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

#### Answers

Let,

**Initial Momentum** =* P _{i} * = m

_{i}v

_{i}and,

**Initilal Kinetic Energy **= *KE* _{ i } = 1/2 m_{i}v_{i}

Now, it is given that the momentum is doubled.

Thus, **New Momentum** = *P _{f} *

_{ }= m

_{f}v

_{f}= 2P

_{i}= 2m

_{i}v

_{i}

From here, ** v_{f} = 2m_{i}v_{i}/m_{f} **

And, **New Kinetic Energy** = *KE _{f} * = 1/2 m

_{f}v

_{f}= 1/2 m

_{f}x 2m

_{i}v

_{i}/m

_{f}= 1/2 x m

_{f}/m

_{f }x m

_{i}v

_{i}= m

_{i}v

_{i}

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

Also Note that *m _{i} = m_{f} = m* as mass doesn 't change in this case.

Let,

**Initial Momentum** =* P _{i} *= m

_{i}v

_{i}and,

**Initilal Kinetic Energy **= *KE* _{ i }= 1/2 m_{i}v_{i} ^{2}

Now, it is given that the momentum is doubled.

Thus, **New Momentum** = *P _{f} *= m

_{f}v

_{f}= 2P

_{i}= 2m

_{i}v

_{i}

From here, ** v_{f} = 2m_{i}v_{i}/m_{f} **

And, **New Kinetic Energy** = *KE _{f} *= 1/2 m

_{f}v

_{f}

^{2}= 1/2 m

_{f}x (2m

_{i}v

_{i}/m

_{f})

^{2}= 1/2 x 4 x m

_{f}/m

_{f}

^{2}x m

_{ i }

^{ 2 }vi

^{2}

= 2 x m^{2}/m^{2} x mv _{ i } ^{ 2 } = 2 mv _{ i } ^{ 2 } = 4 x KE _{ i }

Note that *m _{i} = m_{f} = m* as mass doesn 't change in this case.

Thus, the kinetic energy becomes 4 times the initial.

(EDITED)

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)mv^{2} 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.

This conversation is already closed by Expert