How can kinetic energy be conserved in an elastic collision as collision is said to occur between two bodies if they physically collide against each other or if the path of one of then is affected by the force exerted by the other? If they collide, path of the object will change so velocity should change as velocity is a vector quantity. So kinetic energy should also change.

  • $\begingroup$ Look at the formula for kinetic energy and ask yourself: Does the direction of the velocity matter? $\endgroup$
    – Javier
    Dec 10, 2014 at 2:02
  • $\begingroup$ @JavierBadia but velocity depend on direction $\endgroup$
    – pcforgeek
    Dec 10, 2014 at 3:35
  • $\begingroup$ Kinetic energy doesn't depend on velocity, it depends on speed. $\endgroup$
    – d_b
    Nov 12, 2019 at 19:00

2 Answers 2


When one says that "kinetic energy is conserved in an elastic collision" that means that the total kinetic energy of the system of particles involved in the collision doesn't change. It does not mean that the kinetic energy of each particle is unchanged. For a two particle system, the kinetic energy of each will change, but the sum won't.

Also, your statement about the change in direction of a particle doesn't matter.

$$K = \frac{1}{2}m (\vec{v}\cdot \vec{v})$$ for a single particle


If only internal forces are doing work (no work done by external forces), then there is no change in the total amount of mechanical energy. The total mechanical energy is said to be conserved. In these situations, the sum of the kinetic and potential energy is everywhere the same.

  • $\begingroup$ This is true only if the internal forces are conservative. Internal friction can change the mechanical energy of the system. Inelastic collisions ocur even in absence of external forces acting on systems. $\endgroup$
    – nasu
    Nov 12, 2019 at 19:41

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