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Kinetic Energy

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Kinetic Energy is the energy associated with an object moving with a velocity. For an object of mass m and velocity, its kinetic energy is half of the product of the mass of the object with the square of its velocity. In our daily life, we observe kinetic energy while walking, cycling, throwing a ball, and others. Learn Kinetic Energy and others in detail.

What is Kinetic Energy?

Kinetic energy of 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 which 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.

Examples: Some of the common examples of Kinetic Energy are, a moving bullet, blowing wind, a speeding stone, a rotating wheel, arrow released from the bow that has kinetic energy.

Potential and Kinetic Energy of Bow and arrow

 

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.

Unit of Kinetic Energy

Kinetic energy is measured in various units which are,

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

The dimension Formula for kinetic energy is [M1L2T-2]

Kinetic Energy Examples

Various examples of Kinetic Energy are,

  • A truck travelling down the road has more kinetic energy than a car travelling at the same speed because the truck’s mass is much more than the car’s.
  • Kinetic Energy of an asteroid falling towards the earth is very large as it has a large mass and very high velocity.
  • A bullet has very high kinetic energy as its speed is very high.

Is Kinetic Energy a Vector or a Scalar Quantity?

Mass (m) is a scalar quantity and velocity (v) is a vector quantity. The formula for kinetic energy is,

K = 1/2 m×v2

From the above formula, it is observed that velocity is squared, and it is known that the square of any vector quantity is a scalar quantity. 

Hence, kinetic energy is a scalar quantity.

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.

Kinetic Energy Formula

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

K = 1/2 m×v2

where,
m is the mass of the object,
v is the speed or velocity of the object

This, expression obtained is called the Kinetic Energy Equation.

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 an as,

v2 – u2 = 2as

Solving the 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 that are,

  • Radiant Energy
  • Thermal Energy
  • Sound Energy
  • Electrical Energy
  • Mechanical Energy

Radiant Energy

Radiant energy is a form of kinetic energy, which is the physical energy of matter resulting from electromagnetic radiation. It is radiated from matter into the surrounding environment.

For example, Ultraviolet light, Gamma rays, and X-rays all have electromagnetic radiant energy.

Thermal Energy

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

For Example, Hot Springs, Heated Swimming pools have thermal energy.

Sound Energy

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

For Example, Tuning Forks, Beating Drums have sound energy.

Electrical Energy

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

For Example, Batteries have electrical energy.

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.

For Example, Satellites orbiting around the Earth, Moving Cars all have mechanical energy.

Difference Between Kinetic Energy and Potential Energy

The difference between Kinetic Energy and Potential Energy is discussed below,

Kinetic Energy

Potential Energy

Kinetic energy is the energy of any moving object. Potential energy is the energy of the object due to its position in space.

Formula for kinetic energy is,

K.E. = 1/2mv2

Formula for potential energy is,

P.E. = mgh

Example: Energy of a moving car. Example: Energy of a book placed on top of the table.

Kinetic energy is the energy that an object possesses due to its motion. It is defined as half of the product of the object’s mass and its velocity squared. In other words, the more massive an object is and the faster it moves, the greater its kinetic energy.

The formula for kinetic energy is:

Kinetic energy = 1/2 x mass x velocity^2

where “mass” is the mass of the object and “velocity” is its speed in meters per second.

The unit of kinetic energy is joules (J) in the International System of Units (SI). However, other units such as calories, ergs, or electronvolts can also be used to express kinetic energy.

Kinetic energy is a scalar quantity, which means it has magnitude but no direction. It is also a conserved quantity, which means that it can be transferred between objects or transformed into other forms of energy, but the total amount of kinetic energy in a closed system remains constant.

Kinetic energy is important in many areas of physics and engineering, including mechanics, thermodynamics, and electromagnetism. It is used to calculate the work done by a force on an object, the momentum of an object, and the temperature of a gas. In everyday life, kinetic energy is involved in a wide range of phenomena, such as the movement of vehicles, the flight of birds, and the vibration of molecules in a gas.

Read More:

Solved Examples on Kinetic Energy

Example 1: A vehicle having a 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,

Mass of the vehicle, m = 150 kg,

Velocity of the vehicle, v = 4 m/s

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,

Mass of the ball, m = 2 kg,

Velocity of the ball, v = 10 m/s.

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,

Kinetic energy of the asteroid, K.E. = 4 × 1015 J,

Velocity of the asteroid, v = 1000 Km/s = 106 m/s

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.

For more, Practice Problems on Kinetic Energy

FAQs on Kinetic Energy

Q1: What is Kinetic Energy?

Answer:

Kinetic Energy is the energy posses by the object due to virtue of its motion.

Q2: What is the Kinetic Energy of an Object?

Answer:

The kinetic energy of an object is given by the formula,

K.E. = 1/2 mv2

Q3: How does the Average Kinetic Energy of molecules depend on Absolute Temperature?

Answer:

The average kinetic energy of any molecule depends directly on absolute temperature as the increase in absolute temperature increases the kinetic energy of the molecules.

Q4: Can the kinetic energy be negative?

Answer:

Kinetic Energy of an object can never be negative as it is given by the formula K.E. = 1/2 mv2 here, mass can never be negative and the square of any number is always positive.

Q5: When is the Kinetic Energy Maximum?

Answer:

Kinetic energy of an object is maximum when the potential energy of the object is minimum and the velocity of the object is maximum.

Q6: What happens to the kinetic energy of an object when the speed is doubled?

Answer:

When the speed of an object is doubled its kinetic energy is increased four times as kinetic energy is directly proportional to the square of the speed.

Q7: What is the difference between Kinetic Energy and Potential Energy?

Answer:

Kinetic energy is the energy possessed by any particle due to its motion (speed) whereas potential energy is the energy of an object due to its position.


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Last Updated : 26 Apr, 2023
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