Expression for Kinetic Energy


 
 
Concept Explanation
 

Expression for Kinetic Energy

Kinetic Energy: The energy of an object because of its motion is called its kinetic energy. Its SI unit is Joule (J). A flying bird, a running man, a moving train and a swinging bat are some examples of bodies with kinetic energy. Kinetic energy of a body moving with certain velocity is equal to the work done on it to make it acquire that velocity. Kinetic energy of an object increases with its speed.

· Due to kinetic energy, a bullet fired from a gun can pierce a target.

· A moving hammer, drives a nail into a wooden block. Due to its motion, it has kinetic energy or ability to do work.

The kinetic energy of a body of mass m moving with a velocity v is

K.E. = frac{1}{2}mv^2

Sometimes, a large rock from space hits the earth’s surface at a very high speed. Its huge kinetic energy creates a large crater on the earth’s surface. One such crater was formed thousands of years ago at Lonar in Maharashtra. The diameter of this crater is 1.8 km.

Expression for Kinetic Energy: Suppose a body of mass “m” moving with a uniform velocity “u”. Force “F” starts acting on it in the horizontal direction and displaces it through a distance of “s” and it attains a velocity “v”. Then, work done to increases its velocity from “u” to “v”.

According to equation of motion:

v^2 - u^2 = 2as

So, as the object starts from rest and distance travelled is x

v^2 = 2ax                  (1)

According to the definition of Force

F = ma

 Or a=frac{ F}{m}

Putting the value of a in the Equation  (1), we get  

v^2 =2frac{F}{m} x

mv^2 =2Fx

Fx= frac{1}{2}mv^2

But Fx is the work done by the force on the body. It should be equal to the increase in the kinetic energy of the body as it moves from A to B. Also, since the kinetic energy at A was zero, the increase in kinetic energy should be equal to the kinetic energy at B. So, we conclude the following:

The kinetic energy of a body of mass m moving with a speed v is

KE= frac{1}{2}mv^2

Example:Find the kinetic energy of a ball of mass 200 g moving at a speed of 20 cm/s.

Solution   The kinetic energy is 

KE= frac{1}{2}mv^2

Given  m= 200g = 0.2 Kg

          v = 20 cm/s = 0.2m/s

           K.E. = frac{1}{2} (0.200; kg) times (0.20; m/s)^2 = 0.004 ;J

Q. If a stone of mass 3 kg be thrown with a kinetic energy of 37.5 J, find its velocity.

Solution: Here, mass m = 3 kg, K.E. = 37.5 J, velosity of stone, v = ?

                  From    KE= frac{1}{2}mv^2 ; =; 37.5 = frac{1}{2}times;3v^2

                             v^2:=;frac{75}{3};=;25Rightarrow v;=;5;m/s    

                                        

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Kinetic energy possessed by a car, moving at a speed of 5 m/sec is 5000 J. The mass of the car is

 

Right Option : A
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Question : 2

A body of mass 20 kg is dropped from a height of 2 m. If g is taken to be equal to 10  m/s^{2}, the kinetic energy of the body, just before striking the ground,will be

Right Option : C
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Question : 3

A uniform force of 4N acts on a body of mass 8 kg for a distance of 2.0m. The K.E. acquired by the body is

Right Option : D
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