Everything Science Grade 12

6.4 CHAPTER 6. MOTIONIN TWO DIMENSIONS

1

pf 1 , KEf 1

2

pf 2 , KEf 2

Figure 6.6: Two balls after they collide.

Ball 1 now has a kinetic energy which we call KEf 1 and ball 2 now has a kinetic
energy which we call KEf 2 , it means that the total kinetic energy after the collision is:

KEf= KEf 1 + KEf 2

Since this is an elastic collision, the total momentum before the collision equals the
total momentum after the collision and the total kinetic energy before the collision
equals the total kinetic energy after the collision. Therefore:

Initial Final

pi = pf

pi 1 + pi 2 = pf 1 + pf 2

and

KEi = KEf

KEi 1 + KEi 2 = KEf 1 + KEf 2

Example 8: An Elastic Collision

QUESTION

Consider a collision between two pool balls.Ball 1 is at rest and ball 2 is

moving towards it witha speed of 2 m·s−^1. The mass of each ball is 0.3 kg.

After the balls collide elastically, ball 2 comes toan immediate stop and ball 1

moves off. What is the final velocity of ball 1?

SOLUTION

Step 1 : Determine what is given and what is needed