# Relation Between Kinetic Energy And Momentum

If the momentum of an object is doubled, by what factor will its kinetic energy change?

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 =...

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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.

Approved by eNotes Editorial Team

The momentum of an object with mass m and traveling at a velocity v is given by M = m*v and the kinetic energy is given by `KE = (1/2)*mv^2`

The momentum of the object can be made double by either increasing its mass to twice the initial mass with the velocity remaining the same or by increasing the velocity to twice the initial value.

Assuming the mass of the object is not altered and only the velocity is increased to twice the initial value, the kinetic energy of the object is increased to `(1/2)*m*(2*v)^2 = 4*(1/2)*m*v^2` , or it changes to four times the initial value.

If the momentum of an object is doubled by increasing its velocity, its kinetic energy becomes 4 times the initial value.

Approved by eNotes Editorial Team