Everything Science Grade 12

CHAPTER 6. MOTIONIN TWO DIMENSIONS 6.4

• Mass of ball 1, m 1 = 0.3 kg.


• Mass of ball 2, m 2 = 0.3 kg.


• Initial velocity of ball 1, vi 1 = 0 m·s−^1.


• Initial velocity of ball 2, vi 2 = 2 m·s−^1.


• Final velocity of ball 2, vf 2 = 0 m·s−^1.


• The collision is elastic.
  All quantities are in SI units. We need to find the final velocity
  of ball 1, vf 1. Since the collision is elastic, we know that


• momentum is conserved, m 1 vi 1 + m 2 vi 2 = m 1 vf 1 +
  m 2 vf 2


• energy is conserved,^12 (m 1 v^2 i 1 + m 2 v^2 i 2 ) =^12 (m 1 v^2 f 1 +
  m 2 v^2 f 2 )

Step 2 : Choose a frame of reference

Choose to the right as positive.

Step 3 : Draw a rough sketch of the situation

2

m 2 , vi 2

1

m 1 , vi 1

2

m 2 , vf 2

1

m 1 , vf 1

Before collision After collision

Step 4 : Solve the problem

Momentum is conserved. Therefore:

pi = pf

m 1 vi 1 + m 2 vi 2 = m 1 vf 1 + m 2 vf 2

(0,3)(0) + (0,3)(2) = (0,3)vf 1 + 0

vf 1 = 2 m· s−^1

The final velocity of ball 1 is 2 m·s−^1 to the right.

Example 9: Another Elastic Collision

QUESTION

Consider 2 marbles. Marble 1 has mass 50 g and marble 2 has mass 100 g.

Edward rolls marble 2 along the ground towards marble 1 in the positive x-

direction. Marble 1 is initially at rest and marble2 has a velocity of 3 m·s−^1 in

the positive x-direction. After they collide elastically, both marbles are moving.