Expression of Kinetic Energy in Terms of Momentum


 
 
Concept Explanation
 

Expression for Kinetic Energy in Terms of Momentum

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 in Terms of Momentum:

    Kinetic energy of a body of mass m moving with velocity v is-

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

    Momentum is defined as the product of mass and velocity

    p=mv

    Squaring both sides

    p^2=m^2v^2

    Dividing both sides with m

    mv^2=frac{p^2}{m}

    Dividing both sides with 2

    frac{1}{2}mv^2=frac{1}{2}times frac{p^2}{m}

    K.E.= frac{p^2}{2m}

    Illustration: Find the kinetic energy of a car of mass 200 Kg having momentum as 40 Kg m/s.

    Solution :  The kinetic energy is 

    K.E.= frac{p^2}{2m}

    Given  m= 200 Kg

                p = 40 Kg m/s

                K.E.= frac{p^2}{2m}

               K.E.= frac{40^2}{2times200}

               K.E.= frac{40times40}{2times200}= 4 J

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

    When the momentum of a body decreases by 10%, its K.E. decreases by

    Right Option : D
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    Explanation
    Question : 2

    Two unequal masses possess the same K.E. Then, the heavier mass has

    Right Option : A
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    Explanation
    Question : 3

    A body cannot have momentum when its Kinetic Energy is zero.

    Right Option : A
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    Explanation
     
     
     


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