Short Answer:
Kinetic energy is the energy possessed by a body due to its motion. Any object that is in motion, whether it is moving in a straight line or rotating, has kinetic energy. The amount of kinetic energy depends on the mass of the object and the square of its velocity.
In simple words, when an object starts moving, it gains energy because of its motion. If the object moves faster or has more mass, it will possess more kinetic energy. The SI unit of kinetic energy is Joule (J), and it is given by the formula KE = ½ m v², where m is the mass and v is the velocity.
Detailed Explanation:
Kinetic Energy
The word kinetic is derived from the Greek word kinesis, meaning motion. Hence, kinetic energy refers to the energy a body possesses because it is moving. This energy is a form of mechanical energy, and it plays a very important role in mechanics and engineering applications, such as in engines, turbines, moving vehicles, and machines.
Whenever a body is in motion, work must have been done on it to set it in motion. The energy required to perform that work is stored in the body as kinetic energy. If the body stops moving, the kinetic energy becomes zero.
Thus, kinetic energy can be defined as:
“The energy possessed by a body due to its motion is called kinetic energy.”
Mathematical Expression for Kinetic Energy
Consider a body of mass m moving with an initial velocity u. A force F acts on it and produces a uniform acceleration a, causing the velocity to increase from u to v in a displacement s.
From Newton’s second law of motion:
The work done by the force on the body:
Substituting :
From the equation of motion:
Substituting this in the above equation,
If the body starts from rest (i.e., ), then:
Since the work done on the body is stored as energy,
Thus, the kinetic energy of a moving body depends on two factors:
- Mass of the body (m) – greater the mass, greater the kinetic energy.
- Velocity of the body (v) – greater the velocity, much greater the kinetic energy (since KE ∝ v²).
Units and Dimensions of Kinetic Energy
- SI Unit: Joule (J)
- CGS Unit: Erg
- Dimensional Formula:
Types of Kinetic Energy
Kinetic energy can exist in two main forms depending on the type of motion of the body:
- Translational Kinetic Energy
- Rotational Kinetic Energy
Let us understand them one by one:
- Translational Kinetic Energy
This is the energy possessed by a body moving in a straight line. It depends on the linear velocity of the body.
The expression for translational kinetic energy is:
Examples:
- A car moving on the road.
- A falling stone.
- A bullet fired from a gun.
The faster the body moves, the greater its translational kinetic energy.
- Rotational Kinetic Energy
When a body rotates about an axis, every particle in it has some linear velocity, and therefore, the whole body possesses rotational kinetic energy.
The expression for rotational kinetic energy is:
Where,
- = Moment of inertia of the rotating body (kg·m²)
- = Angular velocity (radians/second)
Examples:
- A spinning wheel or flywheel.
- A rotating shaft in an engine.
- A wind turbine blade in motion.
Thus, both translational and rotational kinetic energy are important in mechanical systems that involve motion.
Relation between Work and Kinetic Energy
The work-energy principle states that:
“The work done on a body is equal to the change in its kinetic energy.”
Mathematically,
This means that when positive work is done on a body, its kinetic energy increases, and when negative work is done (like friction), its kinetic energy decreases.
Example:
- When brakes are applied to a moving vehicle, work is done by the frictional force in the opposite direction of motion, thereby reducing its kinetic energy.
Factors Affecting Kinetic Energy
- Mass of the Object:
- Heavier bodies possess more kinetic energy at the same speed.
- Velocity of the Object:
- Kinetic energy increases with the square of velocity.
- If velocity doubles, kinetic energy becomes four times greater.
- Type of Motion:
- The energy varies with whether the motion is translational or rotational.
- External Forces:
- The work done by forces like gravity or friction affects kinetic energy directly.
Examples of Kinetic Energy in Daily Life
- A moving car or bus possesses kinetic energy due to its motion.
- Flowing water in rivers has kinetic energy, which is used in hydroelectric power plants.
- Wind turbines rotate due to the kinetic energy of moving air.
- A rolling ball on the ground has both translational and rotational kinetic energy.
- A rotating fan or flywheel stores kinetic energy that helps it continue to move even after power is switched off.
Applications of Kinetic Energy
- Transportation Systems:
Used in calculating braking distance and vehicle impact energy. - Power Generation:
Wind and hydroelectric systems convert kinetic energy into electrical energy. - Machinery and Engines:
Rotating components like turbines, shafts, and gears store kinetic energy to maintain smooth operation. - Projectiles and Missiles:
The kinetic energy of moving objects determines their impact power. - Energy Storage Devices:
Flywheels use rotational kinetic energy for storing and releasing energy.
Conclusion
Kinetic energy is the energy possessed by a body due to its motion. It depends on both the mass and the square of the velocity of the object. The faster and heavier an object is, the greater its kinetic energy. It exists mainly as translational or rotational energy and is directly related to the work done by or on a body. Understanding kinetic energy is fundamental in mechanical engineering because it helps in analyzing motion, machine operation, energy conversion, and efficiency of systems.