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# Kinetic Energy

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 Sub Topics When energy causes motion, it acts as a force. Energy can do work; it can cause force to be applied over a distance. For this reason, physicists define energy as the ability to do work. It is implied that energy can be in an object at rest or in an object that is in motion. The ability of the object with energy to do the work can thus be expressed in either the object's state of rest or the object's state of motion. When the object is in motion, the object's ability to do the work is called kinetic energy.

## Definition

The kinetic energy of a particle is equal to the total work that was done to accelerate it from rest to its present speed. Other interpretation of kinetic energy is given by, the kinetic energy of a particle is equal to the total work that particle can do in the process of being brought to rest. This is why you pull your hand and arm backward when you catch a ball. As the ball comes to rest, it does an amount of work on your hand equal to the ball's initial kinetic energy. By pulling your hand back, you maximize the distance over which the force acts and so minimize the force on your hand.

## Formula

When a particle experiences a net force it accelerates. If the net force does positive work, the speed of the particle increases, whereas with negative work its speed decreases. Although we might expect the work done on a particle by the net force to be measured by the change in speed, it is not. Instead, the kinetic energy of a particle is defined in such a way that the work done by the net force equals the change in the kinetic energy of the particle. Kinetic energy is a quantity that involves the speed of a particle and its mass. A particle of mass m moving at speed v has a kinetic energy K defined by,
K = $\frac{1}{2}$m$v^{2}$

## Units

The units of kinetic energy and therefore for all types of energy, are kilograms multiplied by meters per second squared (kgm2/s2). This energy unit is called a joule (J). Kinetic energy differs from momentum in that it is not a vector quantity. An object has the same kinetic energy regardless of its direction as long as its speed does not change.

## Types

Fundamental types of kinetic energy are radiant energy, thermal energy, sound energy, electrical energy and mechanical energy.

Eg: X-rays, Radio waves, Visible light etc.
Thermal energy: If atoms or molecules move fast and collide with each other thermal energy forms. It is due to the collision of atoms or molecules.

Eg: A cup of hot tea, Hot springs etc.
Sound energy: Energy movement through a medium like air or water which is caused by any type of vibrations.

Eg: Clapping, Tuning fork, Voice etc.
Electrical energy: Energy due to the movements of electron through a conductor.

Eg: Doorbells, Lightning, Electricity etc.
Mechanical energy: It is nothing but the energy stored in an object. While the movement, more energy is stored.

Eg: A moving car, Wind, Flywheels etc.

## Examples

Some of the examples of kinetic energy are listed below:
• Geothermal energy
• Sound from a musical instrument
• A whistling cooker
• Audio Speakers
• A bullet from the gun
• Kicking a ball
• Gas molecules in a beaker

## Kinetic and Potential Energy

Kinetic energy and potential energy are two different forms of mechanical energy. Kinetic energy is the energy possessed by an object because it is moving and potential energy is the energy possessed by an object because of its position or condition. We know that when the work is done energy is converted from one form to another. For example, when work is done pushing an object which accelerates this gains motion energy, which we call kinetic energy. An unbalanced or resultant force applied to a body which makes it accelerate thus increases its kinetic energy. However, a force which is used to overcome friction does work against friction, but the energy is converted in to heat energy by the friction process. Where there is no acceleration there is no gain of kinetic energy.

## Can Kinetic Energy be Negative?

Kinetic energy cannot be negative. Kinetic energy is a scalar quantity, so only the magnitude is considered irrespective of the direction. The minimum value of the kinetic energy is zero. If the velocity is negative, here we are considering the square of the velocity. Hence, kinetic energy is always positive.

## Average Kinetic Energy

Average kinetic energy is nothing but the kinetic energy in which the velocity is considered as the average velocity. Average velocity can be calculated from the initial and final velocity. The mathematical representation of average kinetic energy is,

K = $\frac{1}{2}$m$v_{avg}^{2}$
where m is the mass of the object
$v_{avg}$ is the average velocity

$v_{avg}$ = $\frac{u+v}{2}$; u is the initial velocity and v is the final velocity

## How to Calculate Kinetic Energy?

Let us discuss the problems of kinetic energy in this section.

### Solved Examples

Question 1: A 50kg object moving with a velocity of 20m/s. Calculate its kinetic energy?

Solution:

Given parameters are,
Mass of the object, m = 50kg; velocity, v = 20m/s
Kinetic energy formula is given by,

K = $\frac{1}{2}$m$v^{2}$

K = $\frac{1}{2}$$\times50\times20^{2} = 10000J Question 2: Calculate the kinetic energy of a 15kg weight object which is moving with a velocity of 5m/s? Solution: Given parameters are, Mass of the object, m = 15kg; velocity, v = 5m/s Kinetic energy formula is given by, K = \frac{1}{2}mv^{2} K = \frac{1}{2}$$\times15\times5^{2}$ = 187.5J