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Honors Physics

Impulse and Momentum

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Impulse = Momentum

Consider Newton’s 2nd Law and the definition of 

acceleration

Units of Impulse:Units of Momentum:

Momentum is defined as “Inertia in

Motion”  

Ns

Kg x m/s

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Impulse – Momentum Theorem

vm Ft 

IMPULSE CHANGE IN MOMENTUM

This theorem reveals some

interesting relationships such

as the INVERSE relationship

between FORCE and TIME

t 

vm F 

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Impulse – Momentum Relationships

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Impulse – Momentum Relationships

V m  fT 

Constant

Since TIME is directly related to theVELOCITY when the force and mass

are constant, the LONGER the

cannonball is in the barrel the greater 

the velocity.

 Also, you could say that the force acts

over a larger displacement, thus there

is more WORK. The work done on the

cannonball turns into kinetic energy.

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How about a collision?

Consider 2 objects speedingtoward each other. Whenthey collide......

Due to Newton’s 3rd Law the

FORCE they exert on eachother are EQUAL andOPPOSITE.

The TIMES of impact are alsoequal.

Therefore, the IMPULSES of the 2 objects colliding are

also EQUAL21

21

2121

)()(

 J  J 

 Ft  Ft 

t t  F  F 

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How about a collision?

If the Impulses areequal then the

MOMENTUMS are

also equal!

22221111

222111

2211

21

21

)()(oo

oo

vmvmvmvmvvmvvm

vmvm

 p p

 J  J 

22112211 vmvmvmvm

 p p

oo

after before

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Momentum is conserved!

The Law of Conservation of Momentum: “In theabsence of an external fo rce (gravity, fr ict io n),

the total momentum before the col l is ion is 

equal to the total momentum after the 

collision.”  

 smkg  p

 smkg  p

 smkg  p

 smkg  p

 smkg  p

 smkg mv p

total 

car 

truck 

total o

car o

otruck o

/*3300

/*18005.4*400

/*15003*500

/*3300

/*800)2)(400(

/*2500)5)(500(

)(

)(

)(

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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.

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 A “no stick” type collision 

Spbefore = Spafter 

1

1

1

22112211

100010000

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

v

v

v

vmvmvmvm oo

-10 m/s

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Types of Collisions

 Another type of collision is one where the objects“STICK” together. Notice you have TWO objects

before the collision and ONE object after the

collision.

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 A “stick” type of collision 

Spbefore = Spafter 

T 

T 

T 

T T oo

v

v

v

vmvmvm

400020000

)4000(0)20)(1000(

2211

5 m/s

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The “explosion” type 

This type is often referred to as

“backwards inelastic”. Notice you

have ONE object ( we treat this as

a SYSTEM) before the explosion

and TWO objects after the

explosion.

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Backwards Inelastic - Explosions

Suppose we have a 4-kg rifleloaded with a 0.010 kg

bullet. When the rifle is fired

the bullet exits the barrel

with a velocity of 300 m/s.

How fast does the gunRECOIL backwards?

Spbefore = Spafter 

2

2

2

2211

430

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

v

v

v

vmvmvm T T 

-0.75 m/s

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Collision Summary

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

2211)(

022011

2211022011

vmvmvm

vmvmvm

vmvmvmvm

 p p

total ototal 

total total 

after before

When 2 objects collide and DON’T sti

When 2 objects collide and stick toget

When 1 object breaks into 2 objects

Elastic Collision = Kinetic Energy is Conserved

Inelastic Collision = Kinetic Energy is NOT Conser 

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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(5.02

1)(

2

2

22

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

ELASTIC COLLISION.

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Inelastic Collision

 J  After  KE 

 J mv Before KE 

car truck 

car 

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

000,200)20)(1000(5.02

1)(

2

/

22

Since KINETIC ENERGY was NOT conserved during the collision we call

this an INELASTIC COLLISION.

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Example Granny (m=80 kg) whizzesaround the rink with a

velocity of 6 m/s. Shesuddenly collides with Ambrose (m=40 kg) whois at rest directly in her path. Rather than knock

him over, she picks himup and continues inmotion without "braking."Determine the velocity of Granny and Ambrose.

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

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Collisions in 2 Dimensions

The figure to the left showsa collision between twopucks on an air hockeytable. Puck A has amass of 0.025-kg and ismoving along the x-axis

with a velocity of +5.5m/s. It makes a collisionwith puck B, which has amass of 0.050-kg and isinitially at rest. Thecollision is NOT head on.

 After the collision, thetwo pucks fly apart withangles shown in thedrawing. Calculate thespeeds of the pucksafter the collision.

vA 

vB 

vAcosq

vAsinq

vBcosqvBsinq

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Collisions in 2 dimensions

 A B vv 757.0

 smv

v

vv

vv

 A

 A

 A A

 A A

/84.2

04845.01375.0

03785.00106.01375.0

)757.0)(050.0(0106.01375.0

 B A vv 040.00106.01375.0

 smv B /15.2)84.2(757.0