Everything Science Grade 12

CHAPTER 6. MOTIONIN TWO DIMENSIONS 6.4

Elastic Collisions ESCDD

DEFINITION: Elastic Collisions

An elastic collision is acollision where total momentum and total ki-

netic energy are both conserved.

This means that in an elastic collision the total momentum and the total kinetic energy
before the collision is the same as after the collision. For these kinds ofcollisions, the
kinetic energy is not changed into another type of energy.

Before the Collision

Figure 6.5 shows two balls rolling toward each other, about to collide:

1

pi 1 , KEi 1

2

pi 2 , KEi 2

Figure 6.5: Two balls before they collide.

Before the balls collide,the total momentum of the system is equal to allthe individual
momenta added together. Ball 1 has a momentum which we call pi 1 and ball 2 has a
momentum which we call pi 2 , it means the total momentum before the collision is:

pi= pi 1 + pi 2

We calculate the total kinetic energy of the system in the same way. Ball1 has a kinetic
energy which we call KEi 1 and the ball 2 has a kinetic energy which we call KEi 2 , it
means that the total kinetic energy before the collision is:

KEi= KEi 1 + KEi 2

After the Collision

Figure 6.6 shows two balls after they have collided:

After the balls collide and bounce off each other, they have new momenta and new
kinetic energies. Like before, the total momentum of the system is equal to all the
individual momenta added together. Ball 1 nowhas a momentum whichwe call pf 1
and ball 2 now has a momentum which we call pf 2 , it means the total momentum after
the collision is
pf= pf 1 + pf 2