Inelastic collisions

If the interaction force between the bodies are conservative, the total kinetic energy of the system is the same after the collision as before. Such a collision is called an elastic collision.

A collision in which the total kinetic energy after the collision is less than that before the collision is called an inelastic collision. In one kind of inelastic collision the colliding bodies stick together and move as one body after the collision; this is often called a completely inelastic collision.

A completely inelastic collision of two bodies (A and B). Because they stick together after the collision, their final veloxcities must be equal :


vA2=vB2=v2

conservation of momentum gives the relation

mAvA1 + mBvB1 = (mA+mB)v2.

ifd we know the masses and initial velocities, we can compute the common final velocity v2.

suppose, for example, that a body with mass mA and initial velocity v1 along the +x-axis collides inelastically with a body with mass mB that is initially at rest (vB1=0). the common x-component of velocity v2 of both bodies after collision is

v2 =(mA/(mA+mB))v1

Form The kinetic energy K1 and K2 before and after the collision, respectively, are


K1 =1/2 mAv1^2,
K2 = 1/2(mA+mB)v2^2= 1/2 (mA+mB)(mA/(mA+mB))^2v1^2.
The ratio of final to initial kinetic energy is

K2/K1 =mA/(mA+mB)