8/10/2019 Chapter 3.2 and 3.3

1/26

3.2 Linear momentum and its

conservation3.3 Elastic and non-elastic collision

8/10/2019 Chapter 3.2 and 3.3

2/26

A moving object has mass and velocity.

Momentum of an object is defined as theproduct of its mass and velocity .

8/10/2019 Chapter 3.2 and 3.3

3/26

Momentum = mass x velocity

p = m v The SI unit of momentum = kg ms -1

Momentum is a vector quantity. The direction of the momentum is the

same with as the direction of the velocity.

8/10/2019 Chapter 3.2 and 3.3

4/26

The principle of Conservation of Momentum states that The total momentum in a closed system is

constant , if no external force acts on the system.

That is

The total momentum

before a collision

The total momentum

after a collision=

8/10/2019 Chapter 3.2 and 3.3

5/26

In the golf game, the golf club is swung at a highspeed to hit the ball so that a large momentum is

transferred to the ball. In rocket, hot gases are ejected downwards with

high speed , so a large momentum is produced

too. By conservation of momentum, an equaland opposite momentum is acted on rocket ,propelling the rocket upwards.

8/10/2019 Chapter 3.2 and 3.3

6/26

The principle of Conservation of Momentum is

true for

Collision

Explosion

Inelastic collision

Elastic collision

8/10/2019 Chapter 3.2 and 3.3

7/26

Impulse = Momentum

Consider Newtons 2 nd Lawand the definition ofacceleration

Units of Impulse:

Units of Momentum:

Momentum is defined as Inertia in Motion

Ns

Kg x m/s

8/10/2019 Chapter 3.2 and 3.3

8/26

Impulse Momentum Theorem

vm Ft IMPULSE CHANGE IN MOMENTUM

This theorem reveals someinteresting relationships such asthe INVERSE relationship betweenFORCE and TIME

t

vm F

8/10/2019 Chapter 3.2 and 3.3

9/26

Impulse Momentum Relationships

8/10/2019 Chapter 3.2 and 3.3

10/26

Impulse Momentum Relationships

V m fT Constant

Since TIME is directly related to theVELOCITY when the force and mass areconstant, the LONGER the cannonball isin the barrel the greater the velocity.

Also, you could say that the force actsover a larger displacement, thus there ismore WORK. The work done on thecannonball turns into kinetic energy.

8/10/2019 Chapter 3.2 and 3.3

11/26

How about a collision?Consider 2 objects speedingtoward each other. When they

collide......

Due to Newtons 3 rd Law theFORCE they exert on eachother are EQUAL andOPPOSITE.

The TIMES of impact are alsoequal.

Therefore, the IMPULSES of the 2objects colliding are alsoEQUAL

21

21

2121

)()(

J J

Ft Ft

t t F F

8/10/2019 Chapter 3.2 and 3.3

12/26

How about a collision?

If the Impulses are equalthen the MOMENTUMSare also equal!

22221111

222111

2211

21

21

)()(oo

oo

vmvmvmvmvvmvvm

vmvm

p p

J J

22112211 vmvmvmvm

p p

oo

after before

8/10/2019 Chapter 3.2 and 3.3

13/26

8/10/2019 Chapter 3.2 and 3.3

14/26

Types of Collisions

A situation where the objects DO NOT STICK isone type of collision

Notice that in EACH case, you have TWO objects BEFORE and AFTER the collision.

8/10/2019 Chapter 3.2 and 3.3

15/26

The two objects move independently with their

respective velocities after the collision. Total momentum before collision = total momentum after

collision m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2 Kinetic energy is conserved.

m 2 m 1

u 1 u 2

m 1

v 1

m 2

v 2

8/10/2019 Chapter 3.2 and 3.3

16/26

A no stick type collision

S pbefore = S pafter

1

1

1

22112211

100010000

)10)(3000())(1000(0)20)(1000(

v

v

v

vmvmvmvm oo

-10 m/s

8/10/2019 Chapter 3.2 and 3.3

17/26

Types of Collisions

Another type of collision is one where theobjects STICK together. Notice you haveTWO objects before the collision and ONEobject after the collision.

8/10/2019 Chapter 3.2 and 3.3

18/26

The two objects combine and move together with a

common velocity after the collision.

Total momentum before collision = total momentum after collision m 1 u 1 + m 2 u2 = (m 1 + m 2 )v

Kinetic energy is not conserved.

m 2 m 1

u 1 u 2

m 1

v

m 2

8/10/2019 Chapter 3.2 and 3.3

19/26

A stick type of collision

S pbefore = S pafter

T

T

T

T T oo

v

v

v

vmvmvm

400020000

)4000(0)20)(1000(2211

5 m/s

8/10/2019 Chapter 3.2 and 3.3

20/26

The explosion type

This type is often referred to asbackwards inelastic. Notice you haveONE object ( we treat this as aSYSTEM) before the explosion andTWO objects after the explosion.

8/10/2019 Chapter 3.2 and 3.3

21/26

Explosion means the separation of objects

which are initially rest.

m 1

u 1 = u 2 = 0

m 2 m 2

v 2

m 1

v 1

Total momentum before collision = total momentum after collision

m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2

0 = m 1 v 1 + m 2 v 2

8/10/2019 Chapter 3.2 and 3.3

22/26

Backwards Inelastic - ExplosionsSuppose we have a 4-kg rifle

loaded with a 0.010 kg bullet.When the rifle is fired thebullet exits the barrel with avelocity of 300 m/s. How fast

does the gun RECOILbackwards?

S pbefore = S pafter

2

2

2

2211

430

))(4()300)(010.0()0)(010.4(

v

v

v

vmvmvm T T

-0.75 m/s

8/10/2019 Chapter 3.2 and 3.3

23/26

Collision Summary

Sometimes objects stick together or blow apart.In this case, momentum is ALWAYS conserved.

2211)(

022011

2211022011

vmvmvm

vmvmvmvmvmvmvm

p p

total ototal

total total

after before

When 2 objects collide and DONT stick

When 2 objects collide and stick together

When 1 object breaks into 2 objects

Elastic Collision = Kinetic Energy is ConservedInelastic Collision = Kinetic Energy is NOT Conserved

8/10/2019 Chapter 3.2 and 3.3

24/26

Elastic Collision

J Af ter KE

J Af ter KE

J mv Before KE

car

truck

car

000,50)10)(1000(5.0)(

000,150)10)(3000(5.0)(

000,200)20)(1000(5.021)(

2

2

22

Since KINETIC ENERGY is conserved during the collision we call this an ELASTICCOLLISION.

8/10/2019 Chapter 3.2 and 3.3

25/26

Inelastic Collision

J After KE

J mv Before KE

car truck

car

000,50)5)(4000(5.0)(

000,200)20)(1000(5.021)(

2

/

22

Since KINETIC ENERGY was NOT conserved during the collision we call this anINELASTIC COLLISION.

8/10/2019 Chapter 3.2 and 3.3

26/26

ExampleGranny (m=80 kg) whizzes around

the rink with a velocity of 6 m/s.She suddenly collides with Ali(m=40 kg) who is at rest directlyin her path. Rather than knockhim over, she picks him up andcontinues in motion without

"braking." Determine the velocityof Granny and Ali.

How many objects do I have before the collision?

How many objects do I have after the collision?

2

1

T

T

T T oo

ab

v

vvmvmvm

p p

120)0)(40()6)(80(2211

4 m/s