AP Physics B - Impulse and Momentum

8/13/2019 AP Physics B - Impulse and Momentum

1/13

AP Physics B

Impulse and Momentum


2/13

Impulse = MomentumConsider Newtons 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


3/13

ExampleA 100 g ball is dropped from a height of h = 2.00 m above the floor. It

rebounds vertically to a height of h'= 1.50 m after colliding with the

floor. (a) Find the momentum of the ball immediately before it collideswith the floor and immediately after it rebounds, (b) Determine the

average force exerted by the floor on the ball. Assume that the time

interval of the collision is 0.01 seconds.

smghv

mvmgh

KU

EE

o

o

o

AB

/26.62*8.9*22

21 2

===

=

=

=

smghv

UKEE

o

AB

/4.55.1*8.9*22 ===

=

=

smkgp

smkgp

vmp

after

before

/*54.0)4.5(100.0

/*626.0)26.6(100.0

==

==

= rr

NF

F

vvmvmFt o

6.116

))26.6(4.5(100.0)01.0(

)(

=

=

==


4/13

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


5/13

How about a collision?Consider 2 objects speeding toward

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

Due to Newtons 3rd Law the FORCEthey exert on each other areEQUAL and OPPOSITE.

The TIMES of impact are also equal.

Therefore, the IMPULSES of the 2

objects colliding are also EQUAL

21

21

2121

)()(

JJ

FtFt

ttFF

=

=

==


6/13

How about a collision?If the Impulses are equal then

the MOMENTUMS are

also equal!

22221111

222111

2211

21

21

)()(

oo

oo

vmvmvmvm

vvmvvm

vmvmpp

JJ

+=

=

==

=

22112211 vmvmvmvm

pp

oo

afterbefore

+=+

=


7/13

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

an external force (gravity, friction), the totalmomentum before the collision is equal to the totalmomentum after the collision.

smkgpsmkgp

smkgp

smkgp

smkgp

smkgmvp

total

car

truck

totalo

caro

otrucko

/*3300/*18005.4*400

/*15003*500

/*3300

/*800)2)(400(

/*2500)5)(500(

)(

)(

)(

===

==

=

==

===


8/13

Several Types of collisionsSometimes objects stick together or blow apart. In this case,

momentum is ALWAYS conserved.

2211)(

022011

2211022011

vmvmvm

vmvmvm

vmvmvmvm

pp

totalototal

totaltotal

afterbefore

+=

=+

+=+

= 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 Conserved

Inelastic Collision = Kinetic Energy is NOT Conserved


9/13

Example A bird perched on an 8.00 cm tall swing has a mass of 52.0g, and the base of the swing has a mass of 153 g. Assumethat the swing and bird are originally at rest and that thebird takes off horizontally at 2.00 m/s. If the base canswing 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?

1

2

=

+=

+=

=

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

21

22

2

)(

h

g

v

mghmv

UK

EE

o

o

swingswingo

AB

0.024 m


10/13

Example Granny (m=80 kg) whizzesaround the rink with a velocityof 6 m/s. She suddenly collideswith Ambrose (m=40 kg) who

is at rest directly in her path.Rather than knock him over,she picks him up and continuesin 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

v

v

vmvmvm

pp

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

4 m/s


11/13

Collisions in 2 DimensionsThe figure to the left shows a

collision between two pucks

on an air hockey table. Puck Ahas a mass of 0.025-kg and ismoving along the x-axis with avelocity of +5.5 m/s. It makesa collision with puck B, whichhas a mass of 0.050-kg and isinitially at rest. The collision isNOT head on. After thecollision, the two pucks flyapart with angles shown in thedrawing. Calculate the speedsof the pucks after the collision.

vA

vB

vA

cos

vAsin

vBcosvBsin


12/13

Collisions in 2 dimensions

vA

vB

vAcos

vAsin

vBcosvBsin

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

xBBxAAoxBBoxAA

xox

vv

vmvmvmvm

pp

+=+

+=+

=

BA vv 040.00106.01375.0 +=

AB

AB

BA

yBByAA

yoy

vv

vv

vv

vmvm

pp

757.0

0227.00300.0

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

0

=

=

+=

+=

=


13/13

Collisions in 2 dimensions

AB vv 757.0=

smv

v

vv

vv

A

A

AA

AA

/84.2

04845.01375.0

03785.00106.01375.0

)757.0)(050.0(0106.01375.0

=

=

+=

+=

BA vv 040.00106.01375.0 +=

smvB /15.2)84.2(757.0 ==

AP Physics B - Impulse and Momentum

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