The Units of Kinetic Energy

Kinetic Energy is the energy stored in a body due to its motion. When work is done on a body, i.e., a force is applied, the body moves, and the net force is transferred to the body as Kinetic Energy. The Kinetic Energy of a body depends upon factors such as the body’s mass and velocity attained by the body due to the force applied to it. 

Joule is the SI metric unit for Kinetic Energy. 1 Joule can be defined as the energy stored in a body of mass 0.5 kg moving at a velocity of 1 m/s. Similarly, the CGS unit of kinetic energy is erg. 

Foundation of Kinetic Energy 

Kinetic Energy and Potential Energy constitute translational Mechanical Energy. It can be calculated by adding Potential Energy and Kinetic Energy. Mechanical Energy always stays constant. The Kinetic energy interchanges into Potential Energy and vice versa. 

Kinetic Energy is a form of energy based on a body’s motion. It can be transferred from one body to another body. Let us understand Kinetic Energy with an example. 

A cricketer throws a ball. Work gets done on the ball, and it attains Kinetic energy. The ball accelerates up to a certain velocity. The velocity would have been constant without the forces of friction and air resistance. Eventually, the velocity decreases, and the ball stops at a height. Some Kinetic energy gets converted into heat and the rest into Gravitational Potential Energy. When the ball falls, Potential Energy again gets transformed into Kinetic Energy until the catcher catches the ball. 

This example also proves that energy is always conserved. It is neither produced nor destroyed. The Kinetic Energy depends on the ball’s mass and velocity.

Kinetic Energy formula derivation

Kinetic Energy is a scalar quantity. It has only magnitude. The formula for Kinetic Energy of a body is ½ mv2, where the velocity of the body is much less than the speed of light ( v<<<c). 

The formula is derived by calculating the work done on a body. Suppose a force is applied to a body, and the body moves up to a certain distance. Let us assume the following:

• The mass of the body is m.
• The initial velocity of the body is u, and the final velocity of the body is v.
• The acceleration of the body is a.
• The force applied to the body is F.
• The total distance moved by the body is s.
• The work done is W.
• The Kinetic Energy obtained is K.

Now, the initial velocity will be zero, u=0.

According to the equation of motion, v²= u² + 2as

or, v²= 2as

or, a= v²/2s

According to Newton’s law of motion, F= ma

or, F= m x  v²/2s

or, F= 1/2s x mv²

According to the formula of work, W= F x s

    or, W= 1/2s x mv² x s

    or, W= ½ mv² 

We know W=K

Therefore, K=½ mv²

Units of Kinetic Energy

Joule (J) is the SI metric unit for Kinetic Energy. It can also be broken into kg.m²/s². Let us take an example:

A man cycles at a specific velocity. We will assume the following:

• The mass of the man and the bicycle will be x kg.
• The velocity of the bicycle will be y m/s.

Therefore according to the formula of Kinetic Energy, K=½ mv²

Or, K= xy² kg.m²/s²

This kg.m²/s² is also known as Joule(J). It should be noted that:

• 1 KJ= 10³ J
• 1mJ= 10-³ Z

Erg is the CGS unit for Kinetic Energy. To understand erg, we will take the same example of a man riding a bicycle and assume the following:

• The mass of the man plus bicycle will be x g.
• The velocity of the bicycle will be y cm/s.

Therefore according to the formula of Kinetic Energy, K=½ mv²

Or, K= xy² g.cm²/s²

This g.cm²/s² can also be called erg.

Conversion

We can convert the Si metric unit for Kinetic Energy into the CGS unit of kinetic energy, i.e., erg, in the following way: