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Law of Conservation of Energy : Formulas and Derivation

Jul 18, 2022


The existence of organisms on earth varies on energy. It is referred to as the ability to perform work in physics. We are aware that energy can take on several forms in nature. Students must have studied the numerous types of energy, including heat, chemical, electrical and nuclear. In this article, students will understand the major law of conservation of energy. Among these, the most common law is the law of conservation of energy.

What is the law of conservation of energy?

As per the energy conservation law, energy cannot be created or destroyed. However, it is capable of changing from one state to another. An isolated system’s total energy is constant regardless of the types of energy present. All energy sources adhere to the law of conservation of energy. The laws of conservation of  energy explain that:


In an isolated system, i.e., a system closed from all its surroundings, the overall energy is stored.

Therefore, in a closed system like the universe, the object must gain energy in a different area of the system if an equal quantity of energy is lost in one area. There is no known instance of energy conservation being broken, even though people cannot prove it.


The following equation estimates the total amount of energy in any system:

UT = Ui + W + Q


UT = system’s overall energy

Ui = system’s initial energy


Q = the total amount of heat added or removed from the system

W = the work that the system does or delivers.


The equation calculates the changes in the system’s internal energy.

Change U = W + Q


Law of Conservation of Energy Formula and Derivation

Considering that no potential energy is present at the earth’s surface. For instance, let’s look at an apple falling to the ground.

Consider location A on the tree that is H feet above the ground; the apple’s potential energy is at its highest because its velocity is zero.


E = mgH (equation 1)

The apple’s potential energy decreases, and its kinetic energy rises as it falls.

Point B, which is close to the bottom of the tree, the apple is falling quickly under the law of gravity and at a height X from the ground, thereby reaching its maximum speed. It is also moving as it approaches point B. It will therefore possess both potential and kinetic energy at this time.

E = K.E + P.E

P.E = mg X (equation 2)

 As per the third equation of motion,

V2 = 2g (H – X)

½ mv2 = ½ m.2g (H – X)

K.E = ½ m.2g (H – X)

K.E = mg (H – X)

K.E = mg (H – X) (equation 3)

Using equations 1, 2 and 3

E = mg (H – X) + mgX

E = mg (H – X + X)

E = mgH

Like this, mgH will be revealed as the energy at point C, at the base of the tree. The apple falls to the ground, and as it does so, potential energy is transformed into kinetic energy. Therefore, there must be a point at which kinetic and potential energy are equal. Consider that we need to determine the height ‘x’ above the ground. At that time, we are aware of

K.E = P.E

P.E = K.E = E/2 (equation 4)

The body (apple) is X feet above the ground, therefore

P.E = mgX (equation 5)

With equations 4 and 5, we have,

mgX = mgH/2

X = H/2

The new height is referred to as H/2.

Curiously Enough

Energy conservation is not just about reducing the usage of resources that will eventually become completely depleted. Reducing consumption on a finite supply while allowing that supply to start rebuilding itself would be the perfect conservation method. The easiest method to accomplish this is frequently to find a substitute for the energy being utilized.

Examples of the Law of Conservation of Energy

What is the law of conservation of energy? The law of conservation of energy emphasizes the fact that energy cannot be created or destroyed. It’s critical to comprehend what that signifies. It would be inadequate to say that the goal of an experiment is to produce energy because doing so would entail trying to create an impossibility. Instead, energy is continuously changed so that people can use it effectively. For instance, solar energy is not produced by solar panels. They capture solar energy and convert it into a different kind of energy (electricity).

In daily life, there are several examples of the law of conservation of energy in action.

People can exchange energy with one another or with objects. The law of energy conservation is demonstrated in each of these instances.

Examples of Energy Conservation with People

  • When Megan hurried across the room, she ran into her brother and knocked him to the ground. Her brother moved due to receiving the kinetic energy she had created while moving.
  • A collision between two basketball players sent them flying backward on the court. Each player’s energy was transmitted to the other, propelling them in the reverse direction from where they had been going.
  • A person’s energy from his moving arm is transmitted from his body to the cup as he pushes the cup around the table.
  • Energy is transmitted from the goalkeeper’s foot to the football when it is kicked on the ground, establishing the ball in motion. 
  • Samantha needed assistance moving the large sofa as she was rearranging the furniture. When his brother arrived, they could move the sofa all across the room together. The energy was transmitted from the men to the furnishings as the sofa moved across the carpeted floor.
  • When fingers strike the keys, energy is transferred from the pianist’s hand to the piano keys.
  • Jimmy struck the motionless bag with his fist, transmitting energy from his arm to the bag.
  • Amy slammed against the wall so forcefully that she made a hole. The drywall began to move due to Amy’s body transferring energy to it.

Examples of Energy Conservation with Objects

Energy will move from one thing to the other when two objects interact or collide with one another.

  • The pitched ball is aimed at a standing eight-ball while playing pool. The pitched ball is animated. The eight-ball moves when the pitched ball strikes it because the pitch ball’s energy is transferred to it. As a result of its energy being transferred to the eight-ball, the pitched ball loses momentum and comes to a halt.
  • A basketball strikes the window frame, breaking the glass. The glass received energy from the ball, which caused it to break into fragments and fly in different directions.
  • Mechanical energy is transmitted from the speeding vehicle to the parked car when a speeding vehicle hits the parked car and causes the parked car to move.
  • Jessica threw a ball, which struck and broke her mother’s vase. The vase moved due to energy being transferred from the rolling ball to the spill vase.
  • A traffic sign that is struck by a car will topple over. The sign will move due to energy being transmitted from the moving automobile to it.
  • The automobile crashed against the curb and disintegrated. The cement, which was not moving, began to move due to energy being transmitted from the moving car.


According to the law of conservation of energy, energy can only be transformed from one type of energy to the other and cannot be created or destroyed. It indicates that unless energy is added from the outside, a system consistently has the same quantity of energy. In the situation of non-conservative energies, where energy is changed from mechanical energy to thermal energy, yet the overall energy does not change, this is especially perplexing. Thus, energy must be changed from one state to another to be used. 

Frequently Asked Questions 

1. What is the law of conservation of energy?

Ans. According to the physical theory of the law of energy conservation, energy can neither be created nor destroyed, but it can transform from one type to another. The total energy of a closed system stays unchanged or is preserved within a specific frame of reference, which is another way to state this scientific law. 

Energy and mass conservation are two distinct rules in classical physics. However, as per the renowned equation E = mc2, in special relativity, the substance can turn into any form of energy and vice versa. Therefore, it would be more accurate to argue that mass-energy is preserved.

2. What are the consequences of the law of conservation of energy?

Ans. One of the fascinating consequences of the law of conservation of energy is that it is a form of perpetual motion machine that cannot exist. In other words, a system needs an external power source to continually and infinitely send energy to its circumstances.

It’s essential to look that not every system exhibits time translation symmetry; hence it’s not always viable to describe the conservation of energy. For instance, curved spacetimes or time crystals cannot define energy conservation law.

3. Give an illustration of how potential energy gets transformed into kinetic energy.

Ans. The potential energy in a firecracker, for instance, transforms into kinetic energy, light, and heat during an explosion. The total amount of energy equals the potential energy at the beginning.

law of conservation of energy

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