Relation Between Kinetic Energy And Momentum
If the momentum of an object is doubled, by what factor will its kinetic energy change?
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KE = (P²)/(2m)
KE = Kinetic energy
P = Momentium
m = mass
If the momentum of the object is doubled then...
KE is directly propotional to Square of the momentium
So...
(KE1)/(P²1) = (KE2)/(P²2)
KE1 = E
KE2 = x(?)
P²1 = P
P²2 = 4P
Therefore
E/P = x/4P
x = 4E
Thus KE increases by 4 times when momentum is doubled.
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The momentum of an object...
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The relation between kinetic energy is proportional to the square of velocity. Momentum is directly proportional to velocity. If the momentum of an object is doubled, but its mass does not increase (so velocity remains well below the speed of light), then its velocity is doubled. If the velocity is doubled then the kinetic energy increases by the square of 2, or four time.
The relation between kinetic energy and linear momentum is given as:
K.E.=P*P/2M
Where p is linear momentum and
M is mass of the body.
in first case (K.E)1=P*P/2M.....................(1)
Now linear momentum gets doubled,keeping mass of body unchanged
in second case (K.E.)2=2P*2P/2M
or (K.E.)2=4P*P/2M..............(2)
Dividing eq.(2) by eq. (1)
(K.E.)2
_________=4
(K.E)1
Hence kinetic energy of the body will be 4 times to its eirlier value.
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