AP Physics 1

Impulse and Momentum

Momentum

Momentum

The product of a particle’s mass and velocity is called the momentum of the particle:

Momentum is a vector, with units of kg m/s. A particle’s momentum vector can be decomposed into

x- and y-components.

Slide 9-21

The cart’s change of momentum px is

A. –20 kg m/s.B. –10 kg m/s.C. 0 kg m/s.D. 10 kg m/s.E. 30 kg m/s.

QuickCheck 9.1

Slide 9-22

The cart’s change of momentum px is

A. –20 kg m/s.B. –10 kg m/s.C. 0 kg m/s.D. 10 kg m/s.E. 30 kg m/s.

QuickCheck 9.1

px = 10 kg m/s (20 kg m/s) = 30 kg m/s

Negative initial momentum because motion is to the left and vx < 0.

Slide 9-23

Impulse

Impulse = MomentumConsider Newton’s 2nd

Law and the definition of acceleration

Units of Impulse: Units of Momentum:

Momentum is defined as “Inertia in Motion”

NsKg x m/s

Impulse is the AreaSince J=Ft, Impulse is the AREA of a Force vs.

Time graph.

Impulse During a Collision

A large force exerted for a small interval of time is called an impulsive force.

The figure shows a particle with initial velocity .

The particle experiences an impulsive force of short duration t.

The particle leaves with final velocity .

Slide 9-26

Conservation of Momentum

Collisions

A collision is a short-duration interaction between two objects.

The collision between a tennis ball and a racket is quick, but it is not instantaneous.

Notice that the right side of the ball is flattened. It takes time to compress the ball, and more time

for the ball to re-expand as it leaves the racket.

Slide 9-24

Atomic Model of a Collision

Slide 9-25

How about a collision?Consider 2 objects speeding

toward each other. When they collide......

Due to Newton’s 3rd Law the FORCE they exert on each other are EQUAL and OPPOSITE.

The TIMES of impact are also equal.

Therefore, the IMPULSES of the 2 objects colliding are also EQUAL

21

21

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)()(JJFtFt

ttFF

How about a collision?If the Impulses are equal

then the MOMENTUMS are also equal!

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2211

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oo

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22112211 vmvmvmvm

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afterbefore

A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum?

A. The mosquito.

B. The truck.

C. They have the same change of momentum.

D. Can’t say without knowing their initial velocities.

QuickCheck 9.8

Slide 9-60

A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum?

A. The mosquito.

B. The truck.

C. They have the same change of momentum.

D. Can’t say without knowing their initial velocities.

QuickCheck 9.8

Momentum is conserved, so pmosquito + ptruck = 0.Equal magnitude (but opposite sign) changes in momentum.

Slide 9-61

Momentum is conserved!The Law of Conservation of Momentum: “In the

absence of an external force (gravity, friction), the total momentum before the collision is equal to the total momentum after the collision.”

smkgpsmkgpsmkgp

smkgp

smkgp

smkgmvp

total

car

truck

totalo

caro

otrucko

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/*15003*500

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/*2500)5)(500(

)(

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Several Types of collisionsSometimes objects stick together or blow apart.

In this case, momentum is ALWAYS conserved.

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022011

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totalototal

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When 2 objects collide and DON’T 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

Collisions and Explosion

ExampleA bird perched on an 8.00 cm tall swing has a mass of 52.0 g, and the base of the swing has a mass of 153 g. Assume that the swing and bird are originally at rest and that the bird takes off horizontally at 2.00 m/s. If the base can swing freely (without friction) around the pivot, how high will the base of the swing rise above its original level?

How many objects due to have BEFORE the action?

How many objects do you have AFTER the action?

12

swing

swing

ToT

AB

v

vvmvmvm

pp

)2)(052.0()153.0()0)(205.0( )(1

2211

-0.680 m/s

6.19)68.0(

2

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22

2

)(

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o

swingswingo

AB

0.024 m

Example Granny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Ambrose (m=40 kg) who is at rest directly in her path. Rather than knock him over, she picks him up and continues in motion 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

TToo

ab

vv

vmvmvmpp

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4 m/s

Momentum in Two Dimensions

Momentum is conserved only if each component of is conserved:

The total momentum is a vector sum of the momentaof the individual particles.

Slide 9-86

Collisions in 2 DimensionsThe figure to the left shows

a collision between two pucks on an air hockey table. Puck A has a mass of 0.025-kg and is moving along the x-axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.050-kg and is initially at rest. The collision is NOT head on. After the collision, the two pucks fly apart with angles shown in the drawing. Calculate the speeds of the pucks after the collision.

vA

vB

vAcos

vAsin

vBcosvBsin

Collisions in 2 dimensions

vA

vB

vAcos

vAsin

vBcosvBsin

)37cos)(050(.)65cos)(025(.0)5.5)(025.0( BA

xBBxAAoxBBoxAA

xox

vvvmvmvmvm

pp

BA vv 040.00106.01375.0

AB

AB

BA

yBByAA

yoy

vvvv

vv

vmvm

pp

757.00227.00300.0

)37sin)(050.0()65sin)(025.0(0

0

Collisions in 2 dimensions

AB vv 757.0

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vvvv

A

A

AA

AA

/84.204845.01375.0

03785.00106.01375.0)757.0)(050.0(0106.01375.0

BA vv 040.00106.01375.0

smvB /15.2)84.2(757.0