Chapter5 Momentum and Impulse Student

8/20/2019 Chapter5 Momentum and Impulse Student

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PHYSICS CHAPTER 3

CHAPTER 5:CHAPTER 5:

MomentumMomentumand Impulseand Impulse

(2 Hours)(2 Hours)

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PHYSICS CHAPTER 3

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Learnn! "ut#ome:5$% Momentum and Impulse (% &our)

'ene'ene momentum$momentum$

'ene'ene mpulse J = Ft and use F-t !rap&

to determne mpulse$

se p J ∆=

At the end of this chapter, students shouldbe able to:


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PHYSICS CHAPTER 3

5$% Momentum and Impulse

Momentum is defined as t&e produ#t *et+een mass andt&e produ#t *et+een mass and

,elo#t-,elo#t-. is a vector quantity.

Equation :

The S.I. unit of linear momentum is .! m s.! m s/%/%. The dre#ton o t&e momentumdre#ton o t&e momentum is the samesame as the

dre#ton o t&e ,elo#t-dre#ton o t&e ,elo#t-.

3

vm p =

x p

p y p

θ

θ mvθ p p x coscos ==θ mvθ p p y sinsin ==

Momentum can beresolve into

vertical ( y)component &

horizontal ( x)component.


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PHYSICS CHAPTER 3

Impulse0

Let a single #onstant or#e0#onstant or#e0F F

acts on an object in a short timeinterval (collision) thus the !e"ton#s $nd la" can be "ritten as

is defined as t&e produ#t o a or#e0t&e produ#t o a or#e0 F F and t&e tme0and t&e tme0 t t %& t&e #&an!e o momentumt&e #&an!e o momentum.

is a ,e#tor 1uantt-,e#tor 1uantt- "hose dre#tondre#ton is the samesame as the#onstant or#e#onstant or#e on the object.

J

constant===∑dt

pd F F

12 p p pd dt F J −===momentumfinal:2 p"here

momentuminitial:1 p

forceimpulsive: F


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PHYSICS CHAPTER 3

( ) ( ) x x x1 x2 xav x uvm p pdt F J −=−==

!

The S.I. unit of im'ulse is s s or .! m s.! m s %%.

If the or#eor#e acts on the object is not #onstantnot #onstant then

Since im'ulse and momentum are both vector quantities then

it is often easiest to use them in com'onent form :

dt F dt F J avt

t == ∫

2

1

"here forceimpulsiveaverage:av F

( ) ( ) y y y1 y2 yav y uvm p pdt F J −=−==

( ) ( ) z z z 1 z 2 z

av z uvm p pdt F J −=−==

#onsder 2/'#onsder 2/'

#ollson onl-#ollson onl-


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PHYSICS CHAPTER 3

hen t"o objects in collision the im'ulsive force F against

time t gra'h is given by the igure *.+.

"

1

t 2

t

!ure 5$%!ure 5$%

t

0

F

Shaded area under the F − t gra'h , im'ulse


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PHYSICS CHAPTER 3

Example 5.1A car of mass #$$ % is travellin at 2!m's. ind the constant force needed tostop it in seconds.

Solution


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PHYSICS CHAPTER 3

kg0.201 =m

#

- .$ /g tennis ball stri/es the "all hori0ontally "ith a s'eed of +

ms−+ and it bounces off "ith a s'eed of 1 m s−+ in the o''osite

direction.

a. 2alculate the magnitude of im'ulse delivered to the ball by the "all

b. If the ball is in contact "ith the "all for + ms determine the

magnitude of average force e3erted by the "all on the ball.

Soluton :Soluton :

E4ample 5$2 :

all ($)%%

1

sm100

−

=1u

%%1sm70 −=

1

v

0== 22 uv


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PHYSICS CHAPTER 3

12 p pdp J −==

Soluton :Soluton :

a. rom the equation of im'ulse that the force is constant

Therefore the magnitude of the im'ulse is 3 s3 s.

b. 4iven the contact time

N3400=av F


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PHYSICS CHAPTER 3

1$

-n estimated force5time curve for a tennis ball of mass 6. g

struc/ by a rac/et is sho"n in igure *.$. 7etermine

a. the im'ulse delivered to the ball

b. the s'eed of the ball after being struc/ assuming the ball is

being served so it is nearly at rest initially.

E4er#se 5$% :

0.2 1.8 ( )mst 0

( )kN F

1.0

18

!ure 5$2!ure 5$2


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PHYSICS CHAPTER 3

Learnn! "ut#ome:

At t&e end o t&s #&apter0 students s&ould *e a*leAt t&e end o t&s #&apter0 students s&ould *e a*leto:to:

StateState t&e prn#ple o #onser,aton o lnearmomentum$

StateState t&e #ondtons or t&e #ondtons or elast# and nelast#

#ollsons$

Appl- t&e prn#ple o #onser,aton omomentum n elast# and nelast# #ollsons$

11

5$2 Conser,aton o lnear momentum and mpulse(% &our)


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PHYSICS CHAPTER 3

5$2 Prn#ple o #onser,aton o lnear momentum

0=

∑ F

12

states 8In an solated (#losed) s-stem0 t&e total momentum o t&atIn an solated (#losed) s-stem0 t&e total momentum o t&at

s-stem s #onstants-stem s #onstant.”

%&

“ 6&en t&e net e4ternal or#e on a s-stem s 7ero0 t&e total6&en t&e net e4ternal or#e on a s-stem s 7ero0 t&e total

momentum o t&at s-stem s #onstantmomentum o t&at s-stem s #onstant.”

In a 2losed system

rom the !e"ton#s second la" thus

0 ==∑ dt

pd F

0= pd


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PHYSICS CHAPTER 3

-ccording to the 'rinci'le of conservation of

linear momentum "e obtain

%&

13

T&e total o ntal momentum 8 t&e total o nal momentumT&e total o ntal momentum 8 t&e total o nal momentum

∑∑ = f i p p

constant= pconstant=∑ x pconstant=∑ y p

Therefore then


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PHYSICS CHAPTER 3

Elast# #ollsonElast# #ollson

is defined as one n +&#& t&e total .net# ener!-one n +&#& t&e total .net# ener!-(as +ell as total momentum) o t&e s-stem s t&e(as +ell as total momentum) o t&e s-stem s t&e

same *eore and ater t&e #ollsonsame *eore and ater t&e #ollson.

igure *.9 sho"s the head5on collision of t"o billiard

balls.

1

%% 22

efore collision

-t collision

-fter collision

%% 2222um11um

%% 22 22vm11vm

!ure 3$3!ure 3$3


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PHYSICS CHAPTER 3

The propertes o elast# #ollsonpropertes o elast# #ollson are

a. The coefficient of restitution ee 8 %8 %b. The total momentum s #onser,edtotal momentum s #onser,ed.

c. The total .net# ener!- s #onser,edtotal .net# ener!- s #onser,ed.

%&

1!

∑∑ = f i p p

∑∑ = f i K K

222

211

222

211 vmvmumum

2

1

2

1

2

1

2

1+=+


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PHYSICS CHAPTER 3

Inelast# (non/elast#) #ollsonInelast# (non/elast#) #ollson

is defined as one n +&#& t&e total .net# ener!- o t&eone n +&#& t&e total .net# ener!- o t&es-stem s not t&e same *eore and ater t&e #ollsons-stem s not t&e same *eore and ater t&e #ollson

(e,en t&ou!& t&e total momentum o t&e s-stem s(e,en t&ou!& t&e total momentum o t&e s-stem s

#onser,ed)#onser,ed).

igure *.9 sho"s the model of a #ompletel- nelast##ompletel- nelast##ollson#ollson of t"o billiard balls.

1"

%% 22 -t collision

-fter collision

(stic/ together)%% 22

v

!ure 3$!ure 3$

efore collision %% 2211um

0=2u

2m


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PHYSICS CHAPTER 3

2aution: ot allot all the inelastic collision is st#. to!et&er st#. to!et&er . In fact inelastic collisions include man- stuatonsman- stuatons in "hich

the *odes do not st#.*odes do not st#.. The propertes o nelast# #ollsonpropertes o nelast# #ollson are

a. The coefficient of restitution 99 ee % %

b. The total momentum s #onser,edtotal momentum s #onser,ed.

c. The total .net# ener!- s not #onser,edtotal .net# ener!- s not #onser,ed because someof the energy is converted to nternal ener!-nternal ener!- and some of it istransferred a"ay by means of sound or &eatsound or &eat. ut the totaltotalener!- s #onser,edener!- s #onser,ed.

%&

1*

∑∑ = f i p p

∑∑ = f i E E energylosses+=∑∑ f i K K


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PHYSICS CHAPTER 3

Elast# ,ersus nelast# #ollson

Elast# #ollson Inelast# #ollson

e , + 2oefficient ofresituition ≤ e;+


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PHYSICS CHAPTER 3

Lnear momentum n one dmenson #ollsonLnear momentum n one dmenson #ollson

E4ample 5$3 :

igure >.* sho"s an object - of mass $ g collides head5on "ith object of

mass + g. -fter the collision moves at a s'eed of $ m s5+ to the left.

7etermine the velocity of - after 2ollision.

SolutonSoluton::

1

1sm6

−= Au

-

1sm3 −= Bu

!ure 5$5!ure 5$5


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PHYSICS CHAPTER 3

Lnear momentum n t+o dmenson #ollsonLnear momentum n t+o dmenson #ollson

E4ample 5$ :

- tennis ball of mass m+ moving "ith initial velocity u1 collides

"ith a soccer ball of mass m$ initially at rest. -fter thecollision the tennis ball is deflected *° from its initialdirection "ith a velocity v1 as sho"n in figure *.6.Su''ose that m+ , $* g m$ , ? g u1 , $ m s−+ and v1 , 9 m s−+. 2alculate the magnitude and direction of soccerball after the collision. 2$

!ure 5$;!ure 5$;

1u

efore collision -fter collision

m+ m$

m+ 1v

50


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PHYSICS CHAPTER 3

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Soluton :Soluton :

rom the 'rinci'le of conservation of linear momentum

The 35com'onent of linear momentum

∑∑ = f i p p

x22 x11 x22 x11 vmvmumum +=+

sm20kg0.!00kg0.250 1−=== 121 umm0 sm40 1 5θ vu

112 ===

−

∑∑ = fxix p p


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Soluton :Soluton :

The y5com'onent of linear momentum


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+. -n object @ of mass 9 /g moving "ith a velocity 9 ms−+

collides elastically "ith another object A of mass $ /g

moving "ith a velocity > ms−+ to"ards it.

a. 7etermine the total momentum before collision.

b. If @ immediately sto' after the collision calculatethe final velocity of A.

c. If the t"o objects stic/ together after the collision

calculate the final velocity of both objects.AS$ : %9 .! msAS$ : %9 .! ms %%< 5 ms< 5 ms %% to t&e r!&t< %$= m sto t&e r!&t< %$= m s %% to t&e r!&tto t&e r!&t

E4er#se 5$2 :


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!ure 5$=!ure 5$=

$. - ball moving "ith a s'eed of +1 m s−+ stri/es an identical ball

that is initially at rest. -fter the collision the incoming ball has

been deviated by 9*° from its original direction and the struc/

ball moves off at >° from the original direction as sho"n in

igure *.+1. 2alculate the s'eed of each ball after the collision.

2

E4er#se 5$2 :

AS$ : >$>9 m sAS$ : >$>9 m s %%< %2$ m s< %2$ m s %%


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PHYSICS CHAPTER 3

2!

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Chapter5 Momentum and Impulse Student

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