impulse and momentum.pdf

8/14/2019 Impulse and Momentum.pdf

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Chapter 9. Impulse andChapter 9. Impulse and

MomentumMomentumExplosions and collisionsobey some surprisingly

simple laws that makeproblem solving easier whencomparing the situation

beforeand afteraninteraction.

Chapter Goal: To introduce

the ideas of impulse andmomentum and to learn anew problem-solving strategy

based on conservation laws.


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Topics:

Momentum and Impulse Solving Impulse and Momentum

Problems

Chapter 9. Impulse andChapter 9. Impulse andMomentumMomentum

Conservation of Momentum Inelastic Collisions

Explosions

Momentum in Two Dimensions


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Momentum

A B10 m/s

After the collisionA B

v u

3

What is the velocity of ball A after the collision? ball B?

What is conserved during the collision?

MOMENTUM

The total momentum is the sum of momentum of ball A and

momentum of ball B.

p mv====r rr rr rr r


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Momentum

The total momentum of the system is conserved during the collision:

A B10 m/s

AB


,A A i A Bv m v m u= += += += +

4

Momentum is a vector. It has the same direction as corresponding

velocity.

General expression for the momentum conservation: the total

momentum before the collision is equal to the total momentum after

the collision


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Momentum

A

B

A


General expression for the momentum conservation: the totalmomentum before the collision is equal to the total momentum after

the collision

,ivrrrr

,B iv

rrrr

,A fvrrrr

5

B

, , , ,A A i B B i A A f B B f

v m v m v m v+ = ++ = ++ = ++ = +r r r r r r r r r r r r r r r r

,B fv

Usually this equation is written in terms of components.


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Example:

A B10 m/s

After the collision the balls are moving together(have the same velocity). What is their velocity?

1A

m kg==== 4Bm kg====

6

v

, 10

i A A i

g mp m v

s

= == == == =Momentum before the collision:

Momentum after the collision: ( ) 5f A Bp m m v v= + == + == + == + =

Conservation of momentum: i fp p====

10 5v==== 2 /v m s====


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i ixp mv====

0f fx

p mv=


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2

1

1 ,1 1 ,1 ,2 1

t

fx ix x on

t

m v m v F dt = = = =

2

1

2 ,2 2 ,2 ,1 2

t

fx ix x on

t

m v m v F dt = = = =

Newtons third law:

F F= = = =

9

Then

2 2

1 1

,1 2 ,2 1

t t

x on x ont t

F dt F dt= = = =

(((( ))))2 ,2 2 ,2 1 ,1 1 ,1

fx ix fx ix

m v m v m v m v = = = =


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(((( ))))2 ,2 2 ,2 1 ,1 1 ,1fx ix fx ixm v m v m v m v = = = =

1 ,1 2 ,2 1 ,1 2 ,2ix ix fx fxm v m v m v m v+ = ++ = ++ = ++ = +

====

10

, , , ,x x x x

, ,ix total fx total p p====

The law of conservation of momentum


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Momentum

A A


rrrrrrrr

The law of conservation of momentum:

The total momentum of an isolated system (no external forces) does notchange.

Interactions within system do not change the systems total momentum

isolated system

11

B

B

, , , ,A A i B B i A A f B B fv m v m v m v+ = ++ = ++ = ++ = +

r r r r r r r r r r r r r r r r

,

,iv

rrrr

,A f

,B fv

rrrr


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Momentum p mv====r rr rr rr r

The ball is dropped onto a hard floor:

The ball is not an isolated system (interaction with the floor)

no conservation of momentum for the ball

Initial momentum is

Final momentum (after collision) is

i ip mv====

r rr rr rr r

f fp mv====

r rr rr rr r

12

iv

rrrr

vrrrr

The ball+ the floor is an isolated system

The total momentum (ball+floor) is conserved


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Example: Find2x

v

13

Motion with constantacceleration:

2

1 , 1( ) 2 16

x B xv a x= == == == =

1 , 4 /

x Bv m s====

Isolated system

Momentum before the collision:

, 1 , 1 , 1 , 75 4 300

i total B x B C x C B x B

g mp m v m v m v

s

= + = = == + = = == + = = == + = = =

Momentum after the collision:

, 2 , 2 , 2 2( ) 100

total B x B C x C B C x xp m v m v m m v v= + = + == + = + == + = + == + = + =

Conservation of momentum:

, ,f total i totalp p====

2100 300

xv ==== 2 3 /xv m s====


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Perfectly inelastic collision:

A collision in which the two objects stick together and move with a

common final velocity.

, 1 ,1 2 ,2i total ix ixp m v m v= += += += +

14

, 1 2

( )total fx

p m m v= += += += +

1 ,1 2 ,2 1 2( )

ix ix fxm v m v m m v+ = ++ = ++ = ++ = +

1 1

,2 ,1

2 2

3 3

1 0.5 2.25 / 2 2ix fx ix

m mv v v m sm m

= + = = = + = = = + = = = + = =


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General Principles


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General Principles


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Important Concepts


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Important Concepts


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Applications


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Applications


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The carts change of momentum is

A. 30 kg m/s.B. 10 kg m/s.

C.10 kg m/s.

D.20 kg m/s.E.30 kg m/s.


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The carts change of momentum is

A. 30 kg m/s.B. 10 kg m/s.

C.10 kg m/s.

D.20 kg m/s.E.30 kg m/s.


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A. They exert equal impulses because they

A 10 g rubber ball and a 10 g clay ball arethrown at a wall with equal speeds. Therubber ball bounces, the clay ball sticks.

Which ball exerts a larger impulse on thewall?

ave equa momen a.B. The clay ball exerts a larger

impulse because it sticks.C. Neither exerts an impulse on the

wall because the wall doesnt move.D. The rubber ball exerts a larger impulse

because it bounces.


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A. They exert equal impulses because they

A 10 g rubber ball and a 10 g clay ball arethrown at a wall with equal speeds. Therubber ball bounces, the clay ball sticks.

Which ball exerts a larger impulse on thewall?

.B. The clay ball exerts a larger

impulse because it sticks.C. Neither exerts an impulse on the

wall because the wall doesnt move.D. The rubber ball exerts a larger impulse

because it bounces.


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Objects A and C are made of different materials, with differentspringiness, but they have the same mass and are initially at rest.When ball B collides with object A, the ball ends up at rest. When ball B

is thrown with the same speed and collides with object C, the ball

rebounds to the left. Compare the velocities of A and C after thecollisions. Is vA greater than, equal to, or less than vC?

A. vA > vCB. vA < vCC. vA = vC


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Objects A and C are made of different materials, with differentspringiness, but they have the same mass and are initially at rest.When ball B collides with object A, the ball ends up at rest. When ball B

is thrown with the same speed and collides with object C, the ball

rebounds to the left. Compare the velocities of A and C after thecollisions. Is vA greater than, equal to, or less than vC?

A. vA > vCB. vA < vCC. vA = vC


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The two particles are both moving to the right. Particle 1 catches

up with particle 2 and collides with it. The particles stick togetherand continue on with velocity vf. Which of these statements istrue?

A. vf = v2.

B. vf is less than v2.

C. vf

is greater than v2

, but less than v1

.

D. vf = v1.

E. vf is greater than v1.


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The two particles are both moving to the right. Particle 1 catches

up with particle 2 and collides with it. The particles stick togetherand continue on with velocity vf. Which of these statements istrue?

A. vf = v2.

B. vf is less than v2.

C. vf

is greater than v2

, but less than v1

.

D. vf = v1.

E. vf is greater than v1.


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An explosion in a rigid pipe shoots outthree pieces. A 6 g piece comes out theright end. A 4 g piece comes out the left

end with twice the speed of the 6 gpiece. From which end does the third

iece emer e?

A. Right end

B. Left end


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An explosion in a rigid pipe shoots outthree pieces. A 6 g piece comes out theright end. A 4 g piece comes out the left

end with twice the speed of the 6 gpiece. From which end does the third

iece emer e?

A. Right end

B. Left end

impulse and momentum.pdf

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