Principle Of Conservation Of Momentum

In the absence of an external force, the total momentum of a system remains unchanged.

•In any collision or interaction between two or more objects in an isolated system , the total momentum of the system will remain constant •that is the total momentum before collision will be equal to the total momentum after the collision

Types of collision

elastic

inelastic

ELASTIC

After two objects moving with their respective velocities do collide, those two objects will move separately.

The total momentum =

The total before collision

momentum after

collision

22112211 vmvmumum

Elastic collision

6

A trolley of mass trolley 3 kg and moving with a velocity 0.6 ms-1 and collides with a stationary trolley with a mass 2 kg . After collision the trolley of mass 3 kg and moving with a velocity 0.2 ms-1. What is the velocity of the trolley of mass 2 kg after collision?

11

11

1

2.0

6.0

3

msv

msu

kgm

))(2()2.0)(3()0)(2()6.0)(3( 2v22112211 vmvmumum

226.008.1 v

6.08.12 2 v

?

0

2

2

2

2

v

u

kgm

6.02

2.12 v

Velocity of trolley, 2

kg

INELASTIC

After two objects moving with their respective velocities do collide, they stick together and move with a common velocity

Based on The Principle Of Conservation Of Momentum,The total momentum = The total momentum

before collision after collision

vmmumum 212211

A trolley of mass 1 kg and moving with a velocity of 6 ms-1 collides with a stationary trolley with a mass 3 kg . After collision they stick together with a common velocity. What is their common velocity?

11

1

6

1

msu

kgm

0

3

2

2

u

kgm

vmmumum 212211

))(31()0)(3()6)(1( v

v406

5.14

6vCommon

velocity

Similarities and Differences

differences

Elastic collision

Total amount of kinetic energy is

conserved

Inelastic collision

Total amount of kinetic energy

is not conserved

Similarities

Total momentum is conserved

Total energy is conserved

Total mass is conserved

Application in real life:

•Kicking football•Water hose

•Rifle•Playing bowling

Diagram below shows object X and object Y before and after an inelastic collision. The mass of object X and object Y are 5 kg and 1 kg respectively. What is the velocity, v of both object after collision, in m s–1?

Car A Car BCar A of mass 100 kg traveling at 30 m s-1 collides with Car B of mass 90 kg traveling at 20 m s-1 in front of it. Car A and B move separately after collision. If Car A is still moving at 25 m s-1 after collision, determine the velocity of Car B after collision.

Car A of mass 100 kg traveling at 30 m s-1 collides with Car B of mass 90 kg traveling at 20 m s-1 in front of it. Car A is pulled by Car B after collision. Determine the common velocity of Car A and B after collision.

A bullet of mass 2 g is shot from a gun of mass 1 kg with a velocity of 150 m s-1 . Calculate the velocity of the recoil of the gun after firing.

An arrow of mass 150 g is shot into a wooden block of mass 450 g lying at rest on a smooth surface. At the moment of impact, the arrow is travelling horizontally at 15 ms-1. Calculate the common velocity after the impact.