Question

If linear momentum of a particle becomes n times by what factor it's kinetic energy changes?

Answer 1

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

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Expert Answers

JUSTAGUIDE eNotes educator| CERTIFIED EDUCATOR

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.