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HOW DOES THE KINETIC ENERGY OF A BODY CHANGE IF ITS MOMENTUM IS DOUBLED ?

As

The energy possessed by a body when it is in the state of motion is its kinetic energy.

kinetic energy of a body depends on its mass and its speed.

KE =

where m = mass of the body

v = speed/velocity of the body

If the momentum of the body is doubled which clearly signifies velocity has become twice of the previous value since P = MV and mass doesn't vary and we can't change the mass of a body its an inherited property of a body. Therefore

Since Kinetic energy = (1/2)mv2 so incase we see the result in respect of the Kinetic energy of the body which, for twice velocity we can easily conclude its KE must have increased by 300% and becomes four times the previous value.

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Let,

Initial Momentum = Pi = mivi and,

Initilal Kinetic Energy = KEi = 1/2 mivi

Now, it is given that the momentum is doubled.

Thus, New Momentum = Pf = mfvf = 2Pi =  2mivi

From here, vf = 2mivi/mf

And, New Kinetic Energy = KEf = 1/2 mfvf = 1/2 mf x 2mivi/mf = 1/2 x mf/mf x mivi = mivi

Thus, the kinetic energy changes by a factor of 2 or becomes doubled.

Also Note that mi = mf = m as mass doesn't change in this case.

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 Let,

Initial Momentum = Pi = mivi and,

Initilal Kinetic Energy = KE i = 1/2 mivi2

Now, it is given that the momentum is doubled.

Thus, New Momentum = Pf = mfvf = 2Pi = 2mivi

From here, vf = 2mivi/mf

And, New Kinetic Energy = KEf = 1/2 mfvf2 = 1/2 mf x (2mivi/mf)2 = 1/2 x 4 x mf/mf2 x mi2vi2 

= 2 x m2/m2 x mvi2 = 2mvi2 = 4 x KEi

Note that mi = mf = m as mass doesn 't change in this case.

Thus, the kinetic energy becomes 4 times the initial.

 

(EDITED)

 

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