King Fahd University of Petroleum & Minerals

Mechanical EngineeringDynamics ME 201

BYDr. Meyassar N. Al-Haddad

Lecture # 18

Objective

• Newton First Law• To study the conservation of linear

momentum for particles

Principle of Linear Impulse and Momentum

2

1

21 vFvt

t

mdtm

21 mtNtNtmgtFm cc

Principle of Linear Impulse and Momentum for a system of Particles

2

1

21 )(vF)(vt

tiiiii

mdtm

Conservation of Linear Momentum for a system of Particles

2

1

21 )(vF)(vt

tiiiii

mdtm

0

21 )v()(v iiiimm

Conservation of linear momentum equation

Conservation of linear momentum equation

• Applied when particles collide or interact• Identify the forces and determine in what

direction linear momentum is conserved• Internal impulse will be cancelled• “Non impulsive force” : small forces takes

place in a short period which can be ignored. i.e. weigh of a ball

• “impulsive force” : very large force acting for a very short period of time and produce a significant change in momentum. i.e. explosion, accident

Impulse & Average Force

2

1

21 )(vF)(vt

tiiiii

mdtm

tFdtRdtF avg

t

t

2

1

Impulse

tFavgImpulse

Free Body Diagram• Considered the two objects as single system• By inspection, establish the direction of the momentum is conserved• Cancel the internal coupled force• Assume the two object move with v2 in positive direction if coupled• Apply the conservation of linear momentum

• To assess the average force, isolate one object and apply the coupling force as external force. Then apply

• Apply the principle of impulse and momentum

)(tFtFFdt avgavg

211 )()()( BABBAA mmmm

21 )()()( pavgp mtFm

211 )()()( BABBAA mmmm

2)27000()75.0)(12000()5.1)(15000(

sm /5.02

21 )()()()( AavgA mtFm

)5.0)(15000()8.0()5.1)(15000( avgF

kNFavg 8.18

Example 15-4

mA=15 MgmB=12 MgCouple togetherV2=? After couplingFavg = ? In 0.8 s

Example 15-5WC =1200-IbWp = 8-Ibvp=1500ft/st = 0.03 s.

vc2? =Favg? =

2211 )()()()()( ppccppcc mmmm

)1500(2.32

8)(2.32

120000 2 c

sftc /10)( 2

21 )()()()( pavgp mtFm

)1500(2.32

8)03.0(0 avgFFavg

IbFavg 12400

2211 VTVT

12

102

0 )(21)(

21 yWmyWm HHHHHH

smH /13.3)( 1

211 )()()()( pHppHH mmmm

2)800300(0)13.3)(300( sm /854.02

tFdtRdtF avg

t

ty

2

1Impulse

)854.0)(300()13.3)(300( dtR

sNdtR .683Impulse=

0))(300(21)5.0)(81.9)(300(0 2

1 H21 )()( HH mRdtm

Example 15-7

mp = 800 kgmH = 300 kgFrom rest

Impulse? = Couple together