Why is momentum conserved but kinetic energy not conserved in an inelastic collision?

So why is kinetic energy not conserved while momentum is conserved in a perfectly inelastic collision?

Where does the kinetic energy go when the objects collide perfectly inelastically?

Why does conservation of momentum happen? Is momentum a type of energy?

cepheid
Staff Emeritus
Gold Member

So why is kinetic energy not conserved while momentum is conserved in a perfectly inelastic collision?

Where does the kinetic energy go when the objects collide perfectly inelastically?

It goes into heat, sound, work done to deform the colliding bodies etc. Other forms of energy, in other words.

Why does conservation of momentum happen? Is momentum a type of energy?

No, momentum is not a type of energy. Momentum and energy are totally different physical quantities with different physical dimensions.

Conservation of momentum in a system occurs provided that there are no external forces acting on a system. This is a consequence of Newton's 2nd law and Newton's 3rd law.

Newton's 2nd law says that the net force acting on a body is equal to the rate of change of its momentum. (This is the full, general statement of the 2nd law. F = Δp/Δt. If the mass of the body is constant, this reduces to F = m(Δv/Δt) = ma). Therefore, if a net force acts on an object, its momentum will change with time. If there is no net force, then its momentum will not change.

Now, consider a system of interacting particles. The particles are moving around randomly. Every once in a while, two particles (1 and 2) may collide. While this is happening, particle 1 exerts a force on particle 2. However, Newton's 3rd law says that particle 2 must therefore, at the same time, exert a force on particle 1 of equal strength and opposite direction. These forces are also exerted over the same time interval (while the particles are in contact). Therefore, the change in momentum of particle 1 will be equal in magnitude and opposite in direction to the change in momentum of particle 2. These two momentum changes therefore cancel each other out. Each particle may individually change its momentum, but there will be no change to the total momentum of the system. In other words, since Newton's 3rd says that these internal forces always occur in matched "action-reaction" pairs, they cannot ever cause a change to the overall momentum of the system. Only an external force (a force from something that is not part of the system of particles) can cause a change in the total momentum of the system. In the absence of a net external force, Ftot = 0 and hence Δptot = 0. In the absence of external forces, momentum is conserved.

Frigus