Everything Science Grade 12

CHAPTER 6. MOTIONIN TWO DIMENSIONS 6.4

But the total kinetic energy of the system is notconserved:

KEi�= KEf

Example 11: An Inelastic Collision

QUESTION

Consider the collision of two cars. Car 1 is atrest and Car 2 is moving at a

speed of 2 m·s−^1 to the left. Both cars each have a mass of 500 kg. The cars

collide inelastically andstick together. What isthe resulting velocity of the

resulting mass of metal?

SOLUTION

Step 1 : Draw a rough sketch of the situation

Car 1

pi 1 = 0

Car 2

pi 2

Before collision

Car 1 Car 2

After collision

pf

Step 2 : Determine how to approach the problem

We are given:

• mass of car 1, m 1 = 500 kg


• mass of car 2, m 2 = 500 kg


• initial velocity of car 1, vi 1 = 0 m·s−^1


• initial velocity of car 2, vi 2 = 2 m·s−^1 to the left


• the collision is inelastic
  All quantities are in SI units. We are required todetermine
  the final velocity of theresulting mass, vf.
  Since the collision is inelastic, we know that


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


• kinetic energy is not conserved

Step 3 : Choose a frame of reference

Choose to the left as positive.

Step 4 : Solve problem

So we must use conservation of momentum to solve this problem.