Everything Science Grade 11

CHAPTER 12. FORCE,MOMENTUM AND IMPULSE 12.5

vi 1 vi 2

m 1 m 2

Figure 12.10: Before thecollision.

The total momentum ofthe system before the collision, piis:

pi= m 1 vi 1 + m 2 vi 2

After the two balls collide and move away they each have a different momentum. If the first ball has a
final velocity of vf 1 and the second ball hasa final velocity of vf 2 then we have the situation shown
in Figure 12.11.

m 1 m 2

vf 1 vf 2

Figure 12.11: After the collision.

The total momentum ofthe system after the collision, pfis:

pf= m 1 vf 1 + m 2 vf 2

This system of two ballsis isolated since there are no external forces acting on the balls. Therefore, by
the principle of conservation of linear momentum, the total momentumbefore the collision is equal
to the total momentumafter the collision. Thisgives the equation for the conservation of momentum
in a collision of two objects,

pi= pf

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

m 1 : mass of object 1 (kg)

m 2 : mass of object 2 (kg)

vi 1 : initial velocity of object 1 (m·s−^1 + direction)

vi 2 : initial velocity of object 2 (m·s−^1 - direction)

vf 1 : final velocity of object1 (m·s−^1 - direction)

vf 2 : final velocity of object2 (m·s−^1 + direction)

This equation is alwaystrue - momentum is always conserved in collisions.

Example 33: Conservation of Momentum 1

QUESTION

A toy car of mass 1 kg moves westwards with a speed of 2 m·s−^1. It collides head-on with a

toy train. The train hasa mass of 1,5 kg and ismoving at a speed of 1,5 m·s−^1 eastwards. If