = 1200 J
Distance travelled by the object when it falls freely = 5 – 4 = 1 m
So, v2 – u2 = 2as
v2 – 0 = 2 * 10 * 1 = 20 (m/s)2
Thus, v2 = 20 (m/s)2
Hence, its K.E. = 1/2 * 30 * 20 = 300 J
Total mechanical energy of the object at this position = 1200 + 300 = 1500 J.
Similarly, we can calculate the potential energy, kinetic energy, and mechanical energy at a height 3 m, 2 m, and 1 m.
As the object keeps on falling, its potential energy gradually transforms into an equal amount of kinetic energy. But, the sum of potential energy and kinetic energy (i.e. mechanical energy) remains constant (i.e. 1500 J) at every position during its free fall.
When the object is just above the ground, it has zero potential energy because the height h is zero.
Distance travelled by the object = 5 m
From the equation, v2 – u2 = 2as = 2 * 10 * 5 = 100 (m/s)2
v2 = 100 (m/s)2
Thus, K.E. = 1/2mv2 = 1/2 * 30 * 100 = 1500 J
Hence, the mechanical energy of the object when the object is just above the ground = 0 + 1500 = 1500 J.
At this position, all the potential energy is converted into kinetic energy because v becomes maximum. However, the total amount of energy remains the same (1500 J). Hence, it is clear from this example, energy is neither created nor destroyed. When the body strikes the ground, we will understand that the body comes to rest and a sound (of striking) is produced.
The ground where the body strikes also gets slightly heated. Therefore, when the object strikes the ground, it loses its kinetic energy because its whole energy is converted into heat and sound energy. But, the sum of both heat and sound energy remains constant (i.e. 1500 J). This again verifies the law of conservation of energy.
In this tutorial, we have explained the law of conservation of energy in physics with the help of real-time example. Hope that you will have understood the basic concepts and verification of the law of conservation of mechanical energy.
Thanks for reading!!!
