Kinetic Energy Formula

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Kinetic Energy

An object possesses kinetic energy when it is in motion. It is defined as the amount of work that should be done to accelerate a body of a given mass from rest to a certain velocity. As this energy is gained during its acceleration, the body retains this kinetic energy till its speed is varied. While coming back to the state of rest, the same amount of energy is required by the body.

If we will calculate the kinetic energy of a non-rotating object having mass m and traveling with a certain speed v is ½ mv2 in classical mechanics. If the speed of the body is very less in comparison with the speed of light then relative mechanics is followed. The standard unit of kinetic energy is the joule, while the English unit of it is foot-pound. The kinetic energy equation is written as

K.E. = ½ mv2 

Where

Mass of the body = m

The velocity with which the body is traveling = v and

The kinetic energy is articulated in kgm2/s2.

The kinetic energy formula is used to compute the mass, velocity, or kinetic energy of the body if any of the two numerics are given.


To Understand How The Kinetic Energy is Measured Based Upon The Given Details, We Can Study The Following Simple Examples

Example 1

A man is carrying a trolley of 6 kg mass with kinetic energy of 40 J. Calculate the velocity of it.

Solution

Given

Mass m = 6 kg

Kinetic energy K.E. = 40 J

Velocity v = 2 K.E./m

= 2 x 40 J/6 kg

= 13.33

= 3.65 m/s

The man is running with a velocity of 3.65 m/s.


Example 2

A car has a mass of 250 kg and is driven at a velocity of 10 m/s. Calculate its kinetic energy.

Solution

Given,

Mass of the body m = 250 kg

Velocity v = 10 m/s

The kinetic energy formula is given by

K.E. = ½ mv2

K.E. = ½ x 250 kg(10 m/s)2

K.E. = 12500 kg2s2.

The dimensional formula of kinetic energy can be given by

[M1L2T-2]

Where M = mass

L = Length

T = Time

It can be derived as follows

Kinetic energy K.E. = [Mass x Velocity2] x 2-1 ..... (1)

The dimensional formula of mass = [M1L0T0] ....(2)

Since, Velocity = Distance x Time-1 = [L] x [T]-1

Hence, the dimensional formula of velocity = [M0L1T-1] ... (3)

Putting the values of equation (2) and (3) in equation (1) we will get,

Kinetic energy = [Mass x Velocity2] x 2-1

or KE = [M1L0T0] x [M0L1T-1] = [M1L2T-2].

Therefore, the kinetic energy is dimensionally represented as [M1L2T-2]


Conclusion 

Kinetic energy can be transformed into other forms of energy and is transferred between objects. To accelerate an object we need to apply force and to apply force we need to do work. When work is done the energy is transferred to the other object and it starts moving.


FAQ (Frequently Asked Questions)

1. What are the types of kinetic energy?

Usually one can find 5 types of Kinetic energy such as; radiant, thermal, sound, electrical, and mechanical. Examples of each are as below

Radiant energy - Ultraviolet light and gamma rays.

Thermal energy – Hot Springs and heated swimming pool

Sound energy – Tuning forks and beating drums

Electrical energy – Lightning and batteries when in use

Mechanical energy – Orbiting of satellites around the earth and a moving car.

2. What does kinetic energy depend on?

Kinetic energy depends on the velocity of the object squared. This means that when the velocity of the object doubles the kinetic energy quadruples.

3. What is a kinetic energy expression?

Kinetic energy is directly proportional to the mass of the object and the square of its velocity and is expressed by the equation K.E = ½ mv2