Energy exists in various forms on the Earth. These forms are kinetic energy, potential energy, heat energy, chemical energy, sound energy, etc. Kinetic energy is connected with the movement of the object. Kinetic energy occurs in everything that moves. This energy is transferred between objects during collisions or when work is done.
In this article, we will examine the definition of kinetic energy, formula, derivation, and its types. Further, we will look at some solved numerical examples of kinetic energy.
What is Kinetic Energy (K.E)?
The energy that a body has due to its movement is known as Kinetic Energy (K.E). When an object is in motion, it possesses kinetic energy. The amount of K.E. is dependent on the object’s speed and mass. The kinetic energy increases with increasing the object’s velocity and mass.
Kinetic energy is a scalar quantity with magnitude but no direction. A moving car, a flying bird, and a rolling ball are some examples of kinetic energy. Joule (J) is an SI unit of kinetic energy.
The equation to determine the Kinetic Energy:
The equation or formula for finding kinetic energy is given below:
Where,
- K.E is the kinetic energy, that is measured in joule (J)
- m is the mass, that is measured in kilograms (kg).
- v is the velocity, that is measured in meters per second (m/s).
Derive the equation of kinetic Energy:
Let’s suppose an object with mass ‘m’ is moving at velocity ‘v’. The body stops after moving through some distance S due to opposing forces such as the force of friction. The body possesses K.E and is capable to do work against opposing force F until all of its kinetic energy is used up.
∴ K.E of an object = work done by it due to motion
K.E = F × S ____ (Eq. 1)
vi = v
vf = 0
F = ma (Equation of Newton’s second law)
∴ a = – F / m (Force is opposing the motion of the object, therefore acceleration will be negative)
Using the third equation of motion:
2aS = vf2 – vi2
2 (- F / m) S = (0) 2 – (v) 2
F × S = (1/2) mv2
From Eq. 1, we get
K.E = (1/2) mv2
Common types of Kinetic Energy:
Let’s discuss the most common types of kinetic energy:
Translational Kinetic Energy refers to the energy possessed by the body due to its straight or linear motion. A speeding train moving on the tracks, a bullet traveling through the air, or a car accelerating on a highway are some examples of translational kinetic energy.
Rotational kinetic Energy is associated with an object that spins or rotates around an axis. A rotating ceiling fan and a rotating Earth on its axis are examples of rotational K.E.
Vibrational Kinetic Energy is present in objects due to their vibrating or oscillating motion. Examples include a vibrating guitar string or the oscillating motion of a pendulum.
Thermal K.E. is related to the temperature of the object. An object has thermal K.E. due to the arbitrary motion of particles within a substance. Heat energy in a hot cup of coffee or the thermal energy in a boiling pot of water are examples of thermal K.E.
Application of Kinetic Energy:
Kinetic energy has many applications in our daily lives. Some of these are here:
- Kinetic energy is used to generate electricity with different methods. Wind turbines change the
K.E of the wind into electrical energy. Hydroelectric power plants generate electricity using the kinetic energy of flowing water.
- Kinetic energy is used in vehicles like cars, bikes, and trains to move us from one place to another. The engine converts the fuel’s chemical energy into kinetic energy and moves the vehicle forward.
- Different household appliances use kinetic energy to function. For example, blenders, mixers, and food processors use the kinetic energy of rotating blades or beaters to process and mix food ingredients.
- Many sports activities rely on kinetic energy. Running, cycling, swimming, and playing ball sports all involve the conversion of kinetic energy to achieve movement, speed, and performance.
Solved Numerical Examples of Kinetic Energy
Example 1:
A car with a mass of 1350 kg is traveling on the highway at a velocity of 25 ms-1. Estimate the kinetic energy of this car.
Solution:
Given data:
Mass (m) = 1350 kg
Velocity (v) = 25 m/s
∴ K.E = (1/2) mv2
Put the given values:
K.E = (1/2) × 1350 kg × (25 m/s) 2
= (0.5) × 1350 kg × 625 m2/s2
K.E = 421,875 Joules
Thus, the kinetic energy of the car is 421,875 joules.
You can also take assistance from a kinetic energy calculator to find the solution of the numerical problems of K.E with steps.
Example 2:
A boll with a mass of 160 grams is rolling at a velocity of 80 km/h. Measure the kinetic energy of the ball.
Solution:
Given data:
Mass of the ball = 160 grams = 0.16 kg
∴ 1 kilogram = 1000 gram
Velocity of the ball = 80 km / h = 22.22 m/s
∴ 1 hours = 3,600 second
Substitute the given values in the equation of kinetic energy, we get
K.E = (1/2) × 0.16 kg × (22.22 m/s) 2
= 0.5 × 0.16 kg × 493.72 m2/s2
K.E = 39.49 Joule
Hence, the kinetic energy of the ball is 39.49 joules.
Conclusion
In this article, we discussed the definition of kinetic energy. We examined the kinetic energy equation and learned how to derive this equation. We described the common types of kinetic energy. The application of Kinetic energy has been covered in this article.