A Brief Note On Conservation Of Mechanical Energy

Every object has the ability to do mechanical work. An object possesses stored energy and kinetic energy. Both forms of energy together form the total mechanical energy. In a closed system, mechanical energy can neither be increased nor decreased, but it remains constant throughout the motion. This phenomenon is known as the law for the conservation of mechanical energy. 

With the law of conservation of mechanical energy equation, we can find the velocity of an object as well as its total mechanical energy.

What is mechanical energy?

Mechanical energy is an object’s capability to do mechanical work. Energy is stored in an object as potential energy. And the energy acquired due to the motion or movement of the object is kinetic. The sum of stored energy (potential) and kinetic energy in a system equals the total mechanical energy of the closed system.

Mechanical energy = P.E. + K.E.

Types of mechanical energy

The two types of mechanical energy include: 

• Potential Energy

• Kinetic Energy

Potential energy

At rest, the potential energy is the energy stored in a body. It depends upon physical factors like the mass and position of the object. Gravitational, elastic, magnetic, chemical, and electric are the types of potential energy.

The formula for the gravitational potential energy is as follows:

P.E. = mgh 

Where, 

P.E. → Potential energy

m → mass in kilograms 

g → acceleration due to gravity 

h → height in metres

Kinetic energy

The energy caused due to an object’s motion or movement is its kinetic energy. An object’s ability to move depends both on its mass and its movement. The faster a body moves, the greater is its kinetic energy. The highest point to which a body can accelerate is known as the body’s highest kinetic energy.

The formula for Kinetic energy is as follows:

K.E. = 1/2 mv2

Where,

K.E. → Kinetic energy

m → mass

v → velocity

Law of conservation of mechanical energy

As discussed above, mechanical energy is the sum of potential and kinetic energy of an object. This sum always remains constant. The reason for the mechanical energy of an object to remain constant is that it does not increase or decrease based on external factors. But, it only depends on the physical properties of the object under consideration. The law of conservation of mechanical energy thus proves that energy can neither be generated nor destroyed. It is always conserved. The law of conservation of mechanical energy also explains that the energy can only transform into different forms of energy.

An example to understand the law of conservation of mechanical energy

When a simple pendulum is at its mean position, it has zero potential energy and maximum kinetic energy. As the pendulum moves from its resting position, it gains potential energy and the kinetic energy reduces to zero. This is the example of the law of conservation of mechanical energy where all the kinetic energy that was present in the pendulum gets converted into potential energy.  

Law of conservation of mechanical energy equation

The law of conservation of mechanical energy proves that the sum of the potential energy and kinetic energy at any position in a closed system will always remain the same. The amount of potential energy and kinetic energy keeps changing, but the total mechanical energy in a system remains constant.

• It is impossible to create or destroy energy in a system with no non-conservative forces.

• One form of energy can be transformed into another form.

A non-conservative force is a force that is dependent upon the path of the object. Air resistance and friction are non-conservative forces. When there is no non-conservative force present, the mechanical energy is always conserved and hence, it remains constant. The mechanical energy at the start is thus always equal to the mechanical energy at the end.

Mechanical energyi = Mechanical energyf

(P. E.)i  + (K. E.)i  =  (P. E)f + (K. E.)f

mghi  +  1/2 mv2i   =  mghf +  1/2mv2f

m→ mass in kilograms

v→ velocity

h→ height in metres

g→ acceleration due to gravity

Conclusion

The conservation of mechanical energy is the fundamental law of the universe. We can determine the energy capacity of an object using the law of conservation of energy. This object can be a car, a watch or even a tiny particle. Additionally, the sum of the potential energy and the kinetic energy form the total mechanical energy in a closed system. The law of conservation states that this total mechanical energy always remains constant in any part of the universe. Its universality makes it applicable to physics and thermodynamics.