Kinetic Energy

Difficulty Level : Expert
Last Updated : 29 Sep, 2022

If one wants to accelerate an object, then one needs to apply force to it and if the applied force requires doing work. Then, after work has been done, energy must be transferred to the object which moves with a new speed. This energy transferred is known as kinetic energy, and it depends on the mass and speed of the object.

Kinetic energy can be transferred between objects and transformed into another form of energy. For example, a moving object might collide with a stationary object. Following the collision, some initial kinetic energy of the moving object might have been transferred into the stationary object or transformed into some other form of energy.

Energy

The capability to perform work is defined as Energy.
Its unit is similar to that of work, therefore, the SI unit of work or energy is equal to Joule (J).

Types of Energy

Energy is basically classified into two main categories that are:

(i) Kinetic Energy: The type of energy that is present in an object due to the property of its state.
e.g. a downhill skier, falling asteroid, collected water in a lake etc.
(i) Potential Energy: The type of energy that is present in an object due to the property of its motion.
e.g. a yoyo before it is released, a parked car, flowing water through a river etc.

Kinetic Energy

The kinetic energy by an object is defined as the energy that is generated due to the motion of the object. The kinetic energy by an object arises when it is allowed to accelerate, it requires the application of some forces on it that leads to the work done. Therefore, after the work is done the energy is transferred to the objects that lead to the motion of the object at a constant velocity. The energy that is transferred is called kinetic energy that totally depends on the speed and mass of the object in motion.

An object that is moving in a certain direction can do work. An object that is moving faster can do more work than an identical object that is moving relatively slowly. How much amount of energy is possessed by a moving object by virtue of its motion? By definition, it can be said that the kinetic energy of a body moving with a certain velocity is equal to the work done on it to make it acquire that velocity.

e.g. A moving bullet, blowing wind, a speeding stone, a rotating wheel can do work.
It is something to wonder, How does a bullet pierce the target? How does the wind move the blades of a windmill?
Examples of Kinetic Energy
Objects in motion possess energy. This energy is simply known to be kinetic energy. A falling coconut, a flying aircraft, a speeding car, flowing water, a rolling stone, blowing wind, a running athlete, etc. i.e. any moving object possesses kinetic energy.
In short, kinetic energy is the energy possessed by an object due to its motion. The kinetic energy of an object increases when the speed of the object increase.

Kinetic Energy Transformation

Kinetic energy transformation is possible between objects and also among different forms of energy. Dropping the ball is a very good example of kinetic energy transformation. When the ball is resting in hand, the energy contained in the ball is the potential energy due to its height. When it is dropped, the potential energy starts converting into kinetic energy due to its motion. When the ball is about to reach the ground, the entire potential energy is converted into kinetic energy.

Formula for Kinetic Energy

As kinetic energy of an object depends on o its mass and speed therefore mathematically, the kinetic energy is defined as:

$\textbf{K.E.}\bf{=\dfrac{1}{2}mv^2}$
Here, m is the mass of the object and
v is the speed or velocity of the object.

This, expression obtained is called kinetic energy equation.

Unit of Kinetic Energy

SI Unit:
The SI unit of kinetic energy is Joule (J) or kg.m².s^-2.
CGS Unit:
While in CGS system of units, the kinetic energy is defined in erg.

Since, mass (m) is a scalar quantity and velocity (v) is a vector quantity. But from the above formula it is observed that velocity is squared, and it is known that square of any vector quantity gives a scalar quantity.

Hence, kinetic energy is a scalar quantity.

Derivation for Kinetic Energy equation

Consider an object having mass m, initial velocity, u and final velocity, v.

Suppose when a constant force, F is applied to it, it displaces to a distance s.

Now, work is done by the object that is responsible to change in its velocity, the work done is:
W = F × s ……(1)
Let its velocity change from u to v and a is the acceleration produced.
Now, using the equation of motion that relates u, v, s and a as:
v² – u² = 2as
Solve above expression for s as:
$s=\dfrac{v^2-u^2}{2a}$
But it is known that, the net force acting on an object is defined as:
F = ma
Now, Substitute ma for F and \dfrac{v^2-u^2}{2a} for s in the equation (1) and solve to calculate W.
$\begin{aligned}W&=(ma)\left(\frac{v^2-u^2}{2a}\right)\\&=\dfrac{m(v^2-u^2)}{2}\end{aligned}$
Suppose the object is starting from its initial position, i.e. u = 0, then:
$\begin{aligned}W&=\dfrac{m(v^2-(0)^2)}{2}\\&=\dfrac{1}{2}mv^2\end{aligned}$
It is clear that the work done is always equal to the change in the kinetic energy of an object. So, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is
$\begin{aligned}\text{K.E.}=\dfrac{1}{2}mv^2\end{aligned}$

Types of Kinetic Energy

There are five types of kinetic energy:

Radiant Energy

Radiant energy is a form of kinetic energy, in which it is always in motion traveling through a medium or space.

e.g.:
Ultraviolet light
Gamma rays

Thermal Energy

Thermal energy can be also known as heat energy. It is generated due to the motion of atoms when they collide with each other.

e.g.:
Hot springs
Heated swimming pool

Sound Energy

Sound energy is the energy, produced by the vibration of an object. It travels through the medium but cannot travel in vacuum or space, as there are no particles to act as a medium.

e.g.:
Tuning fork
Beating drums

Electrical Energy

Electrical energy can be obtained from the free electrons that are of positive and negative charge.

e.g.:
Lightning
Batteries when in use

Mechanical Energy

The sum of kinetic energy and potential energy is called mechanical energy. It can neither be created nor destroyed but it can be converted from one form to other.

e.g.:
Orbiting of satellites around the earth
A moving car

Difference Between Kinetic Energy and Potential Energy

Kinetic Energy	Potential Energy
Kinetic energy is created by the motion of the object.	Potential energy is created by the position and orientation of the object.
K.E. = 1/2mv²	P.E. = mgh
An example of kinetic energy is vibrational energy.	An example of potential energy is spring energy.

Solved Examples on Kinetic Energy?

Example 1: A vehicle having mass of 150 kg, is moving with a uniform velocity of 4 m/s. What is the amount of kinetic energy possessed by the vehicle?

Solution:

Given that,
The mass of the vehicle, m = 150 kg,
The velocity of the vehicle, v = 4 m/s
The kinetic of the vehicle is,
$\begin{aligned}\text{K.E.}&=\dfrac{1}{2}mv^2\\&=\dfrac{1}{2}\times150\text{ kg}\times(4\text{ m/s})^2\\&=1200\text{ J}\end{aligned}$
Hence, the kinetic energy of the vehicle is equal to 1200 J.

Example 2: A ball having a mass of 2 kg is thrown up with a speed of 10 m/s. What is the kinetic energy stored in the ball at the time of throwing?

Solution:

Given that,
The mass of the ball, m = 2 kg,
The velocity of the ball, v = 10 m/s.
The kinetic of the ball is,
$\begin{aligned}\text{K.E.}&=\dfrac{1}{2}mv^2\\&=\dfrac{1}{2}\times2\text{ kg}\times(10\text{ m/s})^2\\&=100\text{ J}\end{aligned}$
Hence, the kinetic energy of the ball is equal to 100 J.

Example 3: An asteroid is coming towards the earth. Its velocity is 1000 km/s. Its estimated kinetic energy is almost 4 × 10¹⁵ J. Find out the mass of the asteroid.

Solution:

Given that,
The kinetic energy of the asteroid, K.E. = 4 × 10¹⁵ J,
The velocity of the asteroid, v = 1000 Km/s = 10⁶ m/s
Since, the kinetic of the asteroid is given as,
$\begin{aligned}\text{K.E.}&=\dfrac{1}{2}mv^2\\4\times10^{15}\text{ J}&=\dfrac{1}{2}\times m\times(10^6\text{ m/s})^2\\&m=8000\text{ kg}\end{aligned}$
Hence, the mass of the asteroid is equal to 8000 kg.

My Personal Notes

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