Dimensional Formula of Kinetic Energy

Kinetic energy is the energy that is calculated when the object is in motion. The word kinetic is derived from a Greek word named kinetikos. Kinetikos means motion and kinein means ‘to move’. This word was first used around the 19th century.

Kinetic energy has its application in various daily activities. Like when a bullet is fired from a gun, we calculate its kinetic energy; if a car is moving with a certain velocity, then we calculate its kinetic energy. Moving air, running water, a child throwing a ball, a person walking at a certain speed and a rotating fan are other examples of kinetic energy.

Kinetic energy is greater for heavier objects. It changes its value only when the velocity changes as the mass remains constant. It maintains the energy during its acceleration. It can be transformed into other forms of energy, and it is measured in Joules (J).

Dimensional Formula

In terms of dimensions, a dimensional formula is an equation that expresses the relationship between fundamental and derived units (equation). The letters L, M, and T are used to represent the three basic dimensions of length, mass, and time in mechanics.

All physical quantities can be stated in terms of the fundamental (base) units of length, mass, and time, multiplied by some factor (exponent).

The dimension of the amount in that base is the exponent of a base quantity that enters into the expression.

The units of fundamental quantities are expressed as follows to determine the dimensions of physical quantities:

• ‘L’ stands for length

• ‘M’ for mass

• ‘T’ for time

Example: The area is equal to the product of two lengths. As a result, [A] = [L2]. That is, the area has two dimensions of length and zero dimensions of mass and time. In the same way, the volume is the product of three lengths. As a result, [V] = [L3]. That is, the volume dimension has three dimensions: length, mass, and time.

Kinetic Energy

Kinetic energy is also known as the energy of motion. Any moving object has kinetic energy in it.

Potential energy is also called stored energy, and it has several forms. For example, gravitational potential energy is stored in the object, and it is due to the object’s position on the earth’s surface. You must be familiar with roller coaster rides. When a roller coaster is on the top, it has the potential gravitational energy to go down.

Now, let’s learn how an object’s energy changes. When we try to lift any object like a rock from the ground, it increases the object’s potential energy, which is referred to as PE. Likewise, when we put the rock down, the gravitational pull increases the kinetic energy of the stone during this process until the rock is back on the ground.

The kinetic energy of an object depends on its mass and velocity (v). The formula for kinetic energy is:

KE=½ mv²

When we drop the object, the force of gravity starts its work, and it provides kinetic energy to the object. As only the kinetic energy is increasing, there is a change in the value of quantity ½ mv². 

This can be represented mathematically by the work-energy theorem:

W = ΔKE = ½ mv22  – ½ mv12

Where, v2 and v1 refer to the final and initial velocity of the object.

The work-energy theorem is derived from Newton’s Second Law of Motion and the force applied to a particle. The immediate power added to the system is determined by computing the scalar product of the forces with the particle’s velocity.

Dimensional Formula of Kinetic Energy

As we know that KE =  ½ mv²

Unit of M(mass) = M kilograms

Unit of velocity = metre/sec

But, here, we are dealing with v2  = [L2T-2]

Therefore,dimensional formula of KE = [M L2T-2]

Hence, the unit of Kinetic Energy = Mass (Length)2(Time)-2

The Dimensional formula of Kinetic Energy is [ML2T-2].

Where, M denotes the object’s mass, L denotes the length, and T is the time taken. 

Conclusion

Kinetic energy is the energy of an object which is possessed by virtue of its motion. It is defined by its formula, which is KE = ½ mv². Here, m is the mass of the body, and v is the velocity of the object by which it is moving. The dimensional formula of kinetic energy is given by [ML>2T^-2].. KE is a scalar quantity and can never be negative. The unit of kinetic energy is joule.